Mathworks VIDEO AND IMAGE PROCESSING BLOCKSET 3 Reference

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Video and Image Pro

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cessing Blockset™ 3

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Video and Image Processing Blockset™ Reference

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Revision History

March 2007 Online only New for Version 2.3 (Release 2007a) September 2007 Online only Revised for Version 2.4 (Release 2007b) March 2008 Online only Revised for Version 2.5 (Release 2008a) October 2008 Online only Revised for Version 2.6 (Release 2008b) March 2009 Online only Revised for Version 2.7 (Release 2009a) September 2009 Online only Revised for Version 2.8 (Release 2009b) March 2010 Online only Revised for Version 3.0 (Release 2010a)

Block Reference

Analysis & Enhancement ........................... 1-2

Contents

Conversions

Filtering

Geometric Transformations

Morphological Operations

Sinks

Sources

Statistics

Text & Graphics

Transforms

Utilities

............................................. 1-4

....................................... 1-2

.......................................... 1-3

........................................... 1-5

.......................................... 1-5

................................... 1-7

....................................... 1-7

........................................... 1-8

........................ 1-3

.......................... 1-4

Blocks — Alphabetical List

System Object Reference

Analysis & Enhancement ........................... 3-2

Conversions

Filtering

Geometric Transformations

Morphological Operations

Sinks

Sources

Statistics

Text & Graphics

Transforms

Utilities

............................................. 3-4

....................................... 3-2

.......................................... 3-3

........................................... 3-5

.......................................... 3-5

................................... 3-6

....................................... 3-6

........................................... 3-7

........................ 3-3

.......................... 3-4

vi Contents

Alphabetical List

Function Reference

VideoandImageProcessingFunctions .............. 5-2

vii

viii Contents

Block Reference

Analysis & Enhancement (p. 1-2) Analyze or enhance images or video

Conversions (p. 1-2) Perform conversion operations such

as color space conversion

Filtering (p. 1-3)

Geometric Transformations (p. 1-3)

Morphological Operations (p. 1-4) Perform morphological operations

Sinks (p. 1-4)

Sources (p. 1-5) Import imagesorvideointoSimulink

Statistics (p. 1-5) Perform statistical operations on

Text & Graphics (p. 1-7) Annotate images or video

Transforms (p. 1-7) Perform transform operations such

Utilities (p. 1-8) Perform processing operations

Filter images or video

Manipulate size, shape, and orientation of images or video

such as erosion and dilation

Export or display images or video

images or video

as 2-D FFT and 2-D DCT

such as image padding and block processing

1 Block Reference

Analysis & Enhancement

Block Matching Estimate motion between images or

Contrast Adjustment Adjust image contrast by linearly

Corner Detection Calculate corner metric matrix and

video frames

scaling pixel values

find corners in images

Con

versions

Deinterlac

Edge Detec

Histogra

Median F

Optical Flow

Templ

Trace Boundaries Trace object boundaries in binary

Autothreshold Convert intensity image to binary

Chroma Resampling

ing

tion

m Equalization

ilter

ate Matching

Remove motion artifacts by deinterlacing input video signal

Find edges of objects in images using Sobel, Prewitt, Roberts, or Canny method

Enhance contrast of images using histogram equalization

Perform 2-D median filtering

Estima

Locat

images

image

Do c

te object velocities

e a template in an image

wnsample or upsample

hrominance components of images

1-2

olor Space Conversion

Demosaic

onvert color information between

C color spaces

Demosaic Bayer’s format images

Filtering

Gamma Correction Apply or remove gamma correction

from images or video streams

Image Complement Compute comple ment of pixel values

inbinary,intensity,orRGBimages

Image Data Type Conversion Convert and scale input image to

specified output data type

2-D Convolution Compute 2-D discrete convolution of

two input matrices

2-D FIR Filter

Kalman Filter

Median Filter

Geometric Transformations

Apply Geometric Transformation Apply projective or affine

Estimate Geometric Transformation Estimate geometric transformation

Projective Transformation Transform quadrilateral into

Resize Enlarge or shrink image sizes

Rotate

Perform 2-D FIR filtering on input matrix

Predict or estimate states of dynamic systems

Perform 2-D median filtering

transformation to an image

from matching point pairs

another quadrilateral

Rotate im age by specified angle

1-3

1 Block Reference

Shear Shift rows or columns of image by

Translate Translate image in 2-D plane using

Morphological Operations

linearly varying offset

displacement vector

Sinks

Bottom-hat

Closing Perform morphological closing on

Dilation Find local maxima in binary or

Erosion Find local minima in binary or

Label Label connected components in

Opening Perform morphological opening on

Top-hat

Frame Rate Display

Perform bottom-hat filtering on intensity or bina r y images

binary or intensity images

intensity images

binary images

binary or intensity images

Perform top-hat filtering on intensity or binary images

Calculate average update rate of input signal

1-4

To Multimedia File

To Video Display Display video data

Write video frames and audio samples to multimedia file

Sources

VideoToWorkspace

Video Viewer

Write A VI File (Obsolete) Write video frames to uncompressed

Write Binary File

From Multimedia File

Image From File

Image From Workspace

Read Binary File

Video From Workspace

Export video signal to MATLAB workspace

Display binary, intensity, or RGB images or video streams

AVI file

Write binary video data to files

Read video frames and audio samples from compressed multimedia file

Import image from image file

Import image from MATLAB workspace

Read binary video data from files

Import video signal from MATLAB workspace

Statistics

2-D Autocorrelation Compute 2-D autocorrelation of

input matrix

2-D Correlation Com pute 2-D cross-correlation of two

input matrices

2-D Histogram (Obsolete) Generate histogram of each input

matrix

2-D Mean (Obsolete) Find mean value of each input

matrix

1-5

1 Block Reference

2-D Median (Obsolete) Find median value of each input

matrix

2-D S ta n d ard Deviation (Obsolete) Find standard deviation of each

input matrix

2-D Variance (Obsolete) Compute variance of each input

matrix

Blob Analysis Compute statistics for labeled

regions

Find Local Maxima Find local maxima in matrices

Histogram

Maximum Find maximum values in input or

Mean

Median

Minimum Find minimum values in input or

PSNR Compute peak signal-to-noise ratio

Standard Deviation Find standard deviation of each

Variance

Generate histogram of each input matrix

sequence of inputs

Find mean value of each input matrix

Find median value of e ach input matrix

sequence of inputs

(PSNR) between images

input matrix

Compute variance of input or sequence of inputs

1-6

Text & Graphics

Compositing Combine pixel values of two images,

Draw Markers Draw markers by embedding

Text & Graphics

overlay one image over another, or highlight selected pixels

predefined shapes on output image

Transfor

Draw Shapes

Insert Text

2-D DCT Compute 2-D discrete cosine

2-D FFT

2-D IDCT Compute 2-D inverse discrete cosine

2-D IFFT

Gaussian Pyramid Perform Gaussian pyramid

gh Lines

Hou

Hough Transform

Draw rectang circles on im

Draw text on image or video stream.

transform (DCT)

Compute 2-D FFT of input

transform (IDCT)

Compute 2-D IFFT of input

decomposition

Find Cartesian coordinates of lines described by rho and theta pairs

nd lines in images

les, lines, polygon s , or

ages

1-7

1 Block Reference

Utilities

Block Processing

Image Pad Pad signal along its rows, columns,

Variable Selector Specify subset of rows or columns

Repeat user-specified operation on submatrices of input matrix

or both

from input

1-8

Blocks — Alphabetical List

2-D Autocorrelation

Purpose Compute 2-D autocorrelation of input matrix

Library Statistics

Description The 2-D Autocorrelation block computes the two-dimensional

autocorrelation of the input matrix. Assume that input matrix A has dimensions (Ma, Na). The equation for the two-dimensional discrete autocorrelation is

()()

Ci j Amn conj Am in j

(, ) ( , ) ( ( , ))

=⋅++

−

∑∑

where

021≤< −iMa

The output of this block has dimensions

Port

Input

Input/Output Supported Data Types

Vector or matrix of intensity values or a scalar, vector, or matrix that represents one plane oftheRGBvideostream

Output Autocorrelation of the

input matrix

If the data type of the input is floating point, the output of the block has thesamedatatype.

Fixed-Point Data Types

Thefollowingdiagramshowsthedatatypesusedinthe2-D Autocorrelation block for fixed-point s ignals.

021≤< −jNa

and

(,)2121Ma Na−−

• Double-precision floating point

• Single-precision floating point

• Fixed point

• 8-, 16-, 32-bit signed integer

• 8-, 16-, 32-bit unsigned integer

Same as Input port

Complex Val u es Supported

Yes

2-2

2-D Autocorrelation

You can set the product output, accumulator, and output data types in the b lock mask as discussed in “Dialog Box” on page 2-4.

The output of the multiplier is in the product output data type if at least one of the inputs to the multiplier is real. If both of the inputs to the multiplier are complex, the result of the multiplication is in the accumulator data type. For details on the complex multiplication performed, refer to “Multiplication Data Types” in the Signal Processing Blockset™ documentation.

2-3

2-D Autocorrelation

Dialog Box

The Main pane of the 2-D Autocorrelation dialog box appears as shown in the following figure.

2-4

The Data Types pane of the 2-D Autocorrelation dialog box appears asshowninthefollowingfigure.

2-D Autocorrelation

Rounding mode

Select the rounding mode f or fixed-point operations.

Overflow mode

Select the overflow mode for fixed-point operations.

Product output

Use this parameter to specify how to designate the product output word and fraction lengths. Refer to “Fixed-Point Data Types” on page 2-2 and “Multiplication Data Types” in the Signal Pro cessing

2-5

2-D Autocorrelation

Blockset documentation for illustrations depicting the use of the product output data type in this block:

• When you select

thoseoftheinputtotheblock.

• When you select

word length and the fraction length of the product output, in bits.

• When you select

word length, in bits, and the slope of the product output. The bias of all signals in the Video and Image Processing Blockset™ software is 0.

Accumulator

Use this parameter to specify how to designate the accumulator word and fraction lengths. Refer to “Fixed-Point Data Types” on page 2-2 and “Multiplication Data Types” in the Signal Pro cessing Blockset documentation for illustrations depicting the use of the accumulator data type in this block. The accumulator data type is only used when both inputs to the multiplier are complex.

• When you select

characteristics match those of the product output.

• When you select

thoseoftheinputtotheblock.

• When you select

word length and the fraction length of the accumulator, in bits.

Same as input, these characteristics match

Binary point scaling,youcanenterthe

Slope and bias scaling,youcanenterthe

Same as product output,these

Same as input, these characteristics match

Binary point scaling,youcanenterthe

2-6

• When you select

word length, in bits, and the slope of the accumulator. The bias of all signals in the Video and Image Processing Blockset software is 0.

Output

Choose how to specify the output word length and fraction length.

• When you select

thoseoftheinputtotheblock.

Slope and bias scaling,youcanenterthe

Same as input, these characteristics match

2-D Autocorrelation

• When you select Binary point scaling,youcanenterthe

word length and the fraction length of the output, in bits.

See Also

• When you select

word length, in bits, and the slope of the output. The bias of all signals in the Video and Image Processing Blockset software is 0.

Lock data type settings against change by the fixed-point tools

Select this parameter to prevent the fixed-point tools from overriding the data types you specify on the block mask. For more information, see Tool in the Simulink

2-D Correlation

Histogram Video and Image Pro cessing

Mean

Median Video and Image Processing

Standard Deviation

Variance Video and Image Processing

Slope and bias scaling,youcanenterthe

fxptdlg, a reference page on the Fixed-Point

documentation.

VideoandImageProcessing Blockset software

Blockset software

VideoandImageProcessing Blockset software

Blockset software

VideoandImageProcessing Blockset software

Blockset software

Maximum

Minimum

Signal P rocess ing Blockset software

2-7

2-D Convolution

Purpose Compute 2-D discrete convolution of two input matrices

Library Filtering

vipfilter

Description

The 2-D Convolution block computes the two-dimensional convolution of two input matrices. Assume that matrix A has dimensions (Ma, Na) and matrix B has dimensions (Mb, Nb). When the block calculates the full output size, the equation for the 2-D discrete convolution is

()()

Ci j Amn Bi m j n

(, ) ( , )* ( , )

=−−

−

∑∑

2-8

Port

where

01≤< + −iMaMb

01≤< + −jNaNb

and

Input/Output Supported Data Types

Matrix of intensity values or a matrix that represents one plane of the R G B video stream

• Double-precision floating point

• Single-precision floating point

• Fixed point

• 8-, 16-, 32-bit signed integer

• 8-, 16-, 32-bit unsigned integer

Matrix of intensity

Same as I1 port

values or a matrix that

Complex Values Supported

Yes

Port

Input/Output Supported Data Types

represents one plane of the R G B video stream

2-D Convolution

Complex Values Supported

Output Convolution of the input

matrices

If the data type of the input is floating point, the output of the block has thesamedatatype.

The dimensions of the output are dictated by the Output size parameter. Ass um e that the input at port I1 has dimensions (Ma, Na) and the input at port I2 has dimensions (Mb, Nb). If, for the Output size parameter, you choose convolution with dimensions (Ma+Mb-1, Na+Nb-1). If, for the Output size parameter, you choose central part of the convolution with the same dimensions as the input at port I1. If, for the Output size parameter, you choose is only those parts of the convolution that are computed w ithout the zero-padded edges of any input. This output has dimensions (Ma-Mb+1, Na-Nb+1). However, if

If you select the Output normalized convolution check box, the block’s output is divided by

sqrt(sum(dot(I1p,I1p))*sum(dot(I2,I2))),whereI1p is the

portion of the I1 matrix that aligns with the I2 matrix. See “Example 2” on page 2-12 for more information.

Note When you select the Output normalized convolution check box, the block input cannot be fixed point.

Same as I1 port

Full, the output is the full two-dimensional

Same as input port I1, the output is the

Valid, the output

all(size(I1)<size(I2)), the block errors out.

Yes

Fixed-Point Data Types

The following diagram shows the data types used in the 2-D Convolution block for fixed-point signals.

2-9

2-D Convolution

You can set the product output, accumulator, and output data types in the block mask as discussed in “Dialog Box” on page 2-15.

Examples Example 1

Suppose I1, the first input matrix, has dimensions (4,3) and I2, the second input matrix, has dimensions (2,2). If, for the Output size parameter, you choose determine the number of rows and columns of the output m atrix:

The resulting matrix is

2-10

Full, the block uses the following equations to

2-D Convolution

If, for the Output size parameter, you choose Same as input port

, the output is the central part of

the input at port I1, (4,3). However, since a 4-by-3 matrix cannot be

extracted from the exact center of columns on the top and left side of the

Cfull

with the same dimensions as

, the block leaves more rows and

Cfull

matrix and outputs:

Cfull

If, for the Output size parameter, you choose Valid, the block uses the following e quations to determine the number of rows and columns of the output matrix:

2-11

2-D Convolution

In this case, it Therefore, the

is always possible to extract the exact center of

block outputs

Cfull

Example 2

In convolution, the value of an output element is computed as a weighted sum of neighboring elements.

For example, su p p ose the first inp u t matrix represents an image and is defined as

I1 = [17 24 1 8 15

23 5 7 14 16

4 6 13 20 22 10 12 19 21 3 11 18 25 2 9]

2-12

The second input matrix also represents an image and is defined as

I2=[816

357 492]

The following figure shows how to compute the (1,1) output element (zero-based indexing) using these steps:

2-D Convolution

1 Rotate the second input matrix, I2, 180 degrees about its center

element.

2 Slide the center element of I2 so that it lies on top of the (0,0) element

of I1.

3 Multiply each element of the rotated I2 matrix by the element of

I1 underneath.

4 Sum the individual products from step 3.

Hence the (1,1) output element is

0 2 0 9 0 4 0 7 17 5 24 3 0 6 23 1 5 8 220⋅+⋅+⋅+⋅+ ⋅+ ⋅+⋅+ ⋅+⋅=

2-13

2-D Convolution

Values of rotated I2 matrix

Alignment of I2 matrix

Alignment of center element of I2

Image pixel values

Computing the (1,1) Output of Convolution

The normalized convolution of the (1,1) output element is

220/sqrt(sum(dot(I1p,I1p))*sum(dot(I2,I2))) = 0.3459, where I1p = [0 0 0; 0 17 24; 0 23 5].

2-14

11 9

2-D Convolution

Dialog Box

The Main pane of the 2-D Convolution dialog box appears as shown in the following figure.

2-15

2-D Convolution

Output size

Output normalized convolution

The Data Types pane of the 2-D Convolution dialog box appears as shown in the following figure.

This parameter controls the size of the output scalar, vector, or matrix produced as a result of the convolution between the two inputs. If you choose Na+Nb-1). If you choose thesamedimensionsastheinputatportI1. Ifyouchoose output has dimensions (Ma-Mb+1, Na-Nb+1).

If you select this check box, the block’s output is normalized.

Full, the output has dimensions (Ma+Mb-1,

Same as input port I1, the output has

Valid,

2-16

2-D Convolution

2-17

2-D Convolution

Rounding mode

Overflow mode

Product output

Select the rounding mode f or fixed-point operations.

Select the overflow mode for fixed-point operations.

Use this parameter to specify how to designate the product output word and fraction lengths. Refer to “Fixed-Point Data Types” on page 2-9 and “Multiplication Data Types” in the Signal Pro cessing Blockset documentation for illustrations depicting the use of the product output data type in this block:

• When you select

match those of the first input to the block.

• When you select

word length and the fraction length of the product output, in bits.

• When you select

word length, in bits, and the slope of the product output. The bias of all signals in theVideo and Image Processing Blockset software is 0.

The Product Output inherits its sign according to the inputs. If either or both input I1 and I2 aresigned,theProductOutput will be signed. Otherwise, the Product Output is unsigned. The following table shows all cases.

Sign of Input I1 Sign of Input I2 Sign of Product

unsigned unsigned unsigned

unsigned signed signed

signed unsigned signed

signed signed signed

Same as first input, these characteristics

Binary point scaling,youcanenterthe

Slope and bias scaling,youcanenterthe

Output

2-18

2-D Convolution

Accumulator

Use this parameter to specify how to designate the accumulator word and fraction lengths. Refer to “Fixed-Point Data Types” on page 2-9 and “Multiplication Data Types” in the Signal Pro cessing Blockset documentation for illustrations depicting the use of the accumulator data type in this block. The accumulator data type is only used when both inputs to the multiplier are complex:

• When you select

characteristics match those of the product output.

• When you select

match those of the first input to the block.

• When you select

word length and the fraction length of the accumulator, in bits.

• When you select

word length, in bits, and the slope of the accumulator. The bias of all signals in the Video and Image Processing Blockset software is 0.

Output

Choose how to specify the word length and fraction length of the output of the block:

• When you select

match those of the first input to the block.

• When you select

word length and the fraction length of the output, in bits.

• When you select

word length, in bits, and the slope of the output. The bias of all signals in the Video and Image Processing Blockset software is 0.

Same as product output,these

Same as first input, these characteristics

Binary point scaling,youcanenterthe

Slope and bias scaling,youcanenterthe

Same as first input, these characteristics

Binary point scaling,youcanenterthe

Slope and bias scaling,youcanenterthe

Lock data type settings against change by the fixed-point tools

Select this parameter to prevent the fixed-point tools from overriding the data types you specify on the block mask. For more

2-19

2-D Convolution

information, see fxptdlg, a reference page on the Fixed-Point Tool in th e Simulink documentation.

See Also

2-D FIR Filter Video and Image Processing Blockset

software

2-20

2-D Correlation

Purpose Compute 2-D cross-correlation of two input matrices

Library Statistics

vipstatistics

Description The 2-D Correlation block computes the two-dimensional

cross-correlation of two input matrices. Assume that matrix A hasdimensions(Ma,Na)andmatrixBhasdimensions(Mb,Nb). When the block calculates the full output size, the equation f or the two-dimensional discrete cross-correlation is

Ci j Amn conjBm in j

(, ) ( , ) ( ( , ))

=⋅++

−

()()

∑∑

01≤< + −iMaMb

Port

where

Input/Output Supported Data Types

Vector or matrix of intensity values

Scalar, vector, or matrix of intensity values or a scalar, vector, or matrix that represents one plane oftheRGBvideostream

Output Convolution of the input

matrices

01≤< + −jNaNb

and

• Double-precision floating point

• Single-precision floating point

• Fixed point

• 8-, 16-, 32-bit signed integer

• 8-, 16-, 32-bit unsigned integer

Same as I1 port

Complex Valu es Supported

Yes

2-21

2-D Correlation

If the data type of the input is floating point, the output of the block is thesamedatatype.

The dimensions of the output are dictated by the Output size parameter and the sizes of the inputs at ports I1 and I2. For example, assume that the input at port I1 has dimensions (Ma, Na) and the input at port I2 has dimensions (Mb, Nb). If, for the Output size parameter, you choose with dimensions (Ma+Mb-1, Na+Nb-1). If, for the Output size parameter, you choose central part of the cross-correlation with the same dimensions as the inputatportI1. If,fortheOutput size parameter, you choose the output is only those parts of the cross-correlation that are computed without the zero-padded edges of any input. This output has dimensions (Ma-Mb+1, Na-Nb+1). However, if errors out.

If you select the Normalized output check box, the block’s output is divided by

I1p is the portion of the I1 matrix that aligns with the I2 matrix. See

“Example 2” on page 2-25 for more information.

Full, the output is the full two-dimensional cross-correlation

Same as input port I1, the output is the

Valid,

all(size(I1)<size(I2)),theblock

sqrt(sum(dot(I1p,I1p))*sum(dot(I2,I2))),where

2-22

Note When you select the Normalized output check box , the block inputcannotbefixedpoint.

Fixed-Point Data Types

The following diagram shows the data types used in the 2-D Correlation block for fixed-point signals.

2-D Correlation

You can set the product output, accumulator, and output data types in the block mask as discussed in “Dialog Box” on page 2-29.

Example

Suppose input ma you cho the num

The r

I1, the first input matrix, has dimensions (4,3). I2, the second

trix, has dimensions (2,2). If, for the Output size parameter,

ose

Full, the block uses the following equations to determine

ber of rows and columns of the output matrix:

esulting matrix is

2-23

2-D Correlation

If, for the Output size parameter, you choose Same as input port

the input at port I1, (4,3). However, since a 4-by-3 matrix cannot be

extracted from the exact center of columns on the top and left side of the

, the output is the central part of

Cfull

with the same dimensions as

Cfull

, the block leaves more rows and

Cfull

matrix and outputs:

2-24

If, for the Output size parameter, you choose Valid, the block uses the following e quations to determine the number of rows and columns of the output matrix:

2-D Correlation

In this case, it is always possible to extract the exact center of

Cfull

Therefore, the block outputs

Example 2

In cross-correlation, the value of an output element is computed as a weighted sum of neighboring elements.

For example, su p p ose the first inp u t matrix represents an image and is defined as

I1 = [17 24 1 8 15

23 5 7 14 16

4 6 13 20 22 10 12 19 21 3 11 18 25 2 9]

The second input matrix also represents an image and is defined as

I2=[816

357 492]

The following figure shows how to compute the (2,4) output element (zero-based indexing) using these steps:

1 Slide the center element of I2 so that lies on top of the (1,3) element

of I1.

2-25

2-D Correlation

The ( 2,4) output element from the cross-correlation is

2 Multiply each weight in I2 by the element of I1 underneath.

3 Sum the individual products from step 2.

1 8 8 1 15 6 7 3 14 5 16 7 13 4 20 9 22 2 585⋅+⋅+ ⋅+⋅+ ⋅+ ⋅+ ⋅+ ⋅+ ⋅=

2-26

2-D Correlation

Values of I2 matrix

Image pixel values

Alignment of I2 matrix

11 9

Alignment of center element of I2

Computing the (2,4) Output of Cross-Correlation

2-27

2-D Correlation

The normalized cross-correlation of the (2,4) output element is

585/sqrt(sum(dot(I1p,I1p))*sum(dot(I2,I2))) = 0.8070,where I1p = [1 8 15; 7 14 16; 13 20 22].

2-28

2-D Correlation

Dialog Box

The Main pane of the 2-D Correlation dialog box appears as shown in the following figure.

2-29

2-D Correlation

Output size

Normalized output

The Data Types pane of the 2-D Correlation dialog box appears as shown in the following figure.

This parameter controls the size of the output scalar, vector, or matrix produced as a result of the cross-correlation between the two inputs. If you choose (Ma+Mb-1, Na+Nb-1). If you choose output has the same dimensions as the input at port I1. If you choose

If you select this check box, the block’s output is normalized.

Valid, output has dimensions (Ma-Mb+1, Na-Nb+1).

Full, the output has dimensions

Same as input port I1,the

2-30

2-D Correlation

2-31

2-D Correlation

Rounding mode

Overflow mode

Product output

Select the rounding mode f or fixed-point operations.

Select the overflow mode for fixed-point operations.

Use this parameter to specify how to designate the product output word and fraction lengths. Refer to “Fixed-Point Data Types” on page 2-22 and “Multiplication Data Types” in the Signal Processing Blockset documentation for illustrations depicting the use of the product output data type in this block:

• When you select

match those of the first input to the block.

• When you select

word length and the fraction length of the product output, in bits.

• When you select

word length, in bits, and the slope of the product output. The bias of all signals in the Video and Image Processing Blockset software is 0.

Sign of Input I1 Sign of Input I2 Sign of Product

unsigned unsigned unsigned

unsigned signed signed

signed unsigned signed

signed signed signed

Same as first input, these characteristics

Binary point scaling,youcanenterthe

Slope and bias scaling,youcanenterthe

Output

2-32

2-D Correlation

Accumulator

Use this parameter to specify how to designate the accumulator word and fraction lengths. Refer to “Fixed-Point Data Types” on page 2-22 and “Multiplication Data Types” in the Signal Processing Blockset documentation for illustrations depicting the use of the accumulator data type in this block. The accumulator data type is only used when both inputs to the multiplier are complex:

• When you select

characteristics match those of the product output.

• When you select

match those of the first input to the block.

• When you select

word length and the fraction length of the accumulator, in bits.

• When you select

word length, in bits, and the slope of the accumulator. The bias of all signals in the Video and Image Processing Blockset software is 0.

Output

Choose how to specify the word length and fraction length of the output of the block:

• When you select

match those of the first input to the block.

• When you select

word length and the fraction length of the output, in bits.

• When you select

word length, in bits, and the slope of the output. The bias of all signals in the Video and Image Processing Blockset software is 0.

Same as product output,these

Same as first input, these characteristics

Binary point scaling,youcanenterthe

Slope and bias scaling,youcanenterthe

Same as first input, these characteristics

Binary point scaling,youcanenterthe

Slope and bias scaling,youcanenterthe

Lock data type settings against change by the fixed-point tools

Select this parameter to prevent the fixed-point tools from overriding the data types you specify on the block mask. For more

2-33

2-D Correlation

information, see fxptdlg, a reference page on the Fixed-Point Tool in th e Simulink documentation.

See Also

2-D Autocorrelation

Histogram Video and Image Processing Blockset

Mean

Median Video and Image Processing Blockset

Standard Deviation

Variance Video and Image Processing Blockset

Maximum

Minimum

VideoandImageProcessingBlockset software

software

VideoandImageProcessingBlockset software

software

VideoandImageProcessingBlockset software

software

Signal Processing Blockset software

2-34

2-D DCT

Purpose Compute 2-D discrete cosine transform ( DCT)

Library Transforms

viptransforms

Description The 2-D DCT block calculates the two-dimensional discrete cosine

transform of the input signal. T he equation for the two-dimensional DCT is

−

Fmn

(,) ()() (,)cos

221

CmCn f x y

∑∑

xmMy

()

π 112)nNπ

(

cos

where

Cm Cn(),() /= 12

for

mn, = 0

and

The number of rows and columns of the input signal must be powers of two. The output of this block has dimensions the same dimensions as the input.

Port

Input

Input/Output Supported Data Types

Vector or matrix of intensity values

• Double-precision floating point

• Single-precision floating point

• Fixed point

• 8-, 16-, 32-bit signed integer

• 8-, 16-, 32-bit unsigned integer

Output 2-D DCT of the input Same as Input port

If the data type of the input signal is floating point, the output of the block is the same data type.

Cm Cn(),()= 1

otherwise.

Complex Values Supported

2-35

2-D DCT

Use the Sine and cosine computation parameter to specify how the block computes the sine and cosine terms in the D CT algorithm. If you select values during the simulation. If you select computes and stores the trigonometric values before the simulation starts. In this case, the block requires extra memory.

Trigonometric fcn, the block computes the sine and cosine

Table lookup,theblock

Fixed-Point Data Types

The following diagram shows the data types used in the 2-D DCT block for fixed-point signals. Inputs are first cast to the output data type and stored in the output buffer. Each butterfly stage processes signals in the accumulator data type, with the final output of the butterfly being cast back into the output data type.

2-36

2-D DCT

2-37

2-D DCT

The output of the multiplier is in the product output data type when at least one of the inputs to the multiplier is real. When both inputs to the multiplier are complex, the result of the multiplication is in the accumulator data type. For details on the complex multiplication performed, refer to “Multiplication Data Types” in the Signal Processing Blockset documentation. You can set the sine table, product output, accumulator, and output data types in the block mask as discussed in the next section.

2-38

2-D DCT

Dialog Box

The Main pane of the 2-D DCT dialog box appears as shown in the following figure.

and cosine computation

Sine

ify how the block computes the sine and cosine terms in the

Spec

lgorithm. If you select

DCT a

utes the sine and cosine values during the simulation. If

comp

select

you

Table lookup, the block computes and stores the

Trigonometric fcn,theblock

2-39

2-D DCT

trigonometric values before the simulation starts. In this case, the block requires extra memory.

The Data Types pane of the 2-D DCT dialog box appears as shown in the following figure.

2-40

Rounding mode

Select the rounding mode for fixed-point operations. The sine table values do not obey this parameter; they always round to

Overflow mode

Select the overflow mode for fixed-point operations. The sine table values do not obey this parameter; instead, they are always saturated.

Sine table data type

Choose how you specify the word length of the values of the sine table. The fraction length of the sine table values always equals the word length minus one. You can set this parameter to:

2-D DCT

Nearest.

• A rule that inherits a data type, for example,

word length as input

• An expression that evaluates to a valid data type, for example,

fixdt(1,16)

The sine table values do not obey the Roun ding mode and Overflow mode parameters; instead, they are always saturated

and rounded to

Product output data type

Specify the product output data type. See “Fixed-Point Data Types” on page 2-36 and “Multiplication Data Types” for illustrations depicting the use of the product output d a ta type in this block. You can set this parameter to:

• A rule that inherits a data type, for example,

Inherit via internal rule

• An expression that evaluates to a valid data type, for example,

fixdt(1,16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Product output data type parameter.

Nearest.

Inherit: Same

Inherit:

2-41

2-D DCT

See “Using the Data Type Assistant” in Simulink User’s Guide for more information.

Accumulator data type

Specify the accumulator data type. See “Fixed-Point Data Types” on page 2-36 for illustrations depicting the use of the accumulator data type in this block. You can set this parameter to:

• A rule that inherits a data type, for example,

Inherit via internal rule

Inherit:

• An expression that evaluates to a valid data type, for example,

fixdt(1,16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Accumulator data type parameter.

See “Using the Data Type Assistant” in Simulink User’s Guide for more information.

Output data type

Specify the output data type. See “Fixed-Point Data Types” on page 2-36 for illustrations depicting the use of the output data type in this block. You can set this parameter to:

• A rule that inherits a data type, for example,

Inherit via internal rule

When you select

Inherit: Inherit via internal rule,the

Inherit:

block calculates the output word length and fraction length automatically. The internal rule first calculates an ideal output word length and fraction length using the following equations:

2-42

WL WL floor DCT length

ideal output input

FL FL

ideal output input

=+ −+(log ( ))211

Using these ideal results, the internal rule then selects word lengths and fraction lengths that are appropriate for your hardware. For more information, see “Inherit via Internal Rule”.

• An expression that evaluates to a valid data type, for example,

fixdt(1,16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Output data type parameter.

See “Specifying Block Output Data Types” in Simulink User’s Guide for more information.

Lock scaling against changes by the autoscaling tool

Select this parameter to prevent any fixed-point scaling you specify in this block mask from being overridden by the autoscaling tool in the Fixed-Po int Tool. For more information, see

fxptdlg, a reference page on the Fixed-Point Tool in the

Simulink documentation.

2-D DCT

Refere

nces

Lock data type settings against change by the fixed-point tools

Select this parameter to prevent the fixed-point tools from overriding the data types you specify on the block mask. For more information, see Tool in th e Simulink documentation.

[1] Che algor vol. C

[2] Wa the d

Proc

n, W.H, C.H. Smith, and S.C. Fralick, “A fast computational

ithm for the discrete cosine transform,” IEEE Trans. Commun.,

OM-25, pp. 1004-1009. 1977.

ng, Z. “Fast algorithms for the discrete W transform and for

iscrete Fourier transform,” IEEE Trans. Acoust., Speech, Signal

essing, vol. ASSP-32, pp. 803-816, Aug. 1984.

fxptdlg, a reference page on the Fixed-Point

2-43

2-D DCT

See Also

2-D IDCT Video and Image Processing Blockset software

2-D FFT

2-D IFFT

Video and Image Processing Blockset software

2-44

2-D FFT

Purpose Compute 2-D FFT of input

Library Transforms

viptransforms

Description The 2-D FFT b lock computes the fast Fourier transform (FFT) of a

two-dimensional M-by-N input matrix in two steps. First it computes the one-dimensional FFT along one dimension (row or column). Then it computes the FFT of the output of the first step along the other dimension (column or row). The dimensions of the input matrix, M and N, must be powers of two. To work with other input sizes, use the Pad block to pad or truncate these dimensions to powers of two.

The output of the 2-D FFT block is equivalent to the MATLAB

fft2

function:

y = fft2(A) % Equivalent MATLAB code

Computing the FFT of each dimension of the input matrix is equivalent to calculating the two-dimensional discrete Fourier transform (DFT), which is defined by the following equation:

−

Fmn f xye e

where

(,) (,)=

01≤≤−mM

∑∑

01≤≤ −nN

and

−

2ππ

−

2-45

2-D FFT

Port

Description

Supported Data Types

Complex Values Supported

Input

Output 2-D FFT of the input Same as input port

Vector or matrix of intensity v alues

• Double-precision floating

point

• Single-precision floating point

• Fixed point

• 8-, 16-, 32-bit signed integer

• 8-, 16-, 32-bit unsigned

integer

Yes

2-46

2-D FFT

If the input signal data type is floating point, the data type of the output signal uses the same floating-point data type. Otherwise, the output can be any fixed-point data type.

Optimizing the Table of Trigonometric Values

The block computes all the possible trigonometric values of the twiddle factor

2π

−

where K is the greater value of either M or N and

kK=−01,,

Theblockstoresthesevaluesinatableandretrievesthemduring simulation. You can optimize the table of trigonometric values for memory or speed using the Optimize table for parameter. This parameter varies the number of table entries as summarized in the following table.

Optimize Table for Param e ter Setting Num ber of Table Entries for N-Point FFT

Speed

3N/4-floating point

Memory

N -fixedpoint

N/4 -floating point

Not supported for fixed point

Ordering Output Column Entries

Use the Output in bit-reversed order parameter to specify the ordering of the column elements of the output as either linear or bit-reversed. If you select the Output in bit-reversed order check box, the row and column elements are output in bit-reversed order. Thus, the mth row element appears at the kth position, where k is the bit reversed value of m.Also,thenth column element appears at the lth position, where l is the bit reversed value of n.Ifyouclearthe Output in bit-reversed order check box, the channel elements are output in linear order.

2-47

2-D FFT

Note The 2-D FF T block calculates its output in bit-reversed order.

Linearly ordering the 2-D FFT block output requires an extra bit-reversal operation. Thus, in many situations, you can increase the speed of the 2-D FFT block by selecting the Output in bit-reversed order check box.

For more information ordering of the output, see “Bit-Reversed Order” on page 2-50. The 2-D FFT block bit-reverses the order of both the columns and the rows.

Algorithms Used for FFT Computation

Which algorithms the block uses depends on whether the block input is floating-point or fixed-point, real or complex. The choice of algorithms is also affected by whether you want the output in linear or bit-reversed order. Based on these specifications, the block can use any of the following algorithms:

2-48

• Bit-reversal operation

• Double-signal algorithm

• Half-length algorithm

• Radix-2 decimation-in-time (DIT) algorithm

• Radix-2 decimation-in-frequency (DIF) algorithm

Floating-Point Signals

Complexity of Input

Complex

Output Ordering

Linear Bit-reversal operation and radix-2

Bit-reversed Radix-2 DIF

Algorithms Used for FFT Computation

DIT

Floating-Point Signals ( Con tinued)

2-D FFT

Complexity of Input

Real Linear Bit-reversal operation and radix-2

Real Bit-reversed Radix-2 DIF in conjunction with

Fixed-Point Signals

Complexity of Input

Real or complex Line ar Bit-reversal operation and radix-2

Real or complex Bit-reversed Radix-2 DIF

Output Ordering

Algorithms Used for FFT Computation

DIT in conjunction with the half-length and double-signal algorithms

the half-length and double-signal algorithms

Algorithms Used for FFT Computation

DIT

Fixed-Point Data Types

The follo wing diagrams s how the data types used in the 2-D FFT block for fixed-point signals. You can set the sine table, accumulator, product output, and output data types displayed in the diagrams in the 2-D FFT dialog box as discussed in “Dialog Box” on page 2-53.

The block first casts inputs to the output data type and stores them in the output buffer. Each butterfly stage then processes signals in the accumulator data type, with the final output of the butterfly being cast back into the output data type. The block multiplies twiddle factor values before each butterfly stageinadecimation-in-time FFT and after each butterfly stage in a decimation-in-frequency FFT.

2-49

2-D FFT

The output of the multiplier appears in the accumulator data type because both of the inputs to the multiplier are complex. For details on the complex multiplication performed, refer to “Multiplication Data Types” in the Signal Processing Blockset documentati on .

Example Bit-Reversed Order

Two numbers are bit-reversed values of each other when the binary representation of one is the mirror image of the binary representation of the other. For example, in a three-bit syste m , one and four are bit-reversed values of each other because the three-bit binary representation of one, 001, is the mirror image of the three-bit binary

2-50

2-D FFT

representation of four, 100. The following diagram shows the row indices in linear order. To put them in bit-reversed order

1 Translate the in

minimum number bits is three be

2 Find the mirror image of each binary entry, and write it beside the

original binary representation.

3 Translate the indices back to their decimal representation.

The row indi

If, on the 2-D FFT block parameters dialog box, you select the Output in bit-reversed order check box, the block bit-reverses the order of both the columns and the rows. The next diagram illustrates the linear and bit-reversed outputs of the 2-D FFT block. The output values are the same, but they appear in different order.

dices into their binary representation with the

of bits. In this example, the minimum number of

cause the binary representation of 7 is 111.

ces now appear in bit-reversed order.

2-51

2-D FFT

Input to FFT block (must be linear order)

76713623

⎡ ⎢

13787016

⎢ ⎢

44313516

⎢

36743354

⎢ ⎢

77026623

⎢

65214447

⎢ ⎢

31601516

⎢

030055355

⎢

⎣

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

⎦

Output in linear order

Output in bit-reversed order

Output in linear order

Linearly ordered row and column indices

0 1 2

3 4 5

6 7

⎡ ⎢

−−

⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢

−+ − − + + −−

⎢

⎣

Bit-reversed row and column indices

0 1 2 3

4 5 6 7

⎡ ⎢ ⎢ ⎢

18 5 6 3 19

⎢

18 5 6 3 5

⎢ ⎢

43 103 11

−− −

...iiii ii ii−+ − − − − − −+ +

⎢

84 2

..44 11 9 184 251 45 11 34 54 176 94 22 13 1 2ii i i i i i+− − −− − − −+ −−.. .. .. .. . .77

⎢ ⎢

84 24 11 9 45 11 184 251 06 27 22 13 176

⎢

4 4 10 3 1 1 11 5 11 5 6 13 1 6 2 13 3 4 8

... . .. . .

−+ + − + −− − −−... ..7 26 276 66ii i−+

⎢

⎣

245 13 9 0 4 10 5 15 9 21 6 13 15 9 21 6 10 5 13 9

43 10

iii iiii18 5 4 3 10 4 19 24 12 4 11 4 6 3 5 7 16 4 5 4 5 5 1 4−−− − − −−+ + +.. . . .. ..ii

9 163 59 14 31 177 239 1 177 239 14 31 16

−+− + − +3359

84 24 34 54 184 251 22 131 11 9 176 94

+−−−−++−

.. .. . . . . ..

+− −−−++

18 5 5 5 1 4 5 4 5 7 16 4 6 3 12 5 11 3

iii iii119 24 4 3 10 4

44 103 62 13 115 11 26 11 34 8

.. . . . . .......75613127666iii−− − +

.. . . . . .

...... ... . . .3 276 66 56 131 34 87 11 26 115 11 62 13ii i iii i−− −+ −+ − − −− +ii

−−−+−−− +

iii iii84 24 06 27 45 11 176 94 11 9 22 13 184 25.. .. .. .. . .−−+−+ + −−−−+...

.. . . . . .

ii i iii−−− −−

.. . . . .

ii ii i

ii i ii

6 7

13405

45 11 1 27

.. .

+−+

−

Output in bit-reversed order

245 13 10 5 10 5 13 9 0 4 15 9 21 6 15 9 21 6 13 9

91143

−−

−− ++ −

− − + − −− −+

ii i i i i.. .. . . .. . .− − −+ − + −+ −− +994 34 05

ii i i

ii i ii.. . . . . .

11 14 31 163 59 177 239 177 239 163 59

ii iiii

−− + −− −+ − +

24 5 4 4 3 10 4 5 7 16 4 12 4 11 4 5 5 1 4

ii i i ii

44 19 24 55 14 125 113 57 164 34 05

iiiiii

5 6 13 1 11 5 11 27 6 6 6 2 6 3 4 8 7 6 2 13

.. . .. . .. .

++−+−

+−+−−+

.. . . . . ..

.. .. .. ..

.. . . . . .

6 7

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

⎥ ⎥ ⎥ ⎥ ⎥

⎦

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

⎥ ⎥ ⎥ ⎥

⎦

2-52

2-D FFT

Dialog Box

The Main pane of the 2-D FFT dialog box a ppears as shown in the following figure.

2-53

2-D FFT

Optimize table for

Optimize the table of twiddle factor values for This parameter must be set to

Output in bit-reversed order

Designate the order of the output channel elements relative to the ordering of the input elements. When selected, the output channel elements appear in bit-reversed order relative to the input ordering. Otherwise, the output column elements display in linear order relative to the input ordering. Linearly ordering the output requires extra data sorting manipulation. For more information, s ee “Bit-Reversed Order” on page 2-50.

Divide butterfly outputs by two

When you select this parameter, the output of each butterfly of the FFT is divided by two.

The Data Types pane of the 2-D FFT dialog box appears as shown in the following figure.

Speed for fixed-point signals.

Speed or Memory.

2-54

2-D FFT

Roun

ding mode

ect the rounding mode for fixed-point operations. The sine

Sel

le values do not obey this parameter; instead, they always

tab

nd to

rou

Nearest.

2-55

2-D FFT

Overflow mode

Select the overflow mode for fixed-point operations. The sine table values do not obey this parameter; instead, they are always saturated.

Sine table data type

Choose how you specify the word length of the values of the sine table. The fraction length of the sine table values always equals the word length minus one. You can set this parameter to:

• A rule that inherits a data type, for example,

word length as input

• An expression that evaluates to a valid data type, for example,

fixdt(1,16)

The sine table values do not obey the Roun ding mode and Overflow mode parameters; instead, they are always saturated

and rounded to

Product output data type

Specify the product output data type. See “Fixed-Point Data Types” on page 2-49 and “Multiplication Data Types” for illustrations depicting the use of the product output d a ta type in this block. You can set this parameter to:

• A rule that inherits a data type, for example,

Inherit via internal rule

• An expression that evaluates to a valid data type, for example,

fixdt(1,16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Product output data type parameter.

Nearest.

Inherit: Same

Inherit:

2-56

See “Using the Data Type Assistant” in Simulink User’s Guide for more information.

Accumulator data type

Specify the accumulator data type. See “Fixed-Point Data Types” on page 2-49 for illustrations depicting the use of the accumulator data type in this block. You can set this parameter to:

2-D FFT

• A rule that inherits a data type, for example,

Inherit via internal rule

Inherit:

• An expression that evaluates to a valid data type, for example,

fixdt(1,16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Accumulator data type parameter.

See “Using the Data Type Assistant” in Simulink User’s Guide for more information.

Output data type

Specify the output data type. See “Fixed-Point Data Types” on page 2-49 for illustrations depicting the use of the output data type in this block. You can set this parameter to:

• A rule that inherits a data type, for example,

Inherit via internal rule

When you select

Inherit: Inherit via internal rule,the

Inherit:

block calculates the output word length and fraction length automatically. The internal rule first calculates an ideal output word length and fraction length using the following equations:

WL WL floor FFT length

ideal output input

FL FL

ideal output input

g these ideal results, the internal rule then selects word

Usin

gths and fraction lengths that are appropriate for your

len

=+ −+(log ( ))211

2-57

2-D FFT

hardware. For more information, see “Inherit via Internal Rule”.

• An expression that evaluates to a valid data type, for example,

fixdt(1,16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Output data type parameter.

See “Specifying Block Output Data Types” in Simulink User’s Guide for more information.

Lock data type settings against change by the fixed-point tools

Select this parameter to prevent the fixed-point tools from overriding the data types you specify on the block mask. For more information, see Tool in th e Simulink documentation.

fxptdlg, a reference page on the Fixed-Point

2-58

See Also

2-D DCT Video and Image Processing Blockset software

2-D IDCT Video and Image Processing Blockset software

2-D IFFT

FFT

IFFT

Pad

bitrevorder

fft

ifft

Video and Image P roces sing Blockset softw are

Signal Processing Blockset software

Signal Processing Toolbox software

MATLAB

2-D FIR Filter

Purpose Perform 2-D FIR filtering on input matrix

Library Filtering

Description The2-DFiniteImpulseResponse(FIR)filterblockfilterstheinput

Port

matrix and HV.

Input/Output Supported Data Types

I using the coefficient matrix H or the coefficient vectors HH

Complex Valu es Supported

PVa

Output Scalar, vector, or matrix

Vector or matrix of intensity values

Matrix of filter coefficients Same as I port.

Vector of filter coefficients Same as I port. The input to ports

Scalar value that represents the constant pad value

of filtered values

• Double-precision floating point

• Single-precision floating point

• Fixed point

• 8-, 16-, 32-bit signed integer

• 8-, 16-, 32-bit unsigned integer

HH and HV must be the same data type.

ut must have the same data

Inp

eastheinputtoIport.

typ

Same as I port.

Yes

2-59

2-D FIR Filter

If the input has a floating-point data type, then the output uses the same data type. Otherwise, the output can be any fixed-point data type.

Select the Separable filter coefficients check box if your filter coefficients are separable. Using separable filter coefficients reduces the amount of calculations the block must perform to compute the output. For example, suppose your input image is M-by-N and your filter coefficient matrix is x-by-y. For a nonseparable filter with the Output size parameter set to

Same as input port I,itwouldtake

xyMN⋅⋅ ⋅

multiply-accumulate (MAC) operations for the block to calculate the output. For a separable filter, it would only take

()xyMN+⋅⋅

MAC operations. If you do not know whether or not your filter coefficients are separable, use the

isfilterseparable function.

Here is an example of the function syntax,

isfilterseparable(H)

filter kernel,

H, and returns S, HCOL and HROW. Here, S is a Boolean

.Theisfilterseparable function takes the

variable that is 1 if the filter is separable and 0 if it is not. vector of vertical filter coefficients, and

[S, HCOL, HROW] =

HCOL is a

HROW is a vector of horizontal

filter coefficients.

Use the Coefficient source parametertospecifyhowtodefineyour filter coefficients. If you select the Separable filter coefficients check box and then select a Coefficient source of

Specify via dialog,the

Vertical coefficients (across height) and Horizontal coefficients (across width) parameters appear in the dialog box. You can use these

parameters to enter vectors of vertical and horizontal filter coefficients, respectively.

You can also use the variables

isfilterseparable function, for these parameters. If you select the

HCOL and HROW, the output of the

Separable filter coefficients check box and then select a Coefficient source of

Input port, ports HV and HH appear on the block. Use

these ports to specify vectors of vertical and horizontal filter coefficients.

2-60

2-D FIR Filter

If you clear the Separable filter coefficients check b ox and select a Coefficient source of parameter appears in the dialog box. Use this parameter to enter your matrix of filter coefficients.

If you clear the Separable filter coefficients check box and select a Coefficient source of this port to specify your filter coefficient matrix.

The block outputs the result of the filtering operation at the Output port. The

Output size parameter and the sizes of the inputs at ports I

and H dictate the dimensions of the output. For example, assume that the input at port I has dimensions (Mi, Ni) and the input at port H has dimensions (Mh, Nh). If you select anOutput size of hasdimensions(Mi+Mh-1,Ni+Nh-1). IfyouselectanOutput size of

Same as input port I, the output has the same dimensions as the

inputatportI.IfyouselectanOutput size of the input image only where the coefficient matrix f its entirely within it, so no padding is required. The output has dimensions (Mi-Mh+1, Ni-Nh+1). However, if

Specify via dialog,theCoefficients

Input port,portH appears on the block. Use

Full, the output

Valid,theblockfilters

all(size(I)<size(H)), the block errors out.

Use the Padding options parameter to specify how to pad the boundary of your input matrix. To pad your matrix with a constant value, select values, select image, select repetition of its elements, select

Constant. To pad y our input matrix by repeating its border

Replicate. To pad your input matrix with its mirror

Symmetric. To pad your input matrix using a circular

Circular. For more information on

padding, see the Image Pad block reference page.

If, for the Padding options parameter, you select

Constant,the

Pad value source parameter appears in t he dialog box. If you select

Specify via dialog,thePad value parameter appears in the dialog

box. Use this parameter to enter the constant value with which to pad your matrix. If you select Pad value source of

Input port,thePVal

port appears on the block. Use this port to specify the constant value with which to pad your matrix. T he pad value must be real if the input image is real. You will get an error message if the pad value is complex when the input image is real.

2-61

2-D FIR Filter

Use the Filtering based on parameter to specify the algorithm by which the block filters the input matrix. If you select set the Output size parameter to

Full, the block filters your input

Convolution and

using the following algorithm

Ci j Amn Hi m j n

(, ) ( , )* ( , )

=−−

−

()()

∑∑

Input (A) data type

Filter coefﬁcient (H) data type

where

Correlation and set the Output size parameter to Full,theblock

01≤< + −iMaMh

and

01≤< + −jNaNh

.Ifyouselect

filters your input using the following algorithm

Ci j Amn conjHm in j

(, ) ( , ) ( ( , ))

=⋅++

where

01≤< + −iMaMh

−

()()

∑∑

and

01≤< + −jNaNh

The imfilter function from the Image Processing Toolbox™ product similarly performs N-D filtering of multidimension al im ages.

Fixed-Point Data Types

Thefollowingdiagramshowsthedatatypesusedinthe2-DFIRFilter block for fixed-point signals.

The result of each addition remains in the accumulator data type

COMPLEX

MULTIPLIER

Accumulator or Product output data type

CAST

Accumulator data type

ADDER

CAST

Accumulator data type

Output (C) data type

2-62

2-D FIR Filter

You can set the coefficient, product output, accumulator, and output data types in the block mask as discussed in “Dialog Box” on page 2-64.

2-63

2-D FIR Filter

Dialog Box

The Main pane of the 2-D FIR Filter dialog box appears as shown in the following figure.

2-64

2-D FIR Filter

Separable filter coefficients

Select this check box if your filter coefficients are separable. Using separable filter coefficients reduces the amount of calculations the block must perform to compute the output.

Coefficient source

Specify h ow to define your filter coefficients. Select

dialog

box. Select

to enter your coefficients in the block parameters dialog

Input port to specify your filter coefficient matrix

using port H or ports HH and HV.

Coefficients

Enter your real or co m plex -valued filter coefficient matrix. This parameter appears if you clear the Separable filter coefficients check box and then select a Coefficient source of

dialog

. Tunable.

Vertical coefficients (across height)

Enter the vector of vertical filter coefficients for your separable filter. This parameter appe ars if you select the Separable filter coefficients check box and then select aCoefficient source of

Specify via dialog.

Specify via

Horizontal coefficients (across width)

Enter the vector o f horizontal filter coefficients for your separable filter. This parameter appe ars if you select the Separable filter coefficients check box and then select aCoefficient source of

Specify via dialog.

Output size

This parameter controls the size of the filtered output. If you choose If you choose dimensions as the input at port I If you choose

Full, the output has dimensions (Ma+Mh-1, Na+Nh-1).

Same as input port I, the output has the same

Valid,outputhas

dimensions (Ma-Mh+1, Na-Nh+1).

Padding options

Specify how to pad the boundary of your input matrix. Select

Constant to pad your matrix with a constant value. Select Replicate to pad your input matrix by repeating its border

2-65

2-D FIR Filter

values. Select Symmetricto pad your input matrix with its mirror image. Select repetition of its elements. This parameter appears if you select an

Output size of

Pad value source

Use this parameter to specify how to define your constant boundary value. Select in the block parameters dialog box. Select your constant value using the PVal port. This parameter appears if you select a Padding options of

Pad value

Enter the constant value with which to pad your matrix. This parameter is visible if, for the Pad value source parameter, you select

Specify via dialog. Tunable. The pad value must be real

if the input image is real. You w ill get an error message if the pad value is complex when the input image is real.

Filtering based on

Specifythealgorithmbywhichthe block filters the input matrix. You can select

Circular to pad your input matrix using a circular

Full or Same as input port I.

Specify via dialog to enter your value

Input port to specify

Constant.

Convolution or Correlation.

2-66

The Data Types pane of the 2-D FIR Filter dialog box appears as shown in the following figure.

2-D FIR Filter

2-67

2-D FIR Filter

Rounding mode

Select the rounding mode f or fixed-point operations.

Overflow mode

Select the overflow mode for fixed-point operations.

Coefficients

Choose how to specify the word length and the fraction length of the filter coefficients.

• When you select

length of the filter coefficients match that of the input to the block. In this mode, the block automatically sets the fraction length of the coefficients to the binary-point only scaling that provides you with the best precision possible given the value and word length of the coefficients.

• When you select

word length of the coefficients, in bits. I n this mode, the block automatically sets the fraction length of the coefficients to the binary-point only scaling that provides you with the best precision possible given the value and word length of the coefficients.

• When you select

word length and the fraction length of the coefficients, in bits.

• When you select

the word length, in bits, and the slope of the coefficients. All signals in the Video and Image Processing Blockset software have a bias of 0.

The filter coefficients do not obey the Rounding mode and the Overflow mode parameters; instead, they always satur a t ed and rounded to

Product output

Use this parameter to specify how to designate the product output word and fraction lengths. Refer to “Fixed-Point Data Types” on page 2-62 and “Multiplication Data Types” in the Signal

Nearest.

Same word length as input ,theword

Specify word length,youcanenterthe

Binary point scaling,youcanenterthe

Slope and bias scaling,youcanenter

2-68

2-D FIR Filter

Processing Blockset documentation for illustrations depicting the use of the product output data type in this block:

• When you select

thoseoftheinputtotheblock.

• When you select

word length and the fraction length of the product output, in bits.

• When you select

word length, in bits, and the slope of the product output. All signals in the Video and Image Processing Blockset software have a bias of 0.

If you set the Coefficent source (on the Main tab) to

the Product Output will inherit its sign according to the

port

inputs. If either or both input I1 and I2 aresigned,theProduct Output will be signed. Otherwise, the Product Output is unsigned. The following table shows all cases.

Sign of Input I1 Sign of Input I2 Sign of Product

unsigned unsigned unsigned

unsigned signed signed

signed unsigned signed

signed signed signed

Same as input, these characteristics match

Binary point scaling,youcanenterthe

Slope and bias scaling,youcanenterthe

Input

Output

Accumulator

Use this parameter to specify how to designate the accumulator word and fraction lengths. Refer to “Fixed-Point Data Types” on page 2-62 and “Multiplication Data Types” in the Signal Processing Blockset documentation for illustrations depicting the use of the accumulator data type in this block. The accumulator data type is only used when both inputs to the multiplier are complex:

2-69

2-D FIR Filter

• When you select Same as product output,these

characteristics match those of the product output.

• When you select

thoseoftheinputtotheblock.

• When you select

word length and the fraction length of the accumulator, in bits.

• When you select

word length, in bits, and the slope of the accumulator. All signals in the Video and Image Processing Blockset software have a bias of 0.

Output

Choose how to specify the word length and fraction length of the output of the block:

• When you select

thoseoftheinputtotheblock.

• When you select

word length and the fraction length of the output, in bits.

• When you select

word length, in bits, and the slope of the output. All signals in the Video and Image Processing Blockset software have a bias of 0.

Lock data type settings against change by the fixed-point tools

Select this parameter to prevent the fixed-point tools from overriding the data types you specify on the block mask. For more information, see Tool in th e Simulink documentation.

Same as input, these characteristics match

Binary point scaling,youcanenterthe

Slope and bias scaling,youcanenterthe

Same as input, these characteristics match

Binary point scaling,youcanenterthe

Slope and bias scaling,youcanenterthe

fxptdlg, a reference page on the Fixed-Point

2-70

See Also

imfilter

Image Processing Toolbox

2-D Histogram (Obsolete)

Purpose Generate histogram of each input m atrix

Library Statistics

Description

Note The 2-D Histogram block is obsolete. It may b e removed in a

future version of the Video and Image Processing Blockset software. Use the replacement block Histogram.

The 2-D Histogram block computes the frequency distribution of the elements in each input matrix or in a sequence of inputs over a period of time. Use the Running histogram check box to select between the block’s basic and running operation.

The output of the 2-D Histogram block is different than the output of the

imhist function in the Image Processing Toolbox. For intensity

images, the

imhist function defines the pth bin boundaries as

(.)

−

()

−

where A is maximum value of the data type, N is the number of bins in the histogram, and p starts from 1. The 2-D Histogram block defines bin boundaries as

()−

<≤

where A corresponds to the Maximum value of input parameter and the Minimum value of input parameter is assumed to be 0.

≤<

(.)

−

()

−

2-71

2-D Histogram (Obsolete)

Port

Input/Output Supported Data Types

Complex Values Supported

Input / I

Rst

Output Sample-based 1-by-N

Vector or matrix of intensity values

Signal that triggers a reset event

vector that represents the frequency distribution of each M-by-N input matrix or the frequency distributions in a series of M-by-N inputs

Length-M 1-D vector inputs are tr eated as M-by -1 column vectors.

• Double-precision floating p oint

• Single-precision floating point

• Fixed point

• 8-, 16-, and 32-bit signed integer

• 8-, 16-, and 32-bit unsigned integer

• Double-precision floating p oint

• Single-precision floating point

• Boolean

• 8-, 16-, and 32-bit signed integer

• 8-, 16-, and 32-bit unsigned integer

Same as Input port

Yes

2-72

The block sorts the elements of each input matrix into the number of discrete bins, n,specifiedbytheNumber of bins parameter. Complex inputs are sorted by their magnitude squared values.

The histogram value for a given bin represents the frequency of occurrence of the input values bracketed by that bin. You specify the upper b oundary of the highest-valued bin in the Maximum value of input parameter, B

, and the lower boundary of the lowest-valued

2-D Histogram (Obsolete)

bin in the Minimum value of input parameter, Bm. The bins have equal width of

where n isthenumberofbins. Thecentersarelocatedat

Input values that fall on the border between two bins are sorted into the lower-valued bin; that is, each bin includes its upper boundary. For example, a bin of width 4 centered on the value 5 contains the input value 7, but not the input value 3. Input values greater than the

Maximum value of input parameterorlessthanMinimum value of input parameter are sorted into the highest-valued or lowest-valued bin, respectively. The values you enter for the Maximum value of input and Minimum value of input parameters must be real-valued

scalar values.

Basic Operation

If you clear the Running histogram check box, the block computes the f requency distribution of each M-by-N input matrix and outputs a sample-based 1-by-N vector.

111

⎡ ⎢

Forexample,ifyourinputis parameters as follows:

• Minimum value of input =

• Maximum value of input = 4

• Number of bins = 4

222

⎢ ⎢

333

⎣

⎤ ⎥

and you set the block

⎥ ⎥

⎦

2-73

2-D Histogram (Obsolete)

The block outputs [3330].

If you select the Normalized check box, the block scales each element oftheoutputsothat

Running Operation

If you select the Running histogram check box, the block computes the f requency distributions in a series of M-by-N inputs.

For example, if your first input is

222

input is

⎡ ⎢

333

⎢ ⎢

444

⎣

⎤ ⎥ ⎥ ⎥

⎦

sum(v) is 1, where v is the o utput vector.

111

⎡ ⎢

222

⎢ ⎢

333

⎣

, and you set the block parameters as follows:

⎤ ⎥ ⎥ ⎥

⎦

, your second and current

• Minimum value of input =

• Maximum value of input = 4

• Number of bins = 4

The block outputs [3663]. For the next input, the block computes the frequency distribution for the first three inputs, and so on.

Resetting the Running Histogram

The block resets the running histogram whenever a reset event is detected at the optional Rst port. The reset signal and the input data signal must be the same rate.

To enable the Rst port, select the Reset port parameter. You specify the re set event in the Trigger type parameter, and can be one of the following:

•

Rising edge — Triggers a reset operation when the Rst input does

one of the following:

- Rises from a negative value to a positive value or 0

2-74

2-D Histogram (Obsolete)

- Rises from 0 to a positive value, where the rise is not a continuation

ofarisefromanegativevalueto0(seethefollowingfigure)

Rising edge

• Falling edge — Triggers a reset operation when the Rst input does

one of the following:

Rising edge

Not a rising edge because it is a continuation of a rise from a negative value to zero.

- Falls from a positive value to a negative value or 0

- Fallsfromzerotoanegativevalue,wherethefallisnota

continuation of a fall from a positive value to 0 (see the following figure)

Falling edge

Not a falling edge because it is a continuation of a fall from a positive value to zero.

• Either edge -- Triggers a reset operation when the Rst input is a

Rising edge or Falling edge (as described previously)

2-75

2-D Histogram (Obsolete)

• Non-zero sample -- Triggers a reset operation at each sample time

that the

Note When running simulations in the Simulink MultiTasking mode, sample-based reset signals have a one-sample latency, and frame-based reset signals have one frame of latency. Thus, there is a one-sample or one-frame delay between the time the block detects a reset event, and when it applies the reset. For more information on latency and the Simulink tasking modes, see “Configuration Parameters Dialog Box” in the Simulink documentation.

Rst input is not 0

Dialog Box

The Main pane of the 2-D Histogram dialog box:

2-76

2-D Histogram (Obsolete)

Minimum value of input

Enter a real-valued s calar value for the lower boundary, the lowest-valued bin. Tunable.

Maximum value of input

Enter a real-valued scalar value for the upper boundary, the highest-valued bin. Tunable.

Number of bins

Enter the number of bins, n, in the histogram.

Normalized

If you select this check box, the block normalizes the output vector (1-norm). Tunable.

Use of this parameter is not supported for fixed-point signals.

Running histogram

Select this check box to enable the block’s running histogram operation.

Reset port

Enables the Rst input port when selected. The reset signal and theinputdatasignalmustbethesamerate. Thisparameteris visible if you select the Running histogram check box.

,of

Trigger type

The type of event that resets the running histogram. For more information, see “Resetting the Running Histogram” on page 2-74. This parameter is enabled only when you set the Reset port parameter.

The Fixed-point pane of the 2-D Histogram dialog bo x:

2-77

2-D Histogram (Obsolete)

2-78

Note The inputs,

Roundi

Overf

Prod

which are sorted by squared magnitude.

ng mode

Selec

low mode

Selec

uct output

Use t word

• Whe

fixed-point paramete rs are only used for fixed-point complex

t the rounding mode for fixed-point operations.

t the overflow mode for fixed-point operations.

his parameter to specify how to designate the product output

and fraction lengths:

nyouselect

se of the input to the block.

tho

Same as input, these characteristics match

2-D Histogram (Obsolete)

• When you select Binary point scaling,youcanenterthe

word length and the fraction length of the product output, in bits.

• When you select

word length, in bits, and the slope of the product output. This block requires power-of-two slope and a bias of 0.

Accumulator

Use this parameter to specify the accumulator word and fraction lengths resulting from a complex-complex multiplication in the block:

• When you select

characteristics match those of the product output.

• When you select

thoseoftheinputtotheblock.

• When you select

word length and the fraction length of the accumulator, in bits.

• When you select

word length, in bits, and the slope of the accumulator. This block requires power-of-two slope and a bias of 0.

Lock scaling against changes by the autoscaling tool

Select this parameter to prevent any fixed-point scaling you specify in this block mask from being overridden by the autoscaling tool in the Fixed-Po int Tool. For more information, see

fxptdlg, a reference page on the Fixed-Point Tool in the

Simulink documentation.

Slope and bias scaling,youcanenterthe

Same as product output,these

Same as input, these characteristics match

Binary point scaling,youcanenterthe

Slope and bias scaling,youcanenterthe

See Also

2-D Autocorrelation

2-D Correlation

Video and Image Processing Blockset software

2-79

2-D Histogram (Obsolete)

Mean

Median Video and Image Processing Blockset

Standard Deviation

Variance Video and Image Processing Blockset

Histogram

Maximum

Minimum

hist

imhist

Video and Image Processing Blockset software

software

Video and Image Processing Blockset software

software

Signal Processing Blockset software

MATLAB application

Image P roces sing Toolbox software

2-80

Purpose Compute 2-D inverse discrete cosine transform (IDCT)

Library Transforms

viptransforms

Description The 2-D IDCT block calculates the two-dimensional inverse

discrete cosine transform of the input signal. The equation for the two-dimensional IDCT is

−

fxy

(, ) ( ) () ( , )cos

221

CmCnFmn

∑∑

xmMy

()

π 112)nNπ

cos

2-D IDCT

(

Port

Input

where F(m,n) is the DCT of the signal f(x,y) and

mn, = 0

Cm Cn(),()= 1

and

otherwise.

The number of rows and columns of the input signal must be powers of two. The output of this block has dimensions the same dimensions as the input.

Input/Output Supported Data Types

Vector or matrix of intensity values

• Double-precision floating

point

• Single-precision floating

point

• Fixed point

• 8-, 16-, 32-bit signed integer

• 8-, 16-, 32-bit un sign ed

integer

Cm Cn(),()=

Complex Valu es Supported

for

2-81

2-D IDCT

Port

Input/Output Supported Data Types

Complex Valu es Supported

Output 2-D IDCT of the input Same as Input port

If the data type of the input signal is floating point, the output of the block is the same data type.

Use the Sine and cosine computation parameter to specify how the block computes the sine and cosine terms in the IDCT algorithm. If you select values during the simulation. If you select computes and stores the trigonometric values before the simulation starts. In this case, the block requires extra memory.

Trigonometric fcn, the block computes the sine and cosine

Fixed-Point Data Types

Thefollowingdiagramshowsthedatatypesusedinthe2-DIDCTblock for fixed-point signals. Inputs are first cast to the output data type and stored in the output buffer. Each butterfly stage processes signals in the accumulator data type, with the final output of the butterfly being cast back into the output data type.

Table lookup,theblock

2-82

2-D IDCT

2-83

2-D IDCT

The output of the multiplier is in the product output data type when at least one of the inputs to the multiplier is real. When both of the inputs to the multiplier are complex, the result of the multiplication is intheaccumulatordatatype. Fordetails on the com plex multiplication performed, refer to “Multiplication Data Types” in the Signal Processing Blockset documentation. You can set the sine table, product output, accumulator, and output data types in the block mask as discussed in the next section.

2-84

Mathworks VIDEO AND IMAGE PROCESSING BLOCKSET 3 Reference

Specifications and Main Features

Frequently Asked Questions

User Manual

Block Reference

Analysis & Enhancement

Filtering

Geometric Transformations

Morphological Operations

Sinks

Sources

Statistics

Text & Graphics

Utilities

Blocks — Alphabetical List

Floating-Point Signals

Fixed-Point Signals