2D Convolution
Compute 2D discrete convolution of two input matrices
Libraries:
Computer Vision Toolbox /
Filtering
Description
The 2D Convolution block computes the twodimensional 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 2D discrete convolution is:
$$C(i,j)={\displaystyle \sum _{m=0}^{(Ma1)}{\displaystyle \sum _{n=0}^{(Na1)}A(m,n)*B(im,jn)}}$$
where $$0\le i<Ma+Mb1$$ and $$0\le j<Na+Nb1$$.
Examples
Blur Image Using Gaussian Kernel
Perform 2D convolution to blur an image using the Gaussian kernel.
Ports
Input
I1 — Input matrix
matrix
Input matrix, specified as either a matrix of intensity values or a matrix that represents one plane of an RGB video stream.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 fixed point
I2 — Input matrix
matrix
Input matrix, specified as either a matrix of intensity values or a matrix that represents one plane of an RGB video stream.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 fixed point
Output
Output — Convolution
matrix
Convolution of the input matrices, returned as a matrix.
Dependencies
The dimensions of the output are dictated by the Output size parameter.
If the data type of the input is floating point, the output of the block is also floating point.
If
all(size(I1)<size(I2))
, the block returns an error.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 fixed point
Parameters
Main Tab
Output size — Output size
matrix
Dimensions of the output.
The table describes the block output, given the following input dimensions:
I1 — (Ma, Na)
I2 — (Mb, Nb)
Output size  Output  Output Dimension 

Full  Full twodimensional convolution  (Ma+Mb1, Na+Nb1). 
Same as input port I1  Central part of the convolution with the same dimensions as the input at port I1  
Valid  Only the parts of the convolution that are computed without the zeropadded edges of any input.  (MaMb+1, NaNb+1) 
Normalized output — Normalized output
matrix
Normalize output by dividing the output by
sqrt(sum(dot(I1p,I1p))*sum(dot(I2,I2)))
, where
I1p
is the portion of the I1 matrix
that aligns with the I2 matrix.
Note
When you select the Normalized output check box, the block input cannot be fixed point.
Data Types Tab
For details on the fixedpoint block parameters, see Specify FixedPoint Attributes for Blocks (DSP System Toolbox).
Block Characteristics
Data Types 

Multidimensional Signals 

VariableSize Signals 

Algorithms
2D Convolution
In convolution, the value of an output element is computed as a weighted sum of neighboring elements.
For example, suppose the first input 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 = [8 1 6 3 5 7 4 9 2]
The following figure shows how to compute the (1,1) output element by using these steps:
Rotate the second input matrix, I2, 180 degrees around its center element.
Slide the center element of I2 so that it lies on top of the (0,0) element of I1.
Multiply each element of the rotated I2 matrix by the element of I1 underneath.
Sum the individual products from step 3.
The (1,1) output element is $$0\cdot 2+0\cdot 9+0\cdot 4+0\cdot 7+17\cdot 5+24\cdot 3+0\cdot 6+23\cdot 1+5\cdot 8=220$$.
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]
.
Output Sizes
The equations below describe how the block computes the convolution depending on how you set the Output size parameter. For the cases below, the inputs are set as:
I1 — dimensions (4,3)
I2 — dimensions (2,2)
When Output size is set to
Full
, the block uses the following equations:The resulting matrix is:
When Output size is set to
Same as input port I1
, the output is the central part of $$Cfull$$ with the same dimensions as the input at port I1, (4,3). However, since a 4by3 matrix cannot be extracted from the exact center of $$Cfull$$, the block leaves more rows and columns on the top and left side of the $$Cfull$$ matrix and outputs:When the Output size is set to
Valid
, the block uses the following equations to determine the number of rows and columns of the output matrix:In this case, it is always possible to extract the exact center of $$Cfull$$. Therefore, the block outputs:
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
FixedPoint Conversion
Design and simulate fixedpoint systems using FixedPoint Designer™.
When you select the Normalized output check box, the block input cannot be fixed point.
Version History
Introduced before R2006a
See Also
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