2-D Convolution
Compute 2-D discrete convolution of two input matrices
- Library:
Computer Vision Toolbox / Filtering
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:
where and .
Ports
Input
Output
Parameters
Block Characteristics
Data Types |
|
Multidimensional Signals |
|
Variable-Size Signals |
|
Algorithms
2-D 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 .
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 with the same dimensions as the input at port I1, (4,3). However, since a 4-by-3 matrix cannot be extracted from the exact center of , the block leaves more rows and columns on the top and left side of the 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 . Therefore, the block outputs:
