conv2
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Two-dimensional convolution.
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Syntax
Function call
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C = conv2(A,B)— returns two-dimensional convolution of matricesAandB.-
If
A"the matrix, ehB— vector-string (orA— vector is a string, andB— matrix), thenC— this is the convolution of each row of the matrix with a vector. -
If
A"the matrix, ehB— column vector (orA— column vector, andB— matrix), thenC— this is the convolution of each column of the matrix with a vector.
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Arguments
Input arguments
# A — input array
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vector | the matrix
Details
An input array specified as a vector or matrix.
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| Support for complex numbers |
Yes |
# B is the second input array
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vector | the matrix
# u is the input vector
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vector string | column vector
Details
The input vector, specified as a row vector or column vector. u performs convolution with each column of the matrix A.
| Data types |
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| Support for complex numbers |
Yes |
# v is the second input vector
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vector string | column vector
# shape — the section of the convolution
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"full" (by default) | "same" | "valid"
Details
A section of the convolution defined by one of the following values:
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"full"— returns a complete two-dimensional convolution. -
"same"— returns the central part of the convolution, the same size as the original matrixA. -
"valid"— returns only the part of the convolution that is calculated without padding with zeros.
Output arguments
# C — two- dimensional convolution
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vector | the matrix
Details
A two-dimensional convolution returned as a vector or matrix. If A and B — matrices, then convolution C = conv2(A,B) It has a size size(A)+size(B)-1. If m,n = size(A), p = length(u) and q = length(v), then the convolution C = conv2(u,v,A) has m+p-1 lines and n+q-1 columns.
If there are one or more input arguments to the function conv2 have a type Float32, then the output argument will be of type Float32. Otherwise conv2 converts the input data to a type Float64 and returns the type Float64.
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Examples
Two-dimensional convolution
Details
It can be useful to compare the input data of a convolution directly with the output data. Function conv2 allows you to control the size of the output data.
Let’s create random matrices A size and B size . Calculate the complete convolution A and B, which is a matrix of size .
import EngeeDSP.Functions: conv2
A = rand(3, 3)
B = rand(4, 4)
Cfull = conv2(A, B)6×6 Matrix{Float64}:
0.192995 0.882682 0.775044 0.405206 0.103599 0.0162149
0.097371 1.17042 1.53107 1.55316 0.520306 0.126147
0.441852 1.15874 1.98734 3.1404 1.30511 0.484233
0.27297 0.973765 1.87607 2.67335 1.76588 1.15007
0.245543 0.433698 1.24257 1.63366 1.89067 1.4068
0.0713151 0.203243 0.630603 0.901696 1.01698 0.577671Calculate the central part of the convolution Csame, which is a submatrix of Cfull the same size as A. Csame equal to Cfull[3:5, 3:5].
Csame = conv2(A, B, "same")3×3 Matrix{Float64}:
1.98734 3.1404 1.30511
1.87607 2.67335 1.76588
1.24257 1.63366 1.89067Extracting the edges of a two-dimensional pedestal
Details
Sobel’s edge search algorithm uses two-dimensional convolution to detect edges in images and other two-dimensional data.
Let’s create and build a two-dimensional pedestal with an internal height equal to one.
A = zeros(10, 10)
A[3:7, 3:7] .= 1.0
surface(A)
Let’s perform the convolution of the rows of the matrix A with a vector u, and then convolution of the result string with the vector v. The convolution will extract the horizontal edges of the pedestal.
import EngeeDSP.Functions: conv2
u = [1, 0, -1]'
v = [1, 2, 1]
Ch = conv2(u, v, A)
surface(Ch)
To extract the vertical edges of the pedestal, reverse the convolution order from u and v on the way back.
Cv = conv2(v, u, A)
surface(Cv)
Let’s calculate and graph the combined edges of the pedestal.
surface(sqrt.(Ch.^2 .+ Cv.^2))
Additional Info
Two-dimensional convolution
Details
For discrete two-dimensional matrices and the following equation defines the convolution and :
and all values that lead to valid indexes are run through. and .
Using this definition, the function conv2 calculates a direct convolution of two matrices, not an FFT-based convolution.