 Convolution Integral for two dimensional data. More...

## Functions

AFAPI array convolve2 (const array &signal, const array &filter, const convMode mode=AF_CONV_DEFAULT, const convDomain domain=AF_CONV_AUTO)
C++ Interface for convolution on two dimensional signals. More...

AFAPI af_err af_convolve2 (af_array *out, const af_array signal, const af_array filter, const af_conv_mode mode, af_conv_domain domain)
C Interface for convolution on two dimensional signals. More...

## Detailed Description

Convolution Integral for two dimensional data.

A convolution is a common operation between a source array, a, and a filter (or kernel) array b. The answer to the convolution is the same as computing the coefficients in polynomial multiplication, if a and b are the coefficients.

Another way to think about it is that the filter kernel is centered on each pixel in a, and the output for that pixel or data point is the sum of the products.

Depending on the dimensions of the input signal and the filter signal, any one of the following batch mode convolutions take place.

• No Batch - Single filter applied to single input.
• Filter is Batched - Many filters applied on same input
• Signal is Batched - Single filter applied to a set of inputs.
• Identical Batches - A set of filters applied onto to a set of inputs in one-to-one correspondence.
• Non overlapping Batches - All batched filters are applied to all batched signals. The batch dimension of Signal and Filter should not be the same.

For example, if the signal is two dimensional with m & n as sizes along the 0th & 1st dimensions respectively, then the possible batch operations are as follows.

Input Signal Dimensions Filter Dimensions Output Dimensions Batch Mode Explanation
[m n 1 1] [m n 1 1] [m n 1 1] No Batch Output will be a single convolve array
[m n 1 1] [m n p 1] [m n p 1] Filter is Batched p filters applied to same input
[m n p 1] [m n 1 1] [m n p 1] Signal is Batched 1 filter applied to p inputs
[m n p 1] [m n p 1] [m n p 1] Identical Batches p filters applied to p inputs in one-to-one correspondence
[m n p 1] [m n 1 q] [m n p q] Non-overlapping batches q filters applied to p inputs in to produce p x q results
[m n 1 p] [m n q 1] [m n q p] Non-overlapping batches q filters applied to p inputs in to produce q x p results

## ◆ af_convolve2()

 AFAPI af_err af_convolve2 ( af_array * out, const af_array signal, const af_array filter, const af_conv_mode mode, af_conv_domain domain )

C Interface for convolution on two dimensional signals.

Parameters
 [out] out is convolved array [in] signal is the input signal [in] filter is the signal that shall be flipped for the convolution operation [in] mode indicates if the convolution should be expanded or not(where output size equals input) [in] domain specifies if the convolution should be performed in frequency os spatial domain
Returns
AF_SUCCESS if the convolution is successful, otherwise an appropriate error code is returned.
Note
The default parameter of domain, AF_CONV_AUTO, heuristically switches between frequency and spatial domain.

## ◆ convolve2()

 AFAPI array af::convolve2 ( const array & signal, const array & filter, const convMode mode = AF_CONV_DEFAULT, const convDomain domain = AF_CONV_AUTO )

C++ Interface for convolution on two dimensional signals.

//vector<dim4> numDims;
//vector<vector<float> > in;
array signal(numDims, &(in.front()));
//signal dims = [15 17 1 1]
array filter(numDims, &(in.front()));
//filter dims = [5 5 2 1]
array output = convolve2(signal, filter, AF_CONV_DEFAULT);
//output dims = [15 17 1 1] - same as input since expand(3rd argument is false)
//however, notice that the 3rd dimension of filter is > 1.
//So, one to many batch mode will be activated automatically
//where the 2d input signal is convolved with each 2d filter
//and the result will written corresponding slice in the output 3d array
Parameters
 [in] signal is the input signal [in] filter is the signal that shall be flipped for the convolution operation [in] mode indicates if the convolution should be expanded or not(where output size equals input) [in] domain specifies if the convolution should be performed in frequency os spatial domain
Returns
the convolved array
Note
The default parameter of domain, AF_CONV_AUTO, heuristically switches between frequency and spatial domain.
Examples:
getting_started/convolve.cpp.