Separable Convolution

Overview

The Separable Convolution algorithm performs a 2D convolution operation, but takes advantage of the fact that the 2D kernel is separable. The user passes one horizontal and one vertical 1D kernel. This usually leads to better performance, especially for kernels larger than 5x5. For smaller kernels, it's preferable to use Convolution algorithm with a 2D kernel directly.

Input	Sobel kernel	Output
	\begin{eqnarray*} k_{col} &=& \frac{1}{64} \begin{bmatrix} 1 \\ 6 \\ 15 \\ 20 \\ 15 \\ 6 \\ 1 \end{bmatrix} \\ k_{row} &=& \begin{bmatrix} -1 & -5 & -6 & 0 & 6 & 5 & 1 \end{bmatrix} \end{eqnarray*}

Implementation

Discrete 2D convolution is implemented using the following discrete function:

\begin{eqnarray*} I'[x,y] &=& \sum_{m=0}^{k_w} K_{row}[m] \times I[x,y-(m - \lfloor k_w/2 \rfloor)] \\ I''[x,y] &=& \sum_{m=0}^{k_h} K_{col}[m] \times I'[x-(m - \lfloor k_h/2 \rfloor),y] \end{eqnarray*}

Where:

• \(I\) is the input image.
• \(I'\) is the temporary image with convolution along the rows.
• \(I''\) is the final result.
• \(K_{row}\) is the row convolution kernel.
• \(K_{col}\) is the column convolution kernel.
• \(k_w,k_h\) are the kernel's width and height, respectively.

Note

Most computer vision libraries expect the kernel to be reversed before calling their convolution functions. Not so with VPI, we implement a actual convolution, not cross-correlation. Naturally, this is irrelevant if the kernel is symmetric.

Usage

Language: C/C++ Python

1. Import VPI module

   import vpi

2. Define a 3x3 separable Sobel kernel.

   sobel_row = [-1, -5, -6, 0, +6, +5, +1];
   sobel_col = [1/64.0, 6/64.0, 15/64.0, 20/64.0, 15/64.0, 6/64.0, 1/64.0]

3. Run separable convolution filter on input image using the CPU backend and the given kernel. Input and output are VPI images.

   with vpi.Backend.CUDA:
       output = input.convolution(kernel_x=sobel_row, kernel_y=sobel_col, border=vpi.Border.ZERO)

1. Initialization phase
   1. Include the header that defines the needed functions and structures.

      #include <vpi/algo/Convolution.h>

   2. Define the input image object.

          VPIImage input = /*...*/;

   3. Create the output image. It gets its dimensions and format from the input image.

          int32_t w, h;
          vpiImageGetSize(input, &w, &h);
       
          VPIImageFormat type;
          vpiImageGetFormat(input, &type);
       
          VPIImage output;
          vpiImageCreate(w, h, type, 0, &output);

   4. Create the stream where the algorithm will be submitted for execution.

          VPIStream stream;
          vpiStreamCreate(0, &stream);

2. Processing phase
   1. Define the kernel to be used. In this case, a simple 7x7 Sobel filter.

          float sobel_row[7] = {-1, -5, -6, 0, +6, +5, +1};
          float sobel_col[7] = {1/64.f, 6/64.f, 15/64.f, 20/64.f, 15/64.f, 6/64.f, 1/64.f};

   2. Submit the algorithm to the stream, passing the 1D kernels and remaining arguments. I'll be executed by the CUDA backend.

          vpiSubmitSeparableConvolution(stream, VPI_BACKEND_CUDA, input, output, sobel_row, 7, sobel_col, 7, VPI_BORDER_ZERO);

   3. Optionally, wait until the processing is done.

          vpiStreamSync(stream);

3. Cleanup phase
   1. Free resources held by the stream and the input and output images.

          vpiStreamDestroy(stream);
          vpiImageDestroy(input);
          vpiImageDestroy(output);

For more information, see Convolution in the "API Reference" section of VPI - Vision Programming Interface.

Limitations and Constraints

Constraints for specific backends supersede the ones specified for all backends.

All Backends

• Input and output images must have the same dimensions and type.
• The following image formats are accepted:
  • VPI_IMAGE_FORMAT_U8
  • VPI_IMAGE_FORMAT_S8
  • VPI_IMAGE_FORMAT_U16
  • VPI_IMAGE_FORMAT_S16
• Minimum 1D convolution kernel size is 1, maximum is 11.
• The following border extensions are accepted.
  • VPI_BORDER_ZERO
  • VPI_BORDER_CLAMP

PVA

• Only available on Jetson Xavier devices.
• Input and output dimensions must be between 160x92 and 3264x2448.
• Minimum 1D convolution kernel size is 2, maximum is 11.
• Horizontal and vertical kernel sizes must be equal, i.e., only square kernels can be used.
• Kernel weights are restricted to \(|weight| < 1\).
• The following image formats are the only ones accepted:
  • VPI_IMAGE_FORMAT_S16
• The following border extensions are accepted.
  • VPI_BORDER_ZERO

VIC

• Not implemented.

Performance

For information on how to use the performance table below, see Algorithm Performance Tables.
Before comparing measurements, consult Comparing Algorithm Elapsed Times.
For further information on how performance was benchmarked, see Performance Benchmark.

clear filters Device: Jetson AGX Xavier Jetson TX2 Jetson Nano  -  Streams: 1 4 8