Remap

Overview

Remap applies a generic geometrical transformation to an image. Typical uses include:

• Lens distortion correction.
• User-defined border extension.
• Conversion between different projections.

The algorithm can work on dense or sparse warp maps. A dense warp map stores the remapped position of all pixels in the output image, whereas a sparse map stores a subset of that. It's more efficient to process the latter than the former, but quality might decrease depending on how much distortion is applied by the mapping.

The example below shows the famous "Little Planet" (stereographic) projection applied to a equirectangular panorama image, where \(R\) is the planet radius.

Input	Mapping	Result
Kyu Shiba Rikyu Garden: on the bridge by heiwa4126 is licensed under CC BY 2.0	\begin{align*} \theta(x,y) &= \pi + \arctan\left(\frac{y}{x}\right) \\ \phi(x,y) &= \frac{\pi}{2} - 2\arctan\left(\frac{r}{2R}\right) \\ r &= \sqrt{x^2+y^2} \\ \end{align*}	This image is a derivative of Kyu Shiba Rikyu Garden: on the bridge by heiwa4126, used under CC BY 2.0

Implementation

The algorithm uses a user-provided VPIWarpMap that maps every pixel in the output image to the corresponding pixel in the input image. It supports dense and sparse mappings.

Mapping operation

The mapping operation is composed of two steps:

1. A dense map is generated by up-sampling the input sparse map using bi-quadratic interpolation.
2. The pixel in the input image corresponding to the control point in the output image is sampled using the user-provided interpolator.

When the corresponding source pixel falls outside image border, Remap will use the border extension to decide what pixel value to pick.

Warp grid definition

Warp grids can be of 3 types:

• dense: provides maximum quality in exchange for some performance hit.
• uniformly sparse: provides a balance between quality and speed. Useful when the distribution of details in the resulting image isn't known a priori.
• non-uniformly sparse: Useful when distribution of details in the resulting image is known. This allows increased quality and performance by sampling less in areas with low detail, and sampling more densely in areas with more detail.

When defining a sparse map, the output image can be split into at most 16 regions (4 horizontally and 4 vertically), with different control point interval (density) in each row or column of regions. The interval spacing must be expressed in power-of-two number of pixels in between control points. There are some other restrictions in the grid layout. Please consult VPIWarpGrid for more information.

Non-uniform grid

To define a dense map, simply set up the warp grid to have just one region, and both horizontal and vertical spacing to 1.

C API functions

For list of limitations, constraints and backends that implements the algorithm, consult reference documentation of the following functions:

Function	Description
vpiCreateRemap	Create a payload for Remap algorithm.
vpiSubmitRemap	Submits a Remap operation to the stream.

Usage

Language: C/C++ Python

1. Import VPI module

   import vpi

2. Create a identity warp map, i.e., all control points' position will match their position in the output image. Here the warp map is dense with same dimensions as input image.

   warp = vpi.WarpMap(vpi.WarpGrid(input.size))

3. Interpret warp map coordinates as a numpy array. No copies are made. The numpy array has shape (H,W,2) and is a view of the warp map. The shape transposition to (2,W,H) is just to have the x and y coordinates in the arrays wx and wy respectively. This makes coordinates' manipulation easier and more efficient.

   wx,wy = np.asarray(warp).transpose(2,1,0)

4. Generate a custom mapping suitable to render an equirectangular panorama with the "Little Planet" effect. A similar approach is also taken when performing lens distortion correction for a lens whose distortion model doesn't match the ones provided by VPI. See Lens Distortion Correction for more details.

   x = wx-input.width/2
   y = wy-input.height/2
    
   R = input.height/8 # planet radius
   r = np.sqrt(x*x + y*y)
    
   theta = np.pi + np.arctan2(y,x)
   phi = np.pi/2 - 2*np.arctan2(r, 2*R)
    
   wx[:] = np.fmod((theta + np.pi)/(2*np.pi)*(input.width-1), input.width-1)
   wy[:] = (phi + np.pi/2) / np.pi*(input.height-1)

5. Executes the algorithm, it'll transform the VPI image input using the warp map created, writing the result into the output VPI image.

   with vpi.Backend.CUDA:
       output = input.remap(warp)

1. Initialization phase
   1. Include the header that defines the Remap functions and VPIWarpMap definition.

      #include <vpi/WarpMap.h>
      #include <vpi/algo/Remap.h>

   2. Define the input image object.

          VPIImage input = /*...*/;

   3. Create the output image. In this particular case both input and output have same dimensions, but this is not required. The formats must match, though.

          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);

   5. Create an dense warp map.

          VPIWarpMap map;
          memset(&map, 0, sizeof(map));
          map.grid.numHorizRegions  = 1;
          map.grid.numVertRegions   = 1;
          map.grid.regionWidth[0]   = w;
          map.grid.regionHeight[0]  = h;
          map.grid.horizInterval[0] = 1;
          map.grid.vertInterval[0]  = 1;
          vpiWarpMapAllocData(&map);

   6. Generate a custom mapping suitable to render an equirectangular panorama as a little planet. vpiWarpMapGenerateIdentity will fill the warp map with an identity mapping, i.e., all control points' position will match their position in the output image. Once this is done, the code loops through all control points and using the output coordinate, calculates the corresponding coordinate in the input image. This approach is also taken when performing lens distortion correction for a lens whose distortion model doesn't match the ones provided by VPI. See Lens Distortion Correction for more details.

          vpiWarpMapGenerateIdentity(&map);
          int i;
          for (i = 0; i < map.numVertPoints; ++i)
          {
              VPIKeypointF32 *row = (VPIKeypointF32 *)((uint8_t *)map.keypoints + map.pitchBytes * i);
              int j;
              for (j = 0; j < map.numHorizPoints; ++j)
              {
                  float x = row[j].x - w / 2.0f;
                  float y = row[j].y - h / 2.0f;
       
                  const float R = h / 8.0f; /* planet radius */
       
                  const float r = sqrtf(x * x + y * y);
       
                  float theta = M_PI + atan2f(y, x);
                  float phi   = M_PI / 2 - 2 * atan2f(r, 2 * R);
       
                  row[j].x = fmod((theta + M_PI) / (2 * M_PI) * (w - 1), w - 1);
                  row[j].y = (phi + M_PI / 2) / M_PI * (h - 1);
              }
          }

   7. Create the algorithm payload with the created mapping. The payload is created in the CUDA backend.

          VPIPayload warp;
          vpiCreateRemap(VPI_BACKEND_CUDA, &map, &warp);

2. Processing phase
   1. Submit the algorithm to the stream, along with all parameters. The algorithm will be executed by the backend where the payload was created, CUDA.

          vpiSubmitRemap(stream, VPI_BACKEND_CUDA, warp, input, output, VPI_INTERP_LINEAR, VPI_BORDER_ZERO, 0);

   2. Optionally, wait until the processing is done.

          vpiStreamSync(stream);

3. Cleanup phase
   1. Free resources held by the stream, the payload, the warp map and the input and output images.

          vpiStreamDestroy(stream);
          vpiPayloadDestroy(warp);
          vpiWarpMapFreeData(&map);
          vpiImageDestroy(input);
          vpiImageDestroy(output);

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

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 AGX Orin  -  Streams: 1 2 4 8