Rectify an image by transforming it into the plane z=0 of a world coordinate system.

image_to_world_plane rectifies an image Image by transforming it into the plane z=0 (plane of measurements) in a world coordinate system. The resulting rectified image ImageWorld shows neither radial nor perspective distortions; it corresponds to an image acquired by a distortion-free camera that looks perpendicularly onto the plane of measurements. The world coordinate system is chosen by passing its 3D pose relative to the camera coordinate system in WorldPose. In CamParam you must pass the interior camera parameters (see write_cam_par for the sequence of the parameters and the underlying camera model).

In many cases CamParam and WorldPose are the result of calibrating the camera with the operator camera_calibration. See below for an example.

The pixel position of the upper left corner of the output image ImageWorld is determined by the origin of the world coordinate system. The size of the output image ImageWorld can be choosen by the parameters Width, Height, and Scale. Width and Height must be given in pixels.

With the parameter Scale you can specify the size of a pixel in the transformed image. There are two typical scenarios: First, you can scale the image such that pixel coordinates in the transformed image directly correspond to metric units, e.g., that one pixel corresponds to one micron. This is useful if you want to perform measurements in the transformed image, which will then directly result in metric results. The second scenario is to scale the image such that its content appears in a size similar to the original image. This is useful, e.g., if you want to perform shape-based matching in the transformed image.

Scale must be specified as the ratio desired pixel size/original unit. A pixel size of 1µm means that a pixel in the transformed image corresponds to the area 1µm x 1µm in the plane of measurements. The original unit is determined by the coordinates of the calibration object. If the original unit is meters (which is the case if you use the standard calibration plate), you can use the parameter values 'm', 'cm', 'mm', 'microns', or 'µm' to directly set the unit of pixel coordinates in the transformed image.

The parameter Interpolation specifies, whether bilinear interpolation ('bilinear') should be applied between the pixels in the input image or whether the gray value of the nearest neighboring pixel ('none') should be used.

If several images have to be rectified using the same parameters, gen_image_to_world_plane_map in combination with map_image is much more efficient than the operator image_to_world_plane because the mapping function needs to be computed only once.

*  perform camera calibration (with standard calibration plate)
camera_calibration(NX, NY, NZ, NRow, NCol, StartCamParam, NStartPose, 'all',
                   FinalCamParam, NFinalPose, Errors)
*  world coordinate system is defined by calibration plate in first image
FinalPose1 := NFinalPose[0:6]
*  compensate thickness of plate
set_origin_pose(FinalPose1, 0, 0, 0.0006, WorldPose)
*  goal: rectify image
*  first determine parameters such that the entire image content is visible
*    and that objects have a similar size before and after the rectification
*  -> transform image boundary into world plane, determine smallest
*     rectangle around it
get_image_pointer1(Image, Pointer, Type, Width, Height)
gen_rectangle1 (ImageRect, 0, 0, Height-1, Width-1)
gen_contour_region_xld (ImageRect, ImageBorder, 'border')
contour_to_world_plane_xld(ImageBorder, ImageBorderWCS, FinalCamParam, 
                           WorldPose, 1)
smallest_rectangle1_xld (ImageBorderWCS, MinY, MinX, MaxY, MaxX)
*  -> move the pose to the upper left corner of the surrounding rectangle
set_origin_pose(WorldPose, MinX, MinY, 0, PoseForEntireImage)
*  -> determine the scaling factor such that the center pixel has the same
*     size in the original and in the rectified image
*     method: transform corner points of the pixel into the world
*             coordinate system, compute their distances, and use their
*             mean as the scaling factor
image_points_to_world_plane(FinalCamParam, PoseForEntireImage, 
                            [Height/2, Height/2, Height/2+1], 
                            [Width/2, Width/2+1, Width/2], 
                            1, WorldPixelX, WorldPixelY)
distance_pp(WorldPixelY[0], WorldPixelX[0], WorldPixelY[1], WorldPixelX[1], 
            WorldLength1)
distance_pp(WorldPixelY[0], WorldPixelX[0], WorldPixelY[2], WorldPixelX[2], 
            WorldLength2)
ScaleForSimilarPixelSize := (WorldLength1+WorldLength2)/2
*  -> determine output image size such that entire input image fits into it
ExtentX := MaxX-MinX
ExtentY := MaxY-MinY
WidthRectifiedImage := ExtentX/ScaleForSimilarPixelSize
HeightRectifiedImage := ExtentY/ScaleForSimilarPixelSize
*  transform the image with the determined parameters
image_to_world_plane(Image, RectifiedImage, FinalCamParam, 
                     PoseForEntireImage, WidthRectifiedImage, 
                     HeightRectifiedImage, ScaleForSimilarPixelSize, 
                     'bilinear')

image_to_world_plane returns 2 (H_MSG_TRUE) if all parameter values are correct. If necessary, an exception handling is raised.

image_to_world_plane is reentrant and automatically parallelized (on tuple level).

create_pose, hom_mat3d_to_pose, camera_calibration, hand_eye_calibration, set_origin_pose

gen_image_to_world_plane_map, map_image

contour_to_world_plane_xld, image_points_to_world_plane

Camera calibration