Sometimes it is necessary to create a point cloud from a given depth and color (RGB) frame. This is especially the case when a scene is captured using depth cameras such as Kinect. The process of aligning the depth and the RGB frame is called “registration” and it is very easy to do (and the algorithm’s pseudo-code is surprisingly hard to find with a simple Google search! 😀 )

To perform registration, you would need 4 pieces of information:

1. The depth camera intrinsics:
   1. Focal lengths f_xd and f_yd (in pixel units)
   2. Optical centers (sometimes called image centers) C_xd and C_yd
2. The RGB camera intrinsics:
   1. Focal lengths f_xrgb and f_yrgb (in pixel units)
   2. Optical centers (sometimes called image centers) C_xrgb and C_yrgb
3. The extrinsics relating the depth camera to the RGB camera. This is a 4×4 matrix containing rotation and translation values.
4. (Obviously) the depth and the RGB frames. Note that they do not have to have the same resolution. Applying the intrinsics takes care of the resolution issue. Using camera’s such as Kinect, the depth values should usually be in meters (the unit of the depth values is very important as using incorrect units will result in a registration in which the colors and the depth values are off and are clearly misaligned).
   Also, note that some data sets apply a scale and a bias to the depth values in the depth frame. Make sure to account for this scaling and offsetting before proceeding. In order words, make sure there are no scales applied to the depth values of your depth frame.

Let depthData contain the depth frame and rgbData contain the RGB frame. The pseudo-code for registration in MATLAB is as follows:

function [aligned] = ...
                    depth_rgb_registration(depthData, rgbData,...
                    fx_d, fy_d, cx_d, cy_d,...
                    fx_rgb, fy_rgb, cx_rgb, cy_rgb,...
                    extrinsics)

    depthHeight = size(depthData, 1);
    depthWidth = size(depthData, 2);
    
    % Aligned will contain X, Y, Z, R, G, B values in its planes
    aligned = zeros(depthHeight, depthWidth, 6);

    for v = 1 : (depthHeight)
        for u = 1 : (depthWidth)
            % Apply depth intrinsics
            z = single(depthData(v,u)) / depthScale;
            x = single((u - cx_d) * z) / fx_d;
            y = single((v - cy_d) * z) / fy_d;
            
            % Apply the extrinsics
            transformed = (extrinsics * [x;y;z;1])';
            aligned(v,u,1) = transformed(1);
            aligned(v,u,2) = transformed(2);
            aligned(v,u,3) = transformed(3);
        end
    end

    for v = 1 : (depthHeight)
        for u = 1 : (depthWidth)
            % Apply RGB intrinsics
            x = (aligned(v,u,1) * fx_rgb / aligned(v,u,3)) + cx_rgb;
            y = (aligned(v,u,2) * fy_rgb / aligned(v,u,3)) + cy_rgb;
            
            % "x" and "y" are indices into the RGB frame, but they may contain
            % invalid values (which correspond to the parts of the scene not visible
            % to the RGB camera.
            % Do we have a valid index?
            if (x > rgbWidth || y > rgbHeight ||...
                x < 1 || y < 1 ||...
                isnan(x) || isnan(y))
                continue;
            end
            
            % Need some kind of interpolation. I just did it the lazy way
            x = round(x);
            y = round(y);

            aligned(v,u,4) = single(rgbData(y, x, 1);
            aligned(v,u,5) = single(rgbData(y, x, 2);
            aligned(v,u,6) = single(rgbData(y, x, 3);
        end
    end    
end

A few things to note here:

1. The indices x and y in the second group of for loops may be invalid which indicates that the obtained RGB pixel is not visible to the RGB camera.
2. Some kind of interpolation may be necessary when using x and y. I just did rounding.
3. This code can be readily used with savepcd function to save the point cloud into a PCL compatible format.

The registration formulas were obtained from the paper “On-line Incremental 3D Human Body Reconstruction for HMI or AR Applications” by Almeida et al (2011). The same formulas can be found here. Hope this helps 🙂