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copied!<p>Think of (x1, y1, z1) and (x2, y2, z2) as two points spanning a cube that surrounds the point (x,y,z) for which you want to interpolate a value of h. The set of eight points (x1, y1, z1), (x2, y1, z1), (x1, y2, z1), (x1, y1, z2), (x2, y2, z1), (x2, y1, z2), (x1, y2, z2), (x2, y2, z2) forms the complete cube. So trilinear interpolation between (x1, y1, z1) and (x2, y2, z2) actually means interpolation between the 8 points in the 3D histogram space surrounding the point you are interested in! Now to your questions:</p> <p>(x1, y1), (x2, y2) (and (x1,y2) and (x2, y1) represent the centers of bins in the (x,y) plane. In your case these would be the orientation vectors. </p> <p>z1 and z2 represent two bin levels in the orientation direction, as you say. Combined with the four points in the image plane this gives you a total of 8 bins.</p> <p>The bandwidth b=[bx, by, bz] is basically the distance between the centers of neighbouring bins in the x, y and z direction. In your case, with 8 bins in the x-direction and 64 pixels in that direction, 16 bins in the y direction and 128 pixels in the y direction:</p> <pre><code>bx = 8 pixels by = 8 pixels </code></pre> <p>This leaves bz, for which I actually need more data, because I don't know the full range of your gradient (i.e. lowest to highest possible value) but if that range is <code>rg</code> then:</p> <pre><code>bz = rg/9 </code></pre> <p>In general, the bandwidth in any direction equals the full available range in that direction divided by the number of bins in that direction.</p> <p>For a good explanation of trilinear interpolation with pictures look at the link in <a href="https://stackoverflow.com/questions/6565412/hog-trilinear-interpolation-of-histogram-bins/6565446#6565446">whoplisp's answer</a>.</p>

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