About a fix in "compute_radius" (kitti_data_utils.py)

[Owen-Liuyuxuan]

There is an old problem of mis-implementation of the CornetNet. And "has been fixed" in CenterNet https://github.com/Duankaiwen/CenterNet/issues/47.

This repo, by default, makes ground truth heatmap following CenterNet who follows CornerNet.

• The intuition of CornerNet's setting is that "We determine the radius by the size of an object by ensuring that a pair of points within the radius would generate a bounding box with at least t IoU with the ground-truth annotation" (t=0.3 for CornerNet).
• The original implementation has been strange following this idea. Because empirically and theoretically, the only possible way to have the smallest IoU with the original bbox is (w - 2r) (h - 2r). The corresponding equation is (w - 2r)(h-2r) / wh = min_iou. which yields the coefficients of r2 in "compute_radius". No "min(r1, r2, r3)" is actually needed. The fix minimizes the code changes and does not try to further fix this one.
• The quadratic equation has two solution, one is that (w-2r) < 0 && (h-2r) < 0 the other is (w-2r) >0 && (h-2r) >0. The latter one is what we need. It always corresponds to the solution (b2 - sq2) / (2 * a2), while the first solution is r with larger magnitude -> (b2+sq2) / (2*a2). This has been fixed.

I have not thoroughly tested the performance because of hardware limitations. But a possible fix could be?:

def compute_radius(det_size, min_overlap=0.7):
    height, width = det_size

    a2 = 4
    b2 = 2 * (height + width)
    c2 = (1 - min_overlap) * width * height
    sq2 = np.sqrt(b2 ** 2 - 4 * a2 * c2)
    r2 = (b2 - sq2) / (2 * a2)

    return r2

I would also point out that this will not necessarily give better performance. Because the original idea from CornerNet does not necessarily transfer well to RTM3D here.

[maudzung]

Thanks @Owen-Liuyuxuan I'll check your suggestion.