GenerlizedRCNN

• [:, None, None] : Shape [3] -> [3, 1, 1]

• In NumPy the * operator denotes the element-wise product (multiplying corresponding positions)

  • a = np.array([1,2,3])
  • b = np.array([2,2,2])
  • a * b
  • array([ 2., 4., 6.])

• For two matrices a and b, compare their dimensions from the last one backwards; broadcasting is possible only if every dimension satisfies one of the following conditions.

  • They are equal

  • One of them is 1

boxes1 # shape[N,4]
boxes2 # shape[M,4]

    lt = torch.max(boxes1[:, None, :2], boxes2[:, :2])  # left-top [N,M,2]
    rb = torch.min(boxes1[:, None, 2:], boxes2[:, 2:])  # right-bottom [N,M,2]

• Here a dimension is inserted as the second dimension of boxes1, making it [N,1,4], so when it meets boxes2 it is automatically broadcast to [N,M,4]: each row is copied M times (think of them as rows), so every column of boxes1's [:,M,4] is identical, e.g. [1,2,3]->[[1,2,3],[1,2,3]]
• Broadcasting again, when boxes2 meets boxes1 the last two dimensions are now identical, so boxes2 becomes [N,M,4], which amounts to copying the whole of boxes2 N times
• So boxes1's [:,M,4] is really just one box's [xmin,ymin,xmax,ymax] repeated M times; essentially there is only one set of coordinates
• boxes2's [0,:,:] is equivalent to the original boxes2, so this amounts to comparing (computing) the first box's coordinates (row) in boxes1 against all the coordinates in boxes2