Generalized intersection over union between axes-aligned objects

Under objects we understand cuboids in any dimension: segments, bounding boxes, cuboids, etc.

The version for the cuboids aligned with Cartesian axes needs the detection vectors to have at least 6 variables.

In difference to the Mahalanobis metric where the variables are treated uniformly, we need to identify which variables represent position of the cuboids and which variables represent sizes of the cuboids. In order to define this, we use the keyword argument ind_pos_size of the method .set_association_metric()

...
tracker.set_association_metric('giou-axes-aligned', ind_pos_size=(0,1,2,3,4,5))

The keyword argument ind_pos_size defines indices of three position variables and three size variables. If the programmer omits the keyword argument ind_pos_size, then sequence falls back to ind_pos_size=(0,1,2,-3,-2,-1) in 3D case. This choice encodes first variables in the measurement vector being positions and last three variables corresponding to sizes

\[\mathbf{z} = p_x, p_y, p_z, \text{any number of variables}, s_x, s_y, s_z.\]

Such a choice fits the data layout of several datasets including the popular nuScenes dataset. See our suggestion for tracking nuScenes annotations. The performance of the axes-aligned GIoU is suboptimal comparing to GIoU for oriented cuboids.

In general case, the default value of the fancy indices ind_pos_size are constructed based on the dimensionality of the first variable. For example, if the tracker is constructed tracker = NdKkfTracker([3, 1, 1], [2, 1, 2]), then the dimensionality of the first variable is 2. In this case, the default fancy indices will be ind_pos_size=(0, 1, -2, -1). Note, that this convention is similar to the 3D case, which is suitable for nuScenes dataset.