BRIEF

The Census transform does not impose a specific shape on the area used to generate the binary string. This limitation is addressed in (CLSF10), one of the first works to formalize the problem of constructing discriminative binary descriptors.

Most binary descriptors are inspired by Census and generalize it: instead of comparing each pixel only with the center of the area, pairs of pixels selected appropriately are compared. The comparison function is defined as:

$$\tau(\mathbf{x}, \mathbf{y}) = \left\{ \begin{array}{ll} ... ...(\mathbf{y}) \\ 0 & \text{otherwise} \\ \end{array}\right.$$ (7.5)

where $\mathbf {x}$ and $\mathbf{y}$ are the coordinates of two pixels within the patch surrounding the point to be described, and $\tilde{I}(\cdot)$ represents the pixel intensity in a filtered version (typically low-pass filtered) of the original image.

The selection of pixel pairs (the “mask”) is performed through a training process on sample images, with the objective of maximizing the descriptor's discriminative power.

Numerous approaches in the literature address the problem of selecting the points and the type of filtering to apply to the image.

Figure 7.6: Example of a 256-bit BRIEF descriptor.