BRIEF

The Census transform does not impose a specific shape on the region in which comparisons are performed 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 every pixel only with the center of the region, they compare suitably selected pairs of pixels. 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 in the patch around the point being described, and $\tilde{I}(\cdot)$ is the intensity of the pixel in a filtered (typically low-pass) version of the original image.

The pixel pairs (the “mask”) are selected by training on sample images, with the aim of maximizing the descriptor's discriminative power.

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

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