BRIEF

The Census transform does not prescribe a specific shape for the area over which comparisons are performed to generate the binary string. This limitation is addressed in (CLSF10), one of the first works to formally pose the problem of computing a discriminative binary descriptor.

Most binary descriptors are inspired by Census, which is generalized by no longer comparing each pixel solely with the center of the area, but instead performing comparisons between arbitrary pairs of points selected according to specific criteria. The comparison function is defined as:

$$\tau(\mathbf{x}, \mathbf{y}) = \left\{ \begin{array}{ll} ... ...(\mathbf{y}) \\ 0 & \text{otherwise} \\ \end{array}\right.$$ (6.5)

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

To obtain this coordinate mask, a training process is performed on sample images to identify the combination that maximizes correct detections.

Numerous approaches have been proposed in the literature to address the problem of how to filter the image and how to select the points used to construct the descriptor.

Figure 6.6: Example of a 256-bit BRIEF descriptor.