Census Transformation

Figure 6.4: Calculation of the Census transformation in the vicinity of a point: the neighborhood of a point is binarized with respect to the value of the point itself, and from this thresholding, a binary string is constructed.

The Census Transformation (ZW94) involves describing the portion of an image around a point using a bit string. For each pixel in the image, the surrounding area, of fixed size and shape, is systematically analyzed, and each pixel in this area is compared to the generating pixel. If the pixel has a greater gray intensity, it is assigned a bit 1, while if it has a lower intensity, it is assigned a bit 0:

$$\tau(\mathbf{x}) = \left\{ \begin{array}{ll} 1 & I(\mathbf{x}) < I(0) \\ 0 & \text{otherwise} \\ \end{array}\right.$$ (6.3)

By systematically scanning the area, it is possible to generate a binary string. An example of the Census transformation of an area $5 \times 5$ is shown in Figure 6.4: from this area, a binary string of 25-1 bits is generated (the central pixel is effectively negligible).

The Census transformation demonstrates its potential in the case of comparisons: two generic points, instead of being compared through a SAD of the surrounding area, are compared using the Hamming distance between their respective binary strings of the Census transform.

Through the construction of the binary string, leveraging the difference in gray tone, the Census transform is quite invariant to brightness.