Filtering with Gray-Code Kernels

In this paper we introduce a family of filier kernels the Gray-Code Kernels (GCK) and demonstrate their use in image analysis. Filtering an image with a sequence of Gray-Code Kernels is highly efficient and requires only 2 operations per pixel for each filter kernel, independent of the size or dimension of the kernel. We show that the family of kernels is large and includes the Walsh-Hadamard kernels amongst others. The GCK can also be used to approximate arbitrary kernels since a sequence of GCK can form a complete representation. The efficiency of computation using a sequence of GCK filters can be exploited for various real-time applications, such as, pattern detection, feature extraction, texture analysis, and more.