Complementary Color Wavelet: A Novel Tool for the Color Image/Video Analysis and Processing

In human vision, it has been well understood that the red, green, and blue (RGB) trichromatic system, whose colors can be well expressed by an RGB hue ring with complementary color relations, is the most accessible and extensible color representation. However, such color relations rarely play a role in color image/video processing tools such as wavelets. In this paper, the gap between wavelets and complementary color relations is filled by designing a novel color image/video processing tool called the complementary color wavelet transform. Our novel wavelets consist of a family of well-designed 2-D complex wavelets with $2\pi /3$ phase differences copied from the R, G, and B angle relations on the RGB hue ring. Analyses show that our new wavelets can not only utilize the complementary color relations but also inherit and improve upon the advantages of classical complex wavelets, such as their multi-resolution, directional selectivity, and shift-invariance properties. By the newly designed wavelets and by properly adding and/or subtracting the wavelet coefficients of a color image/video, some color-related image/video processing applications that are typically seen as infeasible or difficult to achieve by traditional methods, for instance, capturing and classifying local color changes, statistical modeling of the wavelet coefficients among the color channels, and multi-resolution directional color filtering, can be performed very easily. The cost for this is simply a transform redundancy increase (2.25 times that of classical complex wavelets). We provide three application examples of our method: color filtering, texture retrieval, and video quality assessment. The results show that our new wavelet tool greatly outperforms traditional methods.