Contrast Sensitivity of the Wavelet, Dual Tree Complex Wavelet, Curvelet, and Steerable Pyramid Transforms

Accurate estimation of the contrast sensitivity of the human visual system is crucial for perceptually based image processing in applications such as compression, fusion and denoising. Conventional contrast sensitivity functions (CSFs) have been obtained using fixed-sized Gabor functions. However, the basis functions of multiresolution decompositions such as wavelets often resemble Gabor functions but are of variable size and shape. Therefore to use the conventional CSFs in such cases is not appropriate. We have therefore conducted a set of psychophysical tests in order to obtain the CSF for a range of multiresolution transforms: the discrete wavelet transform, the steerable pyramid, the dual-tree complex wavelet transform, and the curvelet transform. These measures were obtained using contrast variation of each transforms' basis functions in a 2AFC experiment combined with an adapted version of the QUEST psychometric function method. The results enable future image processing applications that exploit these transforms such as signal fusion, superresolution processing, denoising and motion estimation, to be perceptually optimized in a principled fashion. The results are compared with an existing vision model (HDR-VDP2) and are used to show quantitative improvements within a denoising application compared with using conventional CSF values.