Phase-Shifting for Nonseparable 2-D Haar Wavelets

Abstract

In this paper, we present a novel and efficient solution to phase-shifting 2-D nonseparable Haar wavelet coefficients. While other methods either modify existing wavelets or introduce new ones to handle the lack of shift-invariance, we derive the explicit relationships between the coefficients of the shifted signal and those of the unshifted one. We then establish their computational complexity, and compare and demonstrate the superior performance of the proposed approach against classical interpolation tools in terms of accumulation of errors under successive shifting.

Comments on "Phase-Shifting for Nonseparable 2-D Haar Wavelets

“…In this correspondence, we show that the utilized transform of [1] is in-fact the conventional separable Haar transform (Section II). We also correct some minor mistakes made in the transform formulation of [1].…”

“…In this correspondence, we show that the utilized transform of [1] is in-fact the conventional separable Haar transform (Section II). We also correct some minor mistakes made in the transform formulation of [1]. This means that the in-band phase shifting results obtained by [1] can be obtained I with previously-known theoretical and practical results proposed in [2]- [4], as discussed in Section III.…”

“…N a recent paper [1], a wavelet-domain (in-band) solution for the 2D phase-shifting of an input image was derived. The method is formulated for the multilevel 2D "nonseparable" Haar discrete wavelet transform (DWT) and it is parametrical to the (known) image translation (shift) in the spatial domain.…”

“…The method is formulated for the multilevel 2D "nonseparable" Haar discrete wavelet transform (DWT) and it is parametrical to the (known) image translation (shift) in the spatial domain. Experiments are proposed that demonstrate that the proposed in-band solution provides significantly higher quality against conventional interpolation approaches when the input image undergoes a series of subpixel shifts [1].…”

Still Image Action Recognition by Predicting Spatial-Temporal Pixel Evolution

“…In contrast, action recognition in still images remains more challenging and less attended by researchers. The problem may be sometimes exacerbated by the quality of the image, in which case preprocessing steps can be helpful [29]- [31], [44], [72], [100], [115]- [117], [119]- [125], [128], [129], [131], also actions may be located in different parts of the image or present at different visual scales, in which case global registration methods may be helpful [6], [17]- [19], [21]- [24], [27], [28], [58]- [63], [65], [66], [118], [126], [127]. However, in general, the challenge mainly resides in the lack of temporal information, as further described below.…”