Optimization and compression of geometry discontinuities for graph-based representation of piecewise smooth media

Earlier research has shown the efficacy of using geometry discontinuities, encoded using “breakpoints,” in improving the coding efficiency of piecewise smooth media, such as depth maps and motion flows. This work proposes a new structure for encoding these breakpoints that is more suited for piecewise affine media, such as affine motion flows. Here, we choose to employ belief propagation over a graphical model to discover a set of breakpoints that is rate-distortion optimal. Similar to earlier works, the discovered breakpoints are employed in a breakpoint adaptive (BPA) wavelet decomposition of the media under consideration; the resulting BPA wavelet coefficients and the proposed “affine” breakpoints are then compressed using the JPEG2000 format, in a way that provides spatial and quality scalability as well as accessibility. We show that the coding cost of affine breakpoints is moderate, and that, for coding motion flows, the coding efficiency of the proposed approach is comparable to H.264.