Cutset sampling and reconstruction of images

Abstract

This paper presents a new approach to sampling images in which samples are taken on a cutset with respect to a graphical image model. The cutsets considered are Manhattan grids, for example every N th row and column of the image. Cutset sampling is motivated mainly by applications with physical constraints, e.g. a ship taking water samples along its path, but also by the fact that dense sampling along lines might permit better reconstruction of edges than conventional sampling at the same density. The main challenge in cutset sampling lies in the reconstruction of the unsampled blocks. As a first investigation, this paper uses segmentation followed by linear estimation. First, the ACA method [1] is modified to segment the cutset, followed by a binary Markov random field (MRF) inspired segmentation of the unsampled blocks. Finally, block interiors are estimated from the pixels on their boundaries, as well as their segmentation, with methods that include a generalization of bilinear interpolation and linear MMSE methods based on Gaussian MRF models or separable autocorrelation models. The resulting reconstructions are comparable to those obtained with conventional sampling at higher sampling densities, but not generally as good as conventional sampling at lower rates.

Image interpolation from Manhattan cutset samples via orthogonal gradient method

“…At high sampling densities, visual differences between the TV and OG methods were negligible, which is reflected in their similar PSNRs. Finally, one strength of this algorithm is that it can be applied to any Table 1: PSNRs in dB for "MRF model with cutset segmentation" method [7], "piecewise planar" method [8], constrained total variation (TV) minimization for inpainting [9], and the proposed orthogonal gradient (OG) method. Any parameters were chosen according to those given in the respective literature.…”

“…Finally, several algorithms have been proposed for interpolating grayscale images from their Manhattan samples. The algorithms in [7] offered several variations on a three-step algorithm for Manhattan interpolation. First, the Manhattan image samples were segmented into binary regions.…”

Performance-energy tradeoffs in cutset wireless sensor networks

“…The authors proposed using a Manhattan grid sensor layout where sensors are placed along evenly-spaced rows and columns, as shown in Figure 1(e), and showed that in the context of specific decentralized estimation and communication strategies, this permitted a tradeoff in which communication energy could be substantially reduced with only modest decreases in performance. Previously, the Manhattan grid topology was also used in image processing applications, such as 2D bilevel lossy and lossless image coding [9][10][11] and grayscale image reconstruction [12,13]. A sampling theorem for Manhattan grids has also been derived [14].…”

Energy efficient source localization on a Manhattan grid wireless sensor network

“…As we will argue, this Manhattan grid sensor layout has the advantage that communication requires less power than a randomly distributed network or uniform lattice, thereby increasing battery life. Previously, Manhattan grid sampling has been used in bilevel image coding and reconstruction [6,7,8], as well as grayscale image reconstruction [9,10]. A sampling theorem for Manhattan grids has also been derived [11].…”