A Unified Approach to the Change of Resolution: Space and Gray-Level

By Shmuel Peleg, Michael Werman, H. Rom. 1989

It is shown that by defining a suitable measure for the comparison of images, changes in resolution can be treated with the same tool as changes in color resolution. A gray-tone image, for example, can be compared to a half-tone image having only two colors (black and white), but of higher spatial resolution. A graph-theoretical definition of the basic measure used is introduced. This is followed by application to spatial resampling and gray-level requantization. This results in a hybrid treatment of resolution, and the possibility of trading spatial for gray-level resolution and vice versa. >

Subfields: Signal Processing

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Citations in the corpus

Measuring Data (2022, methodology): “Earth Mover’s distance has been used in applications ranging from information retrieval and pattern recognition to calculate the distances between data from different modalities with diverse types of features (e.g. (Peleg et al., 1989; Orlova et al., 2016)).”
Wasserstein Adversarial Examples via Projected Sinkhorn Iterations (2019, background): “Unlike `p balls, this includes standard image transformations (rotations, translations, distortions), making the Wasserstein distance a more natural metric for images in both monochromatic and RGB image problems (Peleg et al., 1989; Rubner et al., 2000).”
Bioimage informatics: a new area of engineering biology (2008, background): “Recent work (Ljosa et al., 2006) shows that a multiresolution LB-index approach can be used to index the EMD scores.”
The Earth Mover's Distance as a Metric for Image Retrieval (2000, unknown): “This observation led to distance measures based on bipartite graph matching (Peleg et al., 1989; Zikan, 1990), defined as the minimum cost of matching elements between the two histograms.”
Fast and robust Earth Mover's Distances (2009, methodology): “Early work using cross-bin distances for histogram comparison can be found in [33, 39, 38, 28].”
Locally Orderless Tracking (2012, methodology): “[15] as an image similarity metric and popularized by Rubner et al.”
A Linear Time Histogram Metric for Improved SIFT Matching (2008, methodology): “2 Previous Work Early work using cross-bin distances for histogram comparison can be found in [24, 25, 22, 26].”
An Efficient Earth Mover's Distance Algorithm for Robust Histogram Comparison (2007, methodology): “Note that, although there is a fast exact EMD algorithm for 1D histograms [38], such a solution does not scale to higher dimensions—while most of the histogrambased local descriptors have two or three dimensions.”