Distance transform

About: Distance transform is a research topic. Over the lifetime, 2886 publications have been published within this topic receiving 59481 citations.

Two-dimensional images in frequency-time representation: direction images and resolution map

Abstract: We discuss the concept of the direction image multiresolution, which is derived as a property of the 2-D discrete Fourier transform, when it splits by 1-D transforms. The N×N image, where N is a power of 2, is considered as a unique set of splitting-signals in paired representation, which is the unitary 2-D frequency and 1-D time representation. The number of splitting-signals is 3N−2, and they have different durations, carry the spectral information of the image in disjoint subsets of frequency points, and can be calculated from the projection data along one of 3N/2 angles. The paired representation leads to the image composition by a set of 3N−2 direction images, which defines the directed multiresolution and contains periodic components of the image. We also introduce the concept of the resolution map, as a result of uniting all direction images into log2 N series. In the resolution map, all different periodic components (or structures) of the image are packed into a N×N matrix, which can be used for image processing in enhancement, filtration, and compression

Planar Structure Matching under Projective Uncertainty for Geolocation

Abstract: Image based geolocation aims to answer the question: where was this ground photograph taken? We present an approach to geolocalating a single image based on matching human delineated line segments in the ground image to automatically detected line segments in ortho images. Our approach is based on distance transform matching. By observing that the uncertainty of line segments is non-linearly amplified by projective transformations, we develop an uncertainty based representation and incorporate it into a geometric matching framework. We show that our approach is able to rule out a considerable portion of false candidate regions even in a database composed of geographic areas with similar visual appearances.

Distance transform: a tool for the study of animal colour patterns

Abstract: Summary The information in animal colour patterns plays a key role in many ecological interactions; quantification would help us to study them, but this is problematic. Comparing patterns using human judgement is subjective and inconsistent. Traditional shape analysis is unsuitable as patterns do not usually contain conserved landmarks. Alternative statistical approaches also have weaknesses, particularly as they are generally based on summary measures that discard most or all of the spatial information in a pattern. We present a method for quantifying the similarity of a pair of patterns based on the distance transform of a binary image. The method compares the whole pattern, pixel by pixel, while being robust to small spatial variations among images. We demonstrate the utility of the distance transform method using three ecological examples. We generate a measure of mimetic accuracy between hoverflies (Diptera: Syrphidae) and wasps (Hymenoptera) based on abdominal pattern and show that this correlates strongly with the perception of a model predator (humans). We calculate similarity values within a group of mimetic butterflies and compare this with proposed pairings of Mullerian comimics. Finally, we characterise variation in clypeal badges of a paper wasp (Polistes dominula) and compare this with previous measures of variation. While our results generally support the findings of existing studies that have used simpler ad hoc methods for measuring differences between patterns, our method is able to detect more subtle variation and hence reveal previously overlooked trends.

Fast Exact Euclidean Distance (FEED): A New Class of Adaptable Distance Transforms

Abstract: A new unique class of foldable distance transforms of digital images (DT) is introduced, baptized: Fast Exact Euclidean Distance (FEED) transforms. FEED class algorithms calculate the DT starting directly from the definition or rather its inverse. The principle of FEED class algorithms is introduced, followed by strategies for their efficient implementation. It is shown that FEED class algorithms unite properties of ordered propagation, raster scanning, and independent scanning DT. Moreover, FEED class algorithms shown to have a unique property: they can be tailored to the images under investigation. Benchmarks are conducted on both the Fabbri et al. data set and on a newly developed data set. Three baseline, three approximate, and three state-of-the-art DT algorithms were included, in addition to two implementations of FEED class algorithms. It illustrates that FEED class algorithms i) provide truly exact Euclidean DT; ii) do no suffer from disconnected Voronoi tiles, which is a unique feature for non-parallel but fast DT; iii) outperform any other approximate and exact Euclidean DT with its time complexity O(N), even after their optimization; and iv) are unequaled in that they can be adapted to the characteristics of the image class at hand. The source code of all algorithms included as well as the data sets used for both benchmarks are provided as supplementary material to this article.

The Schrödinger distance transform (SDT) for point-sets and curves

Abstract: Despite the ubiquitous use of distance transforms in the shape analysis literature and the popularity of fast marching and fast sweeping methods — essentially Hamilton-Jacobi solvers, there is very little recent work leveraging the Hamilton-Jacobi to Schrodinger connection for representational and computational purposes. In this work, we exploit the linearity of the Schrodinger equation to (i) design fast discrete convolution methods using the FFT to compute the distance transform, (ii) derive the histogram of oriented gradients (HOG) via the squared magnitude of the Fourier transform of the wave function, (iii) extend the Schrodinger formalism to cover the case of curves parametrized as line segments as opposed to point-sets, (iv) demonstrate that the Schrodinger formalism permits the addition of wave functions — an operation that is not allowed for distance transforms, and finally (v) construct a fundamentally new Schrodinger equation and show that it can represent both the distance transform and its gradient density — not possible in earlier efforts.