A general non-parametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure: the mean shift. For discrete data, we prove the convergence of a recursive mean shift procedure to the nearest stationary point of the underlying density function and, thus, its utility in detecting the modes of the density. The relation of the mean shift procedure to the Nadaraya-Watson estimator from kernel regression and the robust M-estimators; of location is also established. Algorithms for two low-level vision tasks discontinuity-preserving smoothing and image segmentation - are described as applications. In these algorithms, the only user-set parameter is the resolution of the analysis, and either gray-level or color images are accepted as input. Extensive experimental results illustrate their excellent performance.

Mean shift: a robust approach toward feature space analysis

Bilateral filtering smooths images while preserving edges, by means of a nonlinear combination of nearby image values. The method is noniterative, local, and simple. It combines gray levels or colors based on both their geometric closeness and their photometric similarity, and prefers near values to distant values in both domain and range. In contrast with filters that operate on the three bands of a color image separately, a bilateral filter can enforce the perceptual metric underlying the CIE-Lab color space, and smooth colors and preserve edges in a way that is tuned to human perception. Also, in contrast with standard filtering, bilateral filtering produces no phantom colors along edges in color images, and reduces phantom colors where they appear in the original image.

/pdf/bilateral-filtering-for-gray-and-color-images-jnho720ytd.pdf

Bilateral filtering for gray and color images

We investigate the properties of a metric between two distributions, the Earth Mover's Distance (EMD), for content-based image retrieval. The EMD is based on the minimal cost that must be paid to transform one distribution into the other, in a precise sense, and was first proposed for certain vision problems by Peleg, Werman, and Rom. For image retrieval, we combine this idea with a representation scheme for distributions that is based on vector quantization. This combination leads to an image comparison framework that often accounts for perceptual similarity better than other previously proposed methods. The EMD is based on a solution to the transportation problem from linear optimization, for which efficient algorithms are available, and also allows naturally for partial matching. It is more robust than histogram matching techniques, in that it can operate on variable-length representations of the distributions that avoid quantization and other binning problems typical of histograms. When used to compare distributions with the same overall mass, the EMD is a true metric. In this paper we focus on applications to color and texture, and we compare the retrieval performance of the EMD with that of other distances.

/pdf/the-earth-mover-s-distance-as-a-metric-for-image-retrieval-h8u7zfx61r.pdf

The Earth Mover's Distance as a Metric for Image Retrieval

The nearestor near-neighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search/index structures for performing similarity search over high-dimensional data, e.g., image databases, document collections, time-series databases, and genome databases. Unfortunately, all known techniques for solving this problem fall prey to the \curse of dimensionality." That is, the data structures scale poorly with data dimensionality; in fact, if the number of dimensions exceeds 10 to 20, searching in k-d trees and related structures involves the inspection of a large fraction of the database, thereby doing no better than brute-force linear search. It has been suggested that since the selection of features and the choice of a distance metric in typical applications is rather heuristic, determining an approximate nearest neighbor should su ce for most practical purposes. In this paper, we examine a novel scheme for approximate similarity search based on hashing. The basic idea is to hash the points Supported by NAVY N00014-96-1-1221 grant and NSF Grant IIS-9811904. Supported by Stanford Graduate Fellowship and NSF NYI Award CCR-9357849. Supported by ARO MURI Grant DAAH04-96-1-0007, NSF Grant IIS-9811904, and NSF Young Investigator Award CCR9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and/or special permission from the Endowment. Proceedings of the 25th VLDB Conference, Edinburgh, Scotland, 1999. from the database so as to ensure that the probability of collision is much higher for objects that are close to each other than for those that are far apart. We provide experimental evidence that our method gives signi cant improvement in running time over other methods for searching in highdimensional spaces based on hierarchical tree decomposition. Experimental results also indicate that our scheme scales well even for a relatively large number of dimensions (more than 50).

/pdf/similarity-search-in-high-dimensions-via-hashing-27z92j627a.pdf

Similarity Search in High Dimensions via Hashing

We use a simple statistical analysis to impose one image's color characteristics on another. We can achieve color correction by choosing an appropriate source image and apply its characteristic to another image.

https://www.cs.tau.ac.il/~turkel/imagepapers/ColorTransfer.pdf

Color transfer between images

The colors of the regular rhombohedral selection reported by the OSA Committee on Uniform Color Scales are shown in the CIE 1964 U*V*W* color space.

Uniform color scales: CIE 1964 U * V * W * conversion of OSA Committee selection

A linear-programming technique is used to design examples of spectral power distributions of illuminants that, when irradiating a limited number of given objects, render these objects in prescribed colors. The numerical examples that demonstrate the technique are relevant to problems of designing light sources having a perfect color rendering index, or a high flattery index.

Designing illuminants that render given objects in prescribed colors

Using a large number of specially selected imaginary object colors which are metameric with respect to one set of color-mixture functions, the spatial distribution of these colors with respect to the other set of color-mixture functions provides an illustrative means of measuring the total difference of the two sets of color-mixture functions. The spatial distribution follows a normal trivariate distribution law which allows the computation of an ellipsoid that is expected to contain 95% of all theoretically and practically possible object colors of the same class used to calculate that ellipsoid. A numerical example involving the color-mixture functions of the 1931 CIE standard observer and the color-mixture functions derived from the Stiles 10° pilot data demonstrates the theory.

A Measure for the Total Difference of Two Sets of Color-Mixture Functions

Nonlinear optimization techniques can be used to calculate the theoretical limits of color changes that can occur when the spectral power distribution of the illuminant is permitted to deviate from that of the standard illuminant by specified amounts. The study has a direct bearing on the problem of specifying tolerances for illuminants relative to a given standard illuminant used in colorimetry.

Color changes caused by specified changes in the illuminant

A color-difference-matching experiment was carried out using a computer-interfaced video-display system. Two reference color stimuli (i) and (j), and one test stimulus (i,j) surrounded by a large achromatic or chromatic stimulus were presented on the video screen. An observer was asked to adjust the test stimulus until he perceived it to have a color precisely “half way” between the colors of the given reference stimuli. A satisfactory half-way color was the one that produced perceptually equal color differences between (i) and (i,j) and (j) and (i,j) and simultaneously made these color differences as small as possible. Although the given color difference between the test stimuli (i) and (j) was generally quite large (100–200 just-perceptible color-difference steps) with the achromatic surround condition, the color-difference matching required to obtain the desired half-way color did not present any serious difficulties to the observer. The uncertainty of the chromaticity point of the half-way color was established by an ellipse of small to moderate size surrounding the mean chromaticity setting. The orientation and shape of the uncertainty ellipse was comparable with the orientation and shape of uncertainty ellipses obtained by other investigators studying color-difference matching involving much smaller color differences. The unexpected and noteworthy result of the present study lies in the location of the chromaticity point of (i,j) relative to those of (i) and (j) as a function of surround color. The location of (i,j) depends on the saturation of the surround stimulus but not its hue. Some speculative explanations of the observed results are offered.

Gunter Wyszecki

Papers

Uniform color scales: CIE 1964 U * V * W * conversion of OSA Committee selection

Designing illuminants that render given objects in prescribed colors

A Measure for the Total Difference of Two Sets of Color-Mixture Functions

Color changes caused by specified changes in the illuminant

Matching large color differences with achromatic and chromatic surrounds