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 tristimulus values of object-color stimuli are commonly calculated by means of the weighted-ordinate method at constant wavelength intervals. By assuming that the tristimulus values are calculated accurately when the wavelength interval is Δλ = 5 nm, we have estimated the extreme errors that can occur when Δλ is increased to 10 and 20 nm. We have also estimated the extreme errors that can occur when other approximate numerical integrations are used, such as Simpson’s rule or Durand’s rule of integration. The extreme errors, are always very large and are caused by jagged spectral distributions of the object-color stimuli included in this study.

Extreme errors of numerical integrations in colorimetric calculations

Using a precision spectrometer with a photomultiplier attached to its telescope, the specular reflection of light from various rough surfaces was measured at angles of incidence in the region 80° to 89°. Seven interference filters were used to isolate spectral bands covering the visible spectrum. From the measured values of reflectance the chromaticity of the specularly reflected light was computed, assuming CIE source “A” for the incident light. It was found that at all angles the resulting colors lay in a narrow region near the Planckian locus, being more reddish than the incident light. The maximum redness was found at an angle where the specular reflectance had already become small. It is shown to be likely that if the specularly reflected light could be isolated the surface would form an accurate means of reducing color temperature.

Colors Produced by Reflection at Grazing Incidence from Rough Surfaces

A classification of projective transformations of the plane with respect to their fixed elements is introduced into the whole universe of projective transformations of the CIE-chromaticity diagram. On the basis of the given classification and by using some theorems of projective geometry a graphical method is developed for constructing chromaticity coordinates x′, y′ which correspond to given chromaticity coordinates x, y by a given transformation matrix. The principle of the graphical method holds for all types of projective transformations. In connection with some examples which demonstrate the theory, the intrinsic significance of the fixed points of a projective transformation is discussed with respect to colorimetric problems.

On Projective Transformations of the CIE-Chromaticity Diagram

Theoretical chromaticity-mismatch limits of metamers due to a change from CIE Illuminant D 65 to C

Ordinary fluorescent lamps have mercury-emission lines at approximately 405, 436, 546, and 578 nm, in addition to the continuous spectral power distributions that are emitted by their phosphors. The color of the light from such a fluorescent lamp is affected in part by the radiant powers of the four emission lines. When the values of the radiant powers are allowed to change within a prescribed range, corresponding color changes can be observed. The limiting boundary of these color changes can be estimated by using a Monte Carlo technique of calculation. It can be determined precisely by a geometrical method and by means of nonlinear programming. The merits of the different methods are discussed and numerical examples are given.

Gunter Wyszecki

Papers

Extreme errors of numerical integrations in colorimetric calculations

Colors Produced by Reflection at Grazing Incidence from Rough Surfaces

On Projective Transformations of the CIE-Chromaticity Diagram

Theoretical chromaticity-mismatch limits of metamers due to a change from CIE Illuminant D 65 to C

Colorimetric significance of mercury-emission lines in fluorescent lamps*