Partial Sum Minimization of Singular Values in Robust PCA: Algorithm and Applications

Robust Principal Component Analysis (RPCA) via rank minimization is a powerful tool for recovering underlying low-rank structure of clean data corrupted with sparse noise/outliers. In many low-level vision problems, not only it is known that the underlying structure of clean data is low-rank, but the exact rank of clean data is also known. Yet, when applying conventional rank minimization for those problems, the objective function is formulated in a way that does not fully utilize a priori target rank information about the problems. This observation motivates us to investigate whether there is a better alternative solution when using rank minimization. In this paper, instead of minimizing the nuclear norm, we propose to minimize the partial sum of singular values, which implicitly encourages the target rank constraint. Our experimental analyses show that, when the number of samples is deficient, our approach leads to a higher success rate than conventional rank minimization, while the solutions obtained by the two approaches are almost identical when the number of samples is more than sufficient. We apply our approach to various low-level vision problems, e.g. high dynamic range imaging, motion edge detection, photometric stereo, image alignment and recovery, and show that our results outperform those obtained by the conventional nuclear norm rank minimization method.Comment: Accepted in Transactions on Pattern Analysis and Machine Intelligence (TPAMI). To appea

Terrain analysis using radar shape-from-shading

This paper develops a maximum a posteriori (MAP) probability estimation framework for shape-from-shading (SFS) from synthetic aperture radar (SAR) images. The aim is to use this method to reconstruct surface topography from a single radar image of relatively complex terrain. Our MAP framework makes explicit how the recovery of local surface orientation depends on the whereabouts of terrain edge features and the available radar reflectance information. To apply the resulting process to real world radar data, we require probabilistic models for the appearance of terrain features and the relationship between the orientation of surface normals and the radar reflectance. We show that the SAR data can be modeled using a Rayleigh-Bessel distribution and use this distribution to develop a maximum likelihood algorithm for detecting and labeling terrain edge features. Moreover, we show how robust statistics can be used to estimate the characteristic parameters of this distribution. We also develop an empirical model for the SAR reflectance function. Using the reflectance model, we perform Lambertian correction so that a conventional SFS algorithm can be applied to the radar data. The initial surface normal direction is constrained to point in the direction of the nearest ridge or ravine feature. Each surface normal must fall within a conical envelope whose axis is in the direction of the radar illuminant. The extent of the envelope depends on the corrected radar reflectance and the variance of the radar signal statistics. We explore various ways of smoothing the field of surface normals using robust statistics. Finally, we show how to reconstruct the terrain surface from the smoothed field of surface normal vectors. The proposed algorithm is applied to various SAR data sets containing relatively complex terrain structure

The construction of colorimetry by committee

This paper explores the confrontation of physical and contextual factors involved in the emergence of the subject of color measurement, which stabilized in essentially its present form during the interwar period. The contentions surrounding the specialty had both a national and a disciplinary dimension. German dominance was curtailed by American and British contributions after World War I. Particularly in America, communities of physicists and psychologists had different commitments to divergent views of nature and human perception. They therefore had to negotiate a compromise between their desire for a quantitative system of description and the perceived complexity and human-centeredness of color judgement. These debates were played out not in the laboratory but rather in institutionalized encounters on standards committees. Groups such as this constitute a relatively unexplored historiographic and social site of investigation. The heterogeneity of such committees, and their products, highlight the problems of identifying and following such ephemeral historical 'actors'

A graph-spectral approach to shape-from-shading

In this paper, we explore how graph-spectral methods can be used to develop a new shape-from-shading algorithm. We characterize the field of surface normals using a weight matrix whose elements are computed from the sectional curvature between different image locations and penalize large changes in surface normal direction. Modeling the blocks of the weight matrix as distinct surface patches, we use a graph seriation method to find a surface integration path that maximizes the sum of curvature-dependent weights and that can be used for the purposes of height reconstruction. To smooth the reconstructed surface, we fit quadrics to the height data for each patch. The smoothed surface normal directions are updated ensuring compliance with Lambert's law. The processes of height recovery and surface normal adjustment are interleaved and iterated until a stable surface is obtained. We provide results on synthetic and real-world imagery

Image and Video Processing for Cultural Heritage

Charvillat V., Tonazzini A., Van Gool L., Nikolaidis N., ''Editorial: Image and video processing for cultural heritage'', EURASIP journal on image and video processing, vol. 2009, Article ID 163064, 3 pp., 2010.status: publishe

3D SEM Surface Reconstruction: An Optimized, Adaptive, and Intelligent Approach

Structural analysis of microscopic objects is a longstanding topic in several scientific disciplines, including biological, mechanical, and material sciences. The scanning electron microscope (SEM), as a promising imaging equipment has been around to determine the surface properties (e.g., compositions or geometries) of specimens by achieving increased magnification, contrast, and resolution greater than one nanometer. Whereas SEM micrographs still remain two-dimensional (2D), many research and educational questions truly require knowledge and information about their three-dimensional (3D) surface structures. Having 3D surfaces from SEM images would provide true anatomic shapes of micro samples which would allow for quantitative measurements and informative visualization of the systems being investigated. In this research project, we novel design and develop an optimized, adaptive, and intelligent multi-view approach named 3DSEM++ for 3D surface reconstruction of SEM images, making a 3D SEM dataset publicly and freely available to the research community. The work is expected to stimulate more interest and draw attention from the computer vision and multimedia communities to the fast-growing SEM application area