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This article proposes a new multiscale filter accelerating Monte Carlo renderer. Each pixel in the image is characterized by the colors of the rays that reach its surface. The proposed filter uses a statistical distance to compare with each other the ray color distributions associated with different pixels, at each scale. Based on this distance, it decides whether two pixels can share their rays or not. This simple and easily reproducible algorithm provides a PSNR gain of 10 to 15 decibels, or equivalently accelerates the rendering process by using 10 to 30 times fewer samples without observable bias. The algorithm is consistent, does not assume a particular noise model, and is immediately extendable to synthetic movies. Being based on the ray color values only, it can be combined with all rendering effects. [ABSTRACT FROM AUTHOR]

In this paper we define the continuous Level Lines Shortening evolution of a two-dimensional image as the curve shortening operator acting simultaneously and independently on all the level lines of the initial data, and we show that it computes a viscosity solution for the mean curvature motion. This provides an exact analytical framework for its numerical implementation, which runs on line on any image at http://www.ipol.im. Analogous results hold for its affine variant version, the Level Lines Affine Shortening. [ABSTRACT FROM AUTHOR]

The Gaussian mixture is a patch prior that has enjoyed tremendous success in image processing. In this work, by using Gaussian factor modeling, its dedicated expectation maximization (EM) inference, and a statistical filter selection and algorithm stopping rule, we develop SURE (Stein's unbiased risk estimator) guided piecewise linear estimation (S-PLE), a patch-based prior learning algorithm capable of delivering state-of-the-art performance at image denoising. In light of this algorithm's features and its results, we also seek to address the number of components to be included when setting up a Gaussian mixture for image patch modeling. By juxtaposing both options, we show that a simple learned prior can perform as well as, if not better than, a much richer yet fixed prior. [ABSTRACT FROM AUTHOR]

The frames of a video sequence can be improved by a spatial deconvolution of any motion blur not exceeding two pixels per frame. Yet, this requires an accurate blur estimation and local deconvolution, which is problematic for multiple local motions. We introduce an optimal temporal blur deconvolution filter restoring blindly any nonuniform motion blur with an amplitude below one pixel per frame. The discrete filter has a very low complexity of about 20 operations per pixel. Experiments illustrate the method on simulated data, real movies and on sequences from the Middlebury database. [ABSTRACT FROM PUBLISHER]

In most digital cameras, and even in high-end digital single lens reflex cameras, the acquired images are sampled at rates below the Nyquist critical rate, causing aliasing effects. This work introduces an algorithm for the subpixel estimation of the point spread function (PSF) of a digital camera from aliased photographs. The numerical procedure simply uses two fronto-parallel photographs of any planar textured scene at different distances. The mathematical theory developed herein proves that the camera PSF can be derived from these two images, under reasonable conditions. Mathematical proofs supplemented by experimental evidence show the well-posedness of the problem and the convergence of the proposed algorithm to the camera in-focus PSF. An experimental comparison of the resulting PSF estimates shows that the proposed algorithm reaches the accuracy levels of the best nonblind state-of-the-art methods. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of obtaining a quality photograph of a painting by multi-image fusion methods. The problem is particularly challenging because of the uncontrolled illumination conditions and of the destructive reflection speckle present in most photographs of paintings. A fully automatic image processing chain is described that, starting from several bursts of a painting taken under different angles, permits one to obtain the best possible result by eliminating highlights and motion blur by robust statistics, reducing noise by fusion, and compensating optical distortion in the registration process. This image fusion method is applicable to photographs of a painting taken with a hand-held camera without any particular setup. It works under bad lighting conditions and eliminates motion blur, even when the painting is protected by a glass screen creating structured reflections of the room. The careful discussion of each step of the processing chain also permits one to review and discuss the efficiency of the image fusion tools recently proposed in the literature and insert several new ones in the chain. [ABSTRACT FROM AUTHOR]

Most medium to high quality digital cameras ( dslrs) acquire images at a spatial rate which is several times below the ideal Nyquist rate. For this reason only aliased versions of the cameral point-spread function ( psf) can be directly observed. Yet, it can be recovered, at a sub-pixel resolution, by a numerical method. Since the acquisition system is only locally stationary, this psf estimation must be local. This paper presents a theoretical study proving that the sub-pixel psf estimation problem is well-posed even with a single well chosen observation. Indeed, theoretical bounds show that a near-optimal accuracy can be achieved with a calibration pattern mimicking a Bernoulli(0.5) random noise. The physical realization of this psf estimation method is demonstrated in many comparative experiments. We use an algorithm to accurately estimate the pattern position and its illumination conditions. Once this accurate registration is obtained, the local psf can be directly computed by inverting a well conditioned linear system. The psf estimates reach stringent accuracy levels with a relative error of the order of 2% to 5%. To the best of our knowledge, such a regularization-free and model-free sub-pixel psf estimation scheme is the first of its kind. [ABSTRACT FROM AUTHOR]

Abstract: Image Processing On Line (IPOL) publishes image processing and image analysis algorithms, described in ac-curate literary form, coupled with code. It allows scientists to check directly the published algorithms on line by providing a web execution interface on any uploaded image. This installation acts the universality of image science. It permits to transcend the artificial segmentation of the research community in groups using this or that image software, or working on dedicated incompatible image formats. It promotes reproducible research, and the establishment of a state of the art verifiable by all, and on any image. This paper describes the technical challenges raised by the foundation of this new kind of journal and its scientific evaluation issues. It finally analyzes the first publications, to demonstrate its potential impact on the development of image science. [Copyright &y& Elsevier]

This paper presents a review, analysis, and comparison of numerical methods implementing the curvature motion and the affine curvature motion for two-dimensional (2D) images, shapes, and curves. These curvature scale spaces allow, in principle, one to compute an accurate multiscale curvature in digital images. The fastest and most invariant of them can be used in a complete image processing chain. This numerical chain simulates the accurate subpixel evolution of an image by mean curvature motion or by affine invariant curvature motion. To do so, it lets all the level lines of the image evolve by curvature shortening (of affine shortening), computes the image curvature directly on the smoothed level lines, and reconstructs the evolved image and its curvatures in an intrinsic, grid independent representation. The paper describes a careful implementation of this chain and analyzes its effects on many examples. The microscopic visualization of an image curvature map reveals after processing many image details. This image process improves graphic images and gets rid of compression and aliasing effects. It also gives an accurate tool to explore the validity of Attneave's and Julesz's theories on shape perception and texture discrimination. The "curvature microscope" runs online for any image at http://www.ipol.im/pub/algo/cmmm_image_curvaturemicroscope/. [ABSTRACT FROM AUTHOR]

Can images be decomposed into the sum of a geometric part and a textural part? In a theoretical breakthrough, [Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations. Providence, RI: American Mathematical Society, 2001] proposed variational models that force the geometric part into the space of functions with bounded variation, and the textural part into a space of oscillatory distributions. Meyer's models are simple minimization problems extending the famous total variation model. However, their numerical solution has proved challenging. It is the object of a literature rich in variants and numerical attempts. This paper starts with the linear model, which reduces to a low-pass/high-pass filter pair. A simple conversion of the linear filter pair into a nonlinear filter pair involving the total variation is introduced. This new-proposed nonlinear filter pair retains both the essential features of Meyer's models and the simplicity and rapidity of the linear model. It depends upon only one transparent parameter: the texture scale, measured in pixel mesh. Comparative experiments show a better and faster separation of cartoon from texture. One application is illustrated: edge detection. [ABSTRACT FROM AUTHOR]

We propose a linear-time line segment detector that gives accurate results, a controlled number of false detections, and requires no parameter tuning. This algorithm is tested and compared to state-of-the-art algorithms on a wide set of natural images. [ABSTRACT FROM AUTHOR]

Demosaicking is the process by which from a matrix of colored pixels measuring only one color component per pixel, red, green, or blue, one can infer a whole color information at each pixel. This inference requires a deep understanding of the interaction between colors, and the involvement of image local geometry. Although quite successful in making such inferences with very small relative error, state-of-the-art demosaicking methods fail when the local geometry cannot be inferred from the neighboring pixels. In such a case, which occurs when thin structures or fine periodic patterns were present in the original, state-of-the-art methods can create disturbing artifacts, known as zipper effect, blur, and color spots. The aim of this paper is to show that these artifacts can be avoided by involving the image self-similarity to infer missing colors. Detailed experiments show that a satisfactory solution can be found, even for the most critical cases. Extensive comparisons with state-of-the-art algorithms will be performed on two different classic image databases. [ABSTRACT FROM AUTHOR]

Shape recognition is the field of computer vision which addresses the problem of finding out whether a query shape lies or not in a shape database, up to a certain invariance. Most shape recognition methods simply sort shapes from the database along some (dis-)similarity measure to the query shape. Their main weakness is the decision stage, which should aim at giving a clear-cut answer to the question: “do these two shapes look alike?” In this article, the proposed solution consists in bounding the number of false correspondences of the query shape among the database shapes, ensuring that the obtained matches are not likely to occur “by chance”. As an application, one can decide with a parameterless method whether any two digital images share some shapes or not. [ABSTRACT FROM AUTHOR]

We establish in 2D, the P.D.E. associated with a classical image enhancement filter, the Kramer operator and compare it with another classical shock filter, the Osher-Rudin filter. We show that each one corresponds to a non-flat mathematical morphology operator conditioned by a the sign of an edge detector. In the case of the Kramer operator, the equation is conditioned by the Canny edge detector while in the case of the original Rudin-Osher filter, the equation is conditioned by the sign of the Laplacian. [ABSTRACT FROM AUTHOR]

Abstract. This paper contains a systematic analysis of a natural measure theoretic notion of connectedness for sets of finite perimeter in R[sup N], introduced by H. Federer in the more general framework of the theory of currents. We provide a new and simpler proof of the existence and uniqueness of the decomposition into the so-called M-connected components. Moreover, we study carefully the structure of the essential boundary of these components and give in particular a reconstruction formula of a set of finite perimeter from the family of the boundaries of its components. In the two dimensional case we show that this notion of connectedness is comparable with the topological one, modulo the choice of a suitable representative in the equivalence class. Our strong motivation for this study is a mathematical justification of all those operations in image processing that involve connectedness and boundaries. As an application, we use this weak notion of connectedness to provide a rigorous mathematical basis to a large class of denoising filters acting on connected components of level sets. We introduce a natural domain for these filters, the space WBV (OMEGA) of functions of weakly bounded variation in OMEGA, and show that these filters are also well behaved in the classical Sobolev and BV spaces. [ABSTRACT FROM AUTHOR]