waashk/dblp huggingface dataset:
regularization, scale-space, and edge detection filters. computational vision often needs to deal with derivatives of digital images. such derivatives are not intrinsic properties of digital data; a paradigm is required to make them well-defined. normally, a linear filtering is applied. this can be formulated in terms of scale-space, functional minimization, or edge detection filters. the main emphasis of this paper is to connect these theories in order to gain insight in their similarities and differences. we do not want, in this paper, to take part in any discussion of how edge detection must be performed, but will only link some of the current theories. we take regularization (or functional minimization) as a starting point, and show that it boils down to gaussian scale-space if we require scale invariance and a semi-group constraint to be satisfied. this regularization implies the minimization of a functional containing terms up to infinite order of differentiation. if the functional is truncated at second order, the canny-deriche filter arises. it is also shown that higher dimensional regularization boils down to a rotated version of the one dimensional case, when cartesian invariance is imposed and the image is vanishing at the borders. this means that the results from 1d regularization can be easily generalized to higher dimensions. finally we show how an efficient implementation of regularization of order n can be made by recursive filtering using 2n multiplications and additions per output element without introducing any approximation.
the least-squares error for structure from infinitesimal motion. we analyze the least-squares error for structure from motion with a single infinitesimal motion ("structure from optical flow"). we present asymptotic approximations to the noiseless error over two, complementary regions of motion estimates: roughly forward and non-forward translations. our approximations are powerful tools for understanding the error. experiments show that they capture its detailed behavior over the entire range of motions. we illustrate the use of our approximations by deriving new properties of the least-squares error. we generalize the earlier results of jepson/heeger/maybank on the bas-relief ambiguity and of oliensis on the reflected minimum. we explain the error's complexity and its multiple local minima for roughly forward translation estimates (epipoles within the field of view) and identify the factors that make this complexity likely. for planar scenes, we clarify the effects of the two-fold ambiguity, show the existence of a new, double bas-relief ambiguity, and analyze the error's local minima. for nonplanar scenes, we derive simplified error approximations for reasonable assumptions on the image and scene. for example, we show that the error tends to have a simpler form when many points are tracked. we show experimentally that our analysis for zero image noise gives a good model of the error for large noise. we show theoretically and experimentally that the error for projective structure from motion is simpler but flatter than the error for calibrated images.
iterative extensions of the sturm/triggs algorithm: convergence and nonconvergence. we give the first complete theoretical convergence analysis for the iterative extensions of the sturm/triggs algorithm. we show that the simplest extension, siesta, converges to nonsense results. another proposed extension has similar problems, and experiments with “balanced” iterations show that they can fail to converge or become unstable. we present ciesta, an algorithm which avoids these problems. it is identical to siesta except for one simple extra computation. under weak assumptions, we prove that ciesta iteratively decreases an error and approaches fixed points. with one more assumption, we prove it converges uniquely. our results imply that ciesta gives a reliable way of initializing other algorithms such as bundle adjustment. a descent method such as gauss–newton can be used to minimize the ciesta error, combining quadratic convergence with the advantage of minimizing in the projective depths. experiments show that ciesta performs better than other iterations.
a fast approximation of the bilateral filter using a signal processing approach. the bilateral filter is a nonlinear filter that smoothes a signal while preserving strong edges. it has demonstrated great effectiveness for a variety of problems in computer vision and computer graphics, and fast versions have been proposed. unfortunately, little is known about the accuracy of such accelerations. in this paper, we propose a new signal-processing analysis of the bilateral filter which complements the recent studies that analyzed it as a pde or as a robust statistical estimator. the key to our analysis is to express the filter in a higher-dimensional space where the signal intensity is added to the original domain dimensions. importantly, this signal-processing perspective allows us to develop a novel bilateral filtering acceleration using downsampling in space and intensity. this affords a principled expression of accuracy in terms of bandwidth and sampling. the bilateral filter can be expressed as linear convolutions in this augmented space followed by two simple nonlinearities. this allows us to derive criteria for downsampling the key operations and achieving important acceleration of the bilateral filter. we show that, for the same running time, our method is more accurate than previous acceleration techniques. typically, we are able to process a 2 megapixel image using our acceleration technique in less than a second, and have the result be visually similar to the exact computation that takes several tens of minutes. the acceleration is most effective with large spatial kernels. furthermore, this approach extends naturally to color images and cross bilateral filtering.
matching hierarchical structures using association graphs. it is well-known that the problem of matching two relational structures can be posed as an equivalent problem of finding a maximal clique in a (derived) ¿association graph.¿ however, it is not clear how to apply this approach to computer vision problems where the graphs are hierarchically organized, i.e., are trees, since maximal cliques are not constrained to preserve the partial order. here, we provide a solution to the problem of matching two trees by constructing the association graph using the graph-theoretic concept of connectivity. we prove that, in the new formulation, there is a one-to-one correspondence between maximal cliques and maximal subtree isomorphisms. this allows us to cast the tree matching problem as an indefinite quadratic program using the motzkin-straus theorem, and we use ¿replicator¿ dynamical systems developed in theoretical biology to solve it. such continuous solutions to discrete problems are attractive because they can motivate analog and biological implementations. the framework is also extended to the matching of attributed trees by using weighted association graphs. we illustrate the power of the approach by matching articulated and deformed shapes described by shock trees.
perceptual smoothing and segmentation of colour textures. an approach for perceptual segmentation of colour image textures is described. a multiscale representation of the texture image, generated by a multiband smoothing algorithm based on human psychophysical measurements of colour appearance is used as the input. initial segmentation is achieved by applying a clustering algorithm to the image at the coarsest level of smoothing. using these isolated \em core clusters 3d colour histograms are formed and used for probabilistic assignment of all other pixels to the core clusters to form larger clusters and categorise the rest of the image. the process of setting up colour histograms and probabilistic reassignment of the pixels is then propagated through finer levels of smoothing until a full segmentation is achieved at the highest level of resolution.
a paraperspective factorization method for shape and motion recovery. the factorization method, first developed by tomasi and kanade, recovers both the shape of an object and its motion from a sequence of images, using many images and tracking many feature points to obtain highly redundant feature position information. the method robustly processes the feature trajectory information using singular value decomposition (svd), taking advantage of the linear algebraic properties of orthographic projection. however, an orthographic formulation limits the range of motions the method can accommodate. paraperspective projection, first introduced by ohta, is a projection model that closely approximates perspective projection by modeling several effects not modeled under orthographic projection, while retaining linear algebraic properties. our paraperspective factorization method can be applied to a much wider range of motion scenarios, including image sequences containing motion toward the camera and aerial image sequences of terrain taken from a low-altitude airplane.
bidirectional texture contrast function. three dimensional surface corrugations on globally smooth surfaces give rise to brightness modulations of global shading patterns. we study systematic variations of such 3d image texture as a function of illumination and viewing geometry. the 3d texture is especially noticeable near the shadow terminator (for collimated illumination) or near the dark pole (for hemispherical diffuse illumination). we find that a simple micro-facet model, assuming locally lambertian scattering, suffices to robustly describe texture contrast gradients of a large variety (measured and rendered textures; laboratory and field conditions) in a semi-quantitative manner. robust statistical measures of the texture allows one to draw inferences concerning the nature of the light field (collimated to diffuse) and of surface roughness parameters, which can be used as input to the simplest brdf models.
an optimal solution for mobile camera calibration. the problem of determining the intrinsic and extrinsic parameters of a mobile camera is addressed. an optimal solution which consists of the following steps is presented. first, the camera is calibrated in several working positions and, for each position, the corresponding transformation matrix is computed using a method developed by o.d. faugeras and g. toscani (1987). next, optimal intrinsic parameters are searched for all positions. finally, for each separate position, optimal extrinsic parameters are computed by minimizing a mean square error through a closed-form solution. experimental results show that such a technique yields a very large reduction of calibration errors and a considerable gain relative to other existing on-site calibration techniques
bayesian self-calibration of a moving camera. in this paper, a bayesian self-calibration approach using sequential importance sampling (sis) is proposed. given a set of feature correspondences tracked through an image sequence, the joint posterior distributions of both camera extrinsic and intrinsic parameters as well as the scene structure are approximated by a set of samples and their corresponding weights. the critical motion sequences are explicitly considered in the design of the algorithm. the probability of the existence of the critical motion sequence is inferred from the sample and weight set obtained from the sis procedure. no initial guess for the calibration parameters is required. the proposed approach has been extensively tested on both synthetic and real image sequences and satisfactory performance has been observed.
a fourier theory for cast shadows. cast shadows can be significant in many computer vision applications, such as lighting-insensitive recognition and surface reconstruction. nevertheless, most algorithms neglect them, primarily because they involve nonlocal interactions in nonconvex regions, making formal analysis difficult. however, many real instances map closely to canonical configurations like a wall, a v-groove type structure, or a pitted surface. in particular, we experiment with 3d textures like moss, gravel, and a kitchen sponge, whose surfaces include canonical configurations like v-grooves. this paper takes a first step toward a formal analysis of cast shadows, showing theoretically that many configurations can be mathematically analyzed using convolutions and fourier basis functions. our analysis exposes the mathematical convolution structure of cast shadows and shows strong connections to recent signal-processing frameworks for reflection and illumination.
a new image registration technique with free boundary constraints: application to mammography. in this paper, a new image-matching mathematical model is presented with its application to mammogram registration. in a variatianal framework, an energy minimization problem is formulated and a multigrid resolution algorithm is designed. the model focuses on the matching of regions of interest. it also combines several constraints which are both intensity- and segmentation-based. a new feature of our model is combining region matching and segmentation by formulation of the energy minimization problem with free boundary conditions. moreover, the energy has a new registration constraint. the performances of the new model and an equivalent model with fixed boundary conditions are compared on simulated mammogram pairs. it is shown that the model with free boundary is more robust to initialization inaccuracies than the one with fixed boundary conditions. both models are applied to several real bilateral mammogram pairs. the model ability to compensate significantly for some normal differences between mammograms is illustrated. results suggest that the new model could enable some improvements of mammogram comparisons and tumor detection system performances.
area and lenght preserving geometric invariant scale-spaces. in this paper, area preserving multi-scale representations of planar curves are described. this allows smoothing without shrinkage at the same time preserving all the scale-space properties. the representations are obtained deforming the curve via geometric heat flows while simultaneously magnifying the plane by a homethety which keeps the enclosed area constant. when the euclidean geometric heat flow is used, the resulting representation is euclidean invariant, and similarly it is affine invariant when the affine one is used. the flows are geometrically intrinsic to the curve, and exactly satisfy all the basic requirements of scale-space representations. in the case of the euclidean heat flow, it is completely local as well. the same approach is used to define length preserving geometric flows. a similarity (scale) invariant geometric heat flow is studied as well in this work.
object level grouping for video shots. we describe a method for automatically obtaining object representations suitable for retrieval from generic video shots. the object representation consists of an association of frame regions. these regions provide exemplars of the object's possible visual appearances.two ideas are developed: (i) associating regions within a single shot to represent a deforming object; (ii) associating regions from the multiple visual aspects of a 3d object, thereby implicitly representing 3d structure. for the association we exploit temporal continuity (tracking) and wide baseline matching of affine covariant regions.in the implementation there are three areas of novelty: first, we describe a method to repair short gaps in tracks. second, we show how to join tracks across occlusions (where many tracks terminate simultaneously). third, we develop an affine factorization method that copes with motion degeneracy.we obtain tracks that last throughout the shot, without requiring a 3d reconstruction. the factorization method is used to associate tracks into object-level groups, with common motion. the outcome is that separate parts of an object that are not simultaneously visible (such as the front and back of a car, or the front and side of a face) are associated together. in turn this enables object-level matching and recognition throughout a video.we illustrate the method on the feature film "groundhog day." examples are given for the retrieval of deforming objects (heads, walking people) and rigid objects (vehicles, locations).
on degeneracy of linear reconstruction from three views: linear line complex and applications. this paper investigates the linear degeneracies of projective structure estimation from line features across three views. we show that the rank of the linear system of equations for recovering the trilinear tensor of three views reduces to 23 (instead of 26) when the scene is a linear line complex (a set of lines in space intersecting at a common line). the llc situation is only linearly degenerate, and one can obtain a unique solution when the admissibility constraints of the tensor are accounted for. the line configuration described by an llc, rather than being some obscure case, is in fact quite typical. it includes, as a particular example, the case of a camera moving down a hallway in an office environment or down an urban street. furthermore, an llc situation may occur as an artifact such as in direct estimation from spatio-temporal derivatives of image brightness. therefore, an investigation into degeneracies and their remedy is important also in practice.
data and model-driven selection using color regions. a key problem in model-based object recognition is selection, namely, the problem of determining which regions in the image are likely to come from a single object. in this paper we present an approach that uses color as a cue to perform selection either based solely on image-data (data-driven), or based on the knowledge of the color description of the model (model-driven). specifically, the paper presents a method of color specification in terms of perceptual color categories and shows its relevance for the task of selection. the color categories are used to develop a fast region segmentation algorithm that extracts perceptual color regions in images. the color regions extracted form the basis for performing data and model-driven selection. data-driven selection is achieved by selecting salient color regions as judged by a color-saliency measure that emphasizes attributes that are also important in human color perception. the approach to model-driven selection, on the other hand, exploits the color and other region information in the 3d model object to locate instances of the object in a given image. the approach presented tolerates some of the problems of occlusion, pose and illumination changes that make a model instance in an image appear different from its original description. finally, the utility of color-based selection is demonstrated by showing the extent of search reduction possible when color-based selection is integrated with a recognition system.
shape ambiguities in structure from motion. this paper examines the fundamental ambiguities and uncertainties inherent in recovering structure from motion. by examining the eigenvectors associated with null or small eigenvalues of the hessian matrix, we can quantify the exact nature of these ambiguities and predict how they affect the accuracy of the reconstructed shape. our results for orthographic cameras show that the bas-relief ambiguity is significant even with many images, unless a large amount of rotation is present. similar results for perspective cameras suggest that three or more frames and a large amount of rotation are required for metrically accurate reconstruction.
stereo without search. search is not inherent in the correspondence problem. we propose a representation of images, called intrinsic curves, that combines the ideas of associative storage of images with connectedness of the representation: intrinsic curves are the paths that a set of local image descriptors trace as an image scanline is traversed from left to right. curves become surfaces when full images are considered instead of scanlines. because only the path in the space of descriptors is used for matching, intrinsic curves lose track of space, and are invariant with respect to disparity under ideal circumstances. establishing stereo correspondences then becomes a trivial lookup problem. we also show how to use intrinsic curves to match real images in the presence of noise, brightness bias, contrast fluctuations, and moderate geometric distortion, and we show how intrinsic curves can be used to deal with image ambiguity and occlusions. we carry out experiments on single-scanline matching to prove the feasibility of the approach and illustrate its main features.
impsac: synthesis of importance sampling and random sample consensus. this paper proposes a new method for recovery of epipolar geometry and feature correspondence between images which have undergone a significant deformation, either due to large rotation or wide baseline of the cameras. the method also encodes the uncertainty by providing an arbitrarily close approximation to the posterior distribution of the two view relation. the method operates on a pyramid from coarse to fine resolution, thus raising the problem of how to propagate information from one level to another in a statistically consistent way. the distribution of the parameters at each resolution is encoded nonparametrically as a set of particles. at the coarsest level, a ransac-mcmc estimator is used to initialize this set of particles, the posterior can then be approximated as a mixture of gaussians fitted to these particles. the distribution at a coarser level influences the distribution at a finer level using the technique of sampling-importance-resampling (sir) and mcmc, which allows for asymptotically correct approximations of the posterior distribution. the estimate of the posterior distribution at the level above is being used as the importance sampling function to generate a new set of particles, which can be further improved by mcmc. it is shown that the method is superior to previous single resolution ransac-style feature matchers.
topological reconstruction of a smooth manifold-solid from its occluding contour. this paper describes a simple construction for building a combinatorial model of a smooth manifold-solid from a labeled figure representing its occluding contour. the motivation is twofold. first, deriving the combinatorial model is an essential intermediate step in the visual reconstruction of solid-shape from image contours. a description of solid-shape consists of a metric and a topological component. both are necessary: the metric component specifies how the topological component is embedded in three-dimensional space. the {\it paneling construction} described in this paper is a procedure for generating the topological component from a labeled figure representing the occluding contour. second, the existence of this construction establishes the sufficiency of a labeling scheme for line-drawings of smooth solid-objects originally proposed by huffman. by sufficiency, it is meant that every set of closed plane-curves satisfying this labeling scheme is shown to correspond to a generic view of a manifold-solid. together with the whitney theorem, this confirms that huffman''s labeling scheme correctly distinguishes possible from impossible solid-objects.