Catálogo de publicaciones - libros

We describe an automatic method for building optimal 3D statistical shape models from sets of training shapes. Although shape models show considerable promise as a basis for segmenting and interpreting images, a major drawback of the approach is the need to establish a dense correspondence across a training set of example shapes. It is important to establish the correct correspondence, otherwise poor models can result. In 2D, this can be achieved using manual ‘landmarks’, but in 3D this becomes impractical. We show it is possible to establish correspondences , by casting the correspondence problem as one of finding the ‘optimal’ parameterisation of each shape in the training set. We describe an explicit representation of surface parameterisation, that ensures the resulting correspondences are legal, and show how this representation can be manipulated to minimise the of the training set using the model. This results in compact models with good generalisation properties. Results are reported for two sets of biomedical shapes, showing significant improvement in model properties compared to those obtained using a uniform surface parameterisation.

The thin plate spline (TPS) is an effective tool for modeling coordinate transformations that has been applied successfully in several computer vision applications. Unfortunately the solution requires the inversion of a matrix, where is the number of points in the data set, thus making it impractical for large scale applications. As it turns out, a surprisingly good approximate solution is often possible using only a small subset of corresponding points. We begin by discussing the obvious approach of using the subsampled set to estimate a transformation that is then applied to all the points, and we show the drawbacks of this method. We then proceed to borrow a technique from the machine learning community for function approximation using radial basis functions (RBFs) and adapt it to the task at hand. Using this method, we demonstrate a significant improvement over the naive method. One drawback of this method, however, is that is does not allow for analysis, a technique for studying shape deformations introduced by Bookstein based on the eigenvectors of the . To address this, we describe a third approximation method based on a classic matrix completion technique that allows for principal warp analysis as a by-product. By means of experiments on real and synthetic data, we demonstrate the pros and cons of these different approximations so as to allow the reader to make an informed decision suited to his or her application.

What does it mean for a deforming object to be “moving” (see Fig.1)? How can we separate the overall motion (a finite-dimensional group action) from the more general deformation (a diffeomorphism)? In this paper we propose a definition of motion for a deforming object and introduce a notion of “shape average” as the entity that separates the motion from the deformation. Our definition allows us to derive novel and efficient algorithms to register non-equivalent shapes using region-based methods, and to simultaneously approximate and register structures in grey-scale images. We also extend the notion of shape average to that of a “moving average” in order to track moving and deforming objects through time.

We present a variational approach to the problem of registering planar shapes despite missing parts. Registration is achieved through the evolution of a partial differential equation that simultaneously estimates the shape of the missing region, the underlying “complete shape” and the collection of group elements (Euclidean or affine) corresponding to the registration. Our technique applies both to shapes, for instance represented as characteristic functions (binary images), and to grayscale images, where all intensity levels evolve simultaneously in a partial differential equation. It can therefore be used to perform “region inpainting” and to register collections of images despite occlusions. The novelty of the approach lies on the fact that, rather than estimating the missing region in each image independently, we pose the problem as a joint registration with respect to an underlying “complete shape” from which the complete version of the original data is obtained via a group action.

In the last few years, several new algorithms based on graph cuts have been developed to solve energy minimization problems in computer vision. Each of these techniques constructs a graph such that the minimum cut on the graph also minimizes the energy. Yet because these graph constructions are complex and highly specific to a particular energy function, graph cuts have seen limited application to date. In this paper we characterize the energy functions that can be minimized by graph cuts. Our results are restricted to energy functions with binary variables. However, our work generalizes many previous constructions, and is easily applicable to vision problems that involve large numbers of labels, such as stereo, motion, image restoration and scene reconstruction. We present three main results: a necessary condition for any energy function that can be minimized by graph cuts; a sufficient condition for energy functions that can be written as a sum of functions of up to three variables at a time; and a general-purpose construction to minimize such an energy function. Researchers who are considering the use of graph cuts to optimize a particular energy function can use our results to determine if this is possible, and then follow our construction to create the appropriate graph.

We address the problem of computing the 3-dimensional shape of an arbitrary scene from a set of images taken at known viewpoints. Multi-camera scene reconstruction is a natural generalization of the stereo matching problem. However, it is much more difficult than stereo, primarily due to the difficulty of reasoning about visibility. In this paper, we take an approach that has yielded excellent results for stereo, namely energy minimization via graph cuts. We first give an energy minimization formulation of the multi-camera scene reconstruction problem. The energy that we minimize treats the input images symmetrically, handles visibility properly, and imposes spatial smoothness while preserving discontinuities. As the energy function is NP-hard to minimize exactly, we give a graph cut algorithm that computes a local minimum in a strong sense. We handle all camera configurations where voxel coloring can be used, which is a large and natural class. Experimental data demonstrates the effectiveness of our approach.

We propose Markov chain Monte Carlo sampling methods to address uncertainty estimation in disparity computation. We consider this problem at a postprocessing stage, i.e. once the disparity map has been computed, and suppose that the only information available is the stereoscopic pair. The method, which consists of sampling from the posterior distribution given the stereoscopic pair, allows the prediction of large errors which occur with low probability, and accounts for spatial correlations. The model we use is oriented towards an application to mid-resolution stereo systems, but we give insights on how it can be extended. Moreover, we propose a new sampling algorithm relying on Markov chain theory and the use of importance sampling to speed up the computation. The efficiency of the algorithm is demonstrated, and we illustrate our method with the computation of confidence intervals and probability maps of large errors, which may be applied to optimize a trajectory in a three dimensional environment.

This paper studies the inference of 3D shape from a set of noisy photos. We derive a probabilistic framework to specify what one can infer about 3D shape for arbitrarily-shaped, Lambertian scenes and arbitrary viewpoint configurations. Based on formal definitions of visibility, occupancy, emptiness, and photo-consistency, the theoretical development yields a formulation of the , the tightest probabilistic bound on the scene’s true shape that can be inferred from the photos. We show how to (1) express this distribution in terms of image measurements, (2) represent it compactly by assigning an occupancy probability to each point in space, and (3) design a stochastic reconstruction algorithm that draws fair samples (i.e., 3D photo hulls) from it. We also present experimental results for complex 3D scenes.

We propose a texture similarity measure based on the Kullback-Leibler divergence between gamma distributions (KLGamma). We conjecture that the spatially smoothed Gabor filter magnitude responses of some classes of visually homogeneous stochastic textures are gamma distributed. Classification experiments with disjoint test and training images, show that the KLGamma measure performs better than other parametric measures. It approaches, and under some conditions exceeds, the classification performance of the best non-parametric measures based on binned marginal histograms, although it has a computational cost at least an order of magnitude less. Thus, the KLGamma measure is well suited for use in real-time image segmentation algorithms and time-critical texture classification and retrieval from large databases.

The appearance of an outdoor scene depends on a variety of factors such as viewing geometry, scene structure and reflectance (BRDF or BTF), illumination (sun, moon, stars, street lamps), atmospheric condition (clear air, fog, rain) and weathering (or aging) of materials. Over time, these factors change, altering the way a scene appears. A large set of images is required to study the entire variability in scene appearance. In this paper, we present a database of high quality registered and calibrated images of a fixed outdoor scene captured every hour for over 5 months. The dataset covers a wide range of daylight and night illumination conditions, weather conditions and seasons. We describe in detail the image acquisition and sensor calibration procedures. The images are tagged with a variety of ground truth data such as weather and illumination conditions and actual scene depths. This database has potential implications for vision, graphics, image processing and atmospheric sciences and can be a testbed for many algorithms. We describe an example application - image analysis in bad weather - and show how this method can be evaluated using the images in the database. The database is available online at http://www.cs.columbia.edu/CAVE/. The data collection is ongoing and we plan to acquire images for one year.