Many tasks in computer vision involve assigning a label (such as disparity) to every pixel. A common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist, e.g., at object boundaries. These tasks are naturally stated in terms of energy minimization. The authors consider a wide class of energies with various smoothness constraints. Global minimization of these energy functions is NP-hard even in the simplest discontinuity-preserving case. Therefore, our focus is on efficient approximation algorithms. We present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves, namely expansion moves and swap moves. These moves can simultaneously change the labels of arbitrarily large sets of pixels. In contrast, many standard algorithms (including simulated annealing) use small moves where only one pixel changes its label at a time. Our expansion algorithm finds a labeling within a known factor of the global minimum, while our swap algorithm handles more general energy functions. Both of these algorithms allow important cases of discontinuity preserving energies. We experimentally demonstrate the effectiveness of our approach for image restoration, stereo and motion. On real data with ground truth, we achieve 98 percent accuracy.

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Fast approximate energy minimization via graph cuts

There has been much recent interest in Bayesian image analysis, including such topics as removal of blur and noise, detection of object boundaries, classification of textures, and reconstruction of two- or three-dimensional scenes from noisy lower-dimensional views. Perhaps the most straightforward task is that of image restoration, though it is often suggested that this is an area of relatively minor practical importance. The present paper argues the contrary, since many problems in the analysis of spatial data can be interpreted as problems of image restoration. Furthermore, the amounts of data involved allow routine use of computer intensive methods, such as the Gibbs sampler, that are not yet practicable for conventional images. Two examples are given, one in archeology, the other in epidemiology. These are preceded by a partial review of pixel-based Bayesian image analysis.

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Bayesian image restoration, with two applications in spatial statistics

Rejoinder (Bayesian image restoration,with two applications in spatial statistics)

In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function's smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when very large moves are allowed. The first move we consider is an /spl alpha/-/spl beta/-swap: for a pair of labels /spl alpha/,/spl beta/, this move exchanges the labels between an arbitrary set of pixels labeled a and another arbitrary set labeled /spl beta/. Our first algorithm generates a labeling such that there is no swap move that decreases the energy. The second move we consider is an /spl alpha/-expansion: for a label a, this move assigns an arbitrary set of pixels the label /spl alpha/. Our second algorithm, which requires the smoothness term to be a metric, generates a labeling such that there is no expansion move that decreases the energy. Moreover, this solution is within a known factor of the global minimum. We experimentally demonstrate the effectiveness of our approach on image restoration, stereo and motion.

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We present a novel statistical and variational approach to image segmentation based on a new algorithm, named region competition. This algorithm is derived by minimizing a generalized Bayes/minimum description length (MDL) criterion using the variational principle. The algorithm is guaranteed to converge to a local minimum and combines aspects of snakes/balloons and region growing. The classic snakes/balloons and region growing algorithms can be directly derived from our approach. We provide theoretical analysis of region competition including accuracy of boundary location, criteria for initial conditions, and the relationship to edge detection using filters. It is straightforward to generalize the algorithm to multiband segmentation and we demonstrate it on gray level images, color images and texture images. The novel color model allows us to eliminate intensity gradients and shadows, thereby obtaining segmentation based on the albedos of objects. It also helps detect highlight regions.

Region competition: unifying snakes, region growing, and Bayes/MDL for multiband image segmentation

A statistical framework is used for finding boundaries and for partitioning scenes into homogeneous regions. The model is a joint probability distribution for the array of pixel gray levels and an array of labels. In boundary finding, the labels are binary, zero, or one, representing the absence or presence of boundary elements. In partitioning, the label values are generic: two labels are the same when the corresponding scene locations are considered to belong to the same region. The distribution incorporates a measure of disparity between certain spatial features of block pairs of pixel gray levels, using the Kolmogorov-Smirnov nonparametric measures of difference between the distributions of these features. The number of model parameters is minimized by forbidding label configurations, which are assigned probability zero. The maximum a posteriori estimator of boundary placements and partitionings is examined. The forbidden states introduce constraints into the calculation of these configurations. Stochastic relaxation methods are extended to accommodate constrained optimization. >

Boundary detection by constrained optimization

Local rough set-based feature selection for label distribution learning with incomplete labels

Promoting the management of the over-limit of freight transport vehicles plays an important role in the sustainable development of the highway industry. Vehicle outer contour dimension measurement is a key element in highway over-limit detection. The current detection approaches and research methods, however, are insufficient for high-precision flow detection. Therefore, this study proposes an algorithm for measuring the dimensions of a truck’s outer contours, using unmanned aerial vehicle (UAV) binocular stereo vision. First, this study leverages a binocular camera mounted on a UAV to reconstruct the 3D point clouds of the truck. Second, the point cloud data are clustered using an FoF (Friends-of-Friends algorithm); this recognizes the cluster of truck points according to the truck’s characteristics. Finally, the principal component analysis and the Gaussian kernel density estimation are used to generate the outer contour dimensions of the trucks. Twenty model vehicles are selected as test objects to verify the reliability of the algorithm. The average error of the algorithm is represented by calculating the average value of the difference between the real size and the predicted size of the three dimensions. The experimental results demonstrate that the average error of this measurement approach is less than 2.5%, and the method is both stable and robust. This approach aligns with national regulations for over-limit detection.

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P. Dong

Papers

Boundary detection by constrained optimization

Local rough set-based feature selection for label distribution learning with incomplete labels

Algorithm for Measuring the Outer Contour Dimension of Trucks Using UAV Binocular Stereo Vision

Incomplete label distribution feature selection based on neighborhood-tolerance discrimination index