Ramin Zabih

Fast approximate energy minimization via graph cuts

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.

A taxonomy and evaluation of dense two-frame stereo correspondence algorithms

Stereo matching is one of the most active research areas in computer vision. While a large number of algorithms for stereo correspondence have been developed, relatively little work has been done on characterizing their performance. In this paper, we present a taxonomy of dense, two-frame stereo methods. Our taxonomy is designed to assess the different components and design decisions made in individual stereo algorithms. Using this taxonomy, we compare existing stereo methods and present experiments evaluating the performance of many different variants. In order to establish a common software platform and a collection of data sets for easy evaluation, we have designed a stand-alone, flexible C++ implementation that enables the evaluation of individual components and that can easily be extended to include new algorithms. We have also produced several new multi-frame stereo data sets with ground truth and are making both the code and data sets available on the Web. Finally, we include a comparative evaluation of a large set of todays best-performing stereo algorithms.

Image indexing using color correlograms

We define a new image feature called the color correlogram and use it for image indexing and comparison. This feature distills the spatial correlation of colors, and is both effective and inexpensive for content-based image retrieval. The correlogram robustly tolerates large changes in appearance and shape caused by changes in viewing positions, camera zooms, etc. Experimental evidence suggests that this new feature outperforms not only the traditional color histogram method but also the recently proposed histogram refinement methods for image indexing/retrieval.

Non-parametric local transforms for computing visual correspondence

We propose a new approach to the correspondence problem that makes use of non-parametric local transforms as the basis for correlation. Non-parametric local transforms rely on the relative ordering of local intensity values, and not on the intensity values themselves. Correlation using such transforms can tolerate a significant number of outliers. This can result in improved performance near object boundaries when compared with conventional methods such as normalized correlation. We introduce two non-parametric local transforms: the rank transform, which measures local intensity, and the census transform, which summarizes local image structure. We describe some properties of these transforms, and demonstrate their utility on both synthetic and real data.

Computing visual correspondence with occlusions using graph cuts

Several new algorithms for visual correspondence based on graph cuts have recently been developed. While these methods give very strong results in practice, they do not handle occlusions properly. Specifically, they treat the two input images asymmetrically, and they do not ensure that a pixel corresponds to at most one pixel in the other image. In this paper, we present a new method which properly addresses occlusions, while preserving the advantages of graph cut algorithms. We give experimental results for stereo as well as motion, which demonstrate that our method performs well both at detecting occlusions and computing disparities.

A Comparative Study of Energy Minimization Methods for Markov Random Fields with Smoothness-Based Priors

Among the most exciting advances in early vision has been the development of efficient energy minimization algorithms for pixel-labeling tasks such as depth or texture computation. It has been known for decades that such problems can be elegantly expressed as Markov random fields, yet the resulting energy minimization problems have been widely viewed as intractable. Algorithms such as graph cuts and loopy belief propagation (LBP) have proven to be very powerful: For example, such methods form the basis for almost all the top-performing stereo methods. However, the trade-offs among different energy minimization algorithms are still not well understood. In this paper, we describe a set of energy minimization benchmarks and use them to compare the solution quality and runtime of several common energy minimization algorithms. We investigate three promising methods-graph cuts, LBP, and tree-reweighted message passing-in addition to the well-known older iterated conditional mode (ICM) algorithm. Our benchmark problems are drawn from published energy functions used for stereo, image stitching, interactive segmentation, and denoising. We also provide a general-purpose software interface that allows vision researchers to easily switch between optimization methods. The benchmarks, code, images, and results are available at http://vision.middlebury.edu/MRF/.

Comparing images using color coherence vectors

Color histograms are used to compare images in many applications. Their advantages are efficiency, and insensitivity to small changes in camera viewpoint. However, color histograms lack spatial information, so images with very different appearances can have similar histograms. For example, a picture of fall foliage might contain a large number of scattered red pixels; this could have a similar color histogram to a picture with a single large red object. We describe a histogram-based method for comparing images that incorporates spatial information. We classify each pixel in a given color bucket as either coherent or incoherent, based on whether or not it is part of a large similarly-colored region. A color coherence vector (CCV) stores the number of coherent versus incoherent pixels with each color. By separating coherent pixels from incoherent pixels, CCV’s provide finer distinctions than color histograms. CCV’s can be computed at over 5 images per second on a standard workstation. A database with 15,000 images can be queried for the images with the most similar CCV’s in under 2 seconds. We show that CCV’s can give superior results to color his∗To whom correspondence should be addressed tograms for image retrieval.

Multi-camera Scene Reconstruction via Graph Cuts

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.

A feature-based algorithm for detecting and classifying scene breaks

We describe a new approach to the detection and classification of scene breaks in video sequences. Our method can detect and classify a variety of scene breaks, including cuts, fades, dissolves and wipes, even in sequences involving significant motion. We detect the appearance of intensity edges that are distant from edges in the previous frame. A global motion computation is used to handle camera or object motion. The algorithms we propose withstand compression artifacts such as those introduced by JPEG and MPEG, even at very high compression rates. Experimental evidence demonstrates that our method can detect and classify scene breaks that are difficult to detect with previous approaches. An initial implementation runs at approximately 2 frames per second on a Sun workstation.

Histogram refinement for content-based image retrieval

Color histograms are widely used for content-based image retrieval. Their advantages are efficiency, and insensitivity to small changes in camera viewpoint. However, a histogram is a coarse characterization of an image, and so images with very different appearances can have similar histograms. We describe a technique for comparing images called histogram refinement, which imposes additional constraints on histogram based matching. Histogram refinement splits the pixels in a given bucket into several classes, based upon some local property. Within a given bucket, only pixels in the same class are compared. We describe a split histogram called a color coherence vector (CCV), which partitions each histogram bucket based on spatial coherence. CCVs can be computed at over 5 images per second on a standard workstation. A database with 15,000 images can be queried using CCVs in under 2 seconds. We demonstrate that histogram refinement can be used to distinguish images whose color histograms are indistinguishable.