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     

What energy functions can be minimized via graph cuts?

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 give a characterization of the energy functions that can be minimized by graph cuts. Our results are restricted to functions of 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 give a precise characterization of what energy functions can be minimized using graph cuts, among the energy functions that can be written as a sum of terms containing three or fewer binary variables. We also provide a general-purpose construction to minimize such an energy function. Finally, we give a necessary condition for any energy function of binary variables to be minimized by graph cuts. 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. A software implementation is freely available.     

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. Recently, 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 tradeoffs 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 running time of several common energy minimization algorithms. We investigate three promising recent methods graph cuts, LBP, and tree-reweighted message passing in addition to the well-known older iterated conditional modes (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. Benchmarks, code, images, and results are available at http://vision.middlebury.edu/MRF/.     

A variable window approach to early vision

Early vision relies heavily on rectangular windows for tasks such as smoothing and computing correspondence. While rectangular windows are efficient, they yield poor results near object boundaries. We describe an efficient method for choosing an arbitrarily shaped connected window, in a manner that varies at each pixel. Our approach can be applied to several problems, including image restoration and visual correspondence. It runs in linear time, and takes a few seconds on traditional benchmark images. Performance on both synthetic and real imagery appears promising     

Spatial Color Indexing and Applications

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 when computed efficiently, turns out to be both effective and inexpensive for content-based image retrieval. The correlogram is robust in tolerating large changes in appearance and shape caused by changes in viewing position, camera zoom, etc. Experimental evidence shows that this new feature outperforms not only the traditional color histogram method but also the recently proposed histogram refinement methods for image indexing/retrieval. We also provide a technique to cut down the storage requirement of the correlogram so that it is the same as that of histograms, with only negligible performance penalty compared to the original correlogram.We also suggest the use of color correlogram as a generic indexing tool to tackle various problems arising from image retrieval and video browsing. We adapt the correlogram to handle the problems of image subregion querying, object localization, object tracking, and cut detection. Experimental results again suggest that the color correlogram is more effective than the histogram for these applications, with insignificant additional storage or processing cost.     

Comparing images using joint histograms

Color histograms are widely used for content-based image retrieval due to their efficiency and robustness. However, a color histogram only records an image's overall color composition, so images with very different appearances can have similar color histograms. This problem is especially critical in large image databases, where many images have similar color histograms. In this paper, we propose an alternative to color histograms called a joint histogram, which incorporates additional information without sacrificing the robustness of color histograms. We create a joint histogram by selecting a set of local pixel features and constructing a multidimensional histogram. Each entry in a joint histogram contains the number of pixels in the image that are described by a particular combination of feature values. We describe a number of different joint histograms, and evaluate their performance for image retrieval on a database with over 210,000 images. On our benchmarks, joint histograms outperform color histograms by an order of magnitude.     

A feature-based algorithm for detecting and classifying production effects

We describe a new approach to the detection and classification of production effects in video sequences. Our method can detect and classify a variety of effects, including cuts, fades, dissolves, wipes and captions, 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 algorithm we propose withstands JPEG and MPEG artifacts, even at high compression rates. Experimental evidence demonstrates that our method can detect and classify production effects that are difficult to detect with previous approaches.     

A maximum likelihood approach to parallel imaging with coil sensitivity noise

Parallel imaging is a powerful technique to speed up magnetic resonance (MR) image acquisition via multiple coils. Both the received signal of each coil and its sensitivity map, which describes its spatial response, are needed during reconstruction. Widely used schemes such as SENSE assume that sensitivity maps of the coils are noiseless while the only errors are in coil outputs. In practice, however, sensitivity maps are subject to a wide variety of errors. At first glance, sensitivity noise appears to result in an errors-in-variables problem of the kind that is typically solved using total least squares (TLSs). However, existing TLS algorithms are in general inappropriate for the specific type of block structure that arises in parallel imaging. In this paper, we take a maximum likelihood approach to the problem of parallel imaging in the presence of independent Gaussian sensitivity noise. This results in a quasi-quadratic objective function, which can be efficiently minimized. Experimental evidence suggests substantial gains over conventional SENSE, especially in nonideal imaging conditions like low signal-to-noise ratio (SNR), high g-factors and large acceleration, using sensitivity maps suffering from misalignment, ringing, and random noise.