A tree-based context model for object recognition.

There has been a growing interest in exploiting contextual information in addition to local features to detect and localize multiple object categories in an image. A context model can rule out some unlikely combinations or locations of objects and guide detectors to produce a semantically coherent interpretation of a scene. However, the performance benefit of context models has been limited because most of the previous methods were tested on data sets with only a few object categories, in which most images contain one or two object categories. In this paper, we introduce a new data set with images that contain many instances of different object categories, and propose an efficient model that captures the contextual information among more than a hundred object categories using a tree structure. Our model incorporates global image features, dependencies between object categories, and outputs of local detectors into one probabilistic framework. We demonstrate that our context model improves object recognition performance and provides a coherent interpretation of a scene, which enables a reliable image querying system by multiple object categories. In addition, our model can be applied to scene understanding tasks that local detectors alone cannot solve, such as detecting objects out of context or querying for the most typical and the least typical scenes in a data set.

Learning the dynamics and time-recursive boundary detection of deformable objects.

We propose a principled framework for recursively segmenting deformable objects across a sequence of frames. We demonstrate the usefulness of this method on left ventricular segmentation across a cardiac cycle. The approach involves a technique for learning the system dynamics together with methods of particle-based smoothing as well as nonparametric belief propagation on a loopy graphical model capturing the temporal periodicity of the heart. The dynamic system state is a low-dimensional representation of the boundary, and the boundary estimation involves incorporating curve evolution into recursive state estimation. By formulating the problem as one of state estimation, the segmentation at each particular time is based not only on the data observed at that instant, but also on predictions based on past and future boundary estimates. Although this paper focuses on left ventricle segmentation, the method generalizes to temporally segmenting any deformable object.

A recursive model-reduction method for approximate inference in Gaussian Markov random fields.

This paper presents recursive cavity modeling--a principled, tractable approach to approximate, near-optimal inference for large Gauss-Markov random fields. The main idea is to subdivide the random field into smaller subfields, constructing cavity models which approximate these subfields. Each cavity model is a concise, yet faithful, model for the surface of one subfield sufficient for near-optimal inference in adjacent subfields. This basic idea leads to a tree-structured algorithm which recursively builds a hierarchy of cavity models during an "upward pass" and then builds a complementary set of blanket models during a reverse "downward pass." The marginal statistics of individual variables can then be approximated using their blanket models. Model thinning plays an important role, allowing us to develop thinned cavity and blanket models thereby providing tractable approximate inference. We develop a maximum-entropy approach that exploits certain tractable representations of Fisher information on thin chordal graphs. Given the resulting set of thinned cavity models, we also develop a fast preconditioner, which provides a simple iterative method to compute optimal estimates. Thus, our overall approach combines recursive inference, variational learning and iterative estimation. We demonstrate the accuracy and scalability of this approach in several challenging, large-scale remote sensing problems.

MCMC curve sampling for image segmentation.

We present an algorithm to generate samples from probability distributions on the space of curves. We view a traditional curve evolution energy functional as a negative log probability distribution and sample from it using a Markov chain Monte Carlo (MCMC) algorithm. We define a proposal distribution by generating smooth perturbations to the normal of the curve and show how to compute the transition probabilities to ensure that the samples come from the posterior distribution. We demonstrate some advantages of sampling methods such as robustness to local minima, better characterization of multi-modal distributions, access to some measures of estimation error, and ability to easily incorporate constraints on the curve.

A state-space analysis for reconstruction of goal-directed movements using neural signals.

The execution of reaching movements involves the coordinated activity of multiple brain regions that relate variously to the desired target and a path of arm states to achieve that target. These arm states may represent positions, velocities, torques, or other quantities. Estimation has been previously applied to neural activity in reconstructing the target separately from the path. However, the target and path are not independent. Because arm movements are limited by finite muscle contractility, knowledge of the target constrains the path of states that leads to the target. In this letter, we derive and illustrate a state equation to capture this basic dependency between target and path. The solution is described for discrete-time linear systems and gaussian increments with known target arrival time. The resulting analysis enables the use of estimation to study how brain regions that relate variously to target and path together specify a trajectory. The corresponding reconstruction procedure may also be useful in brain-driven prosthetic devices to generate control signals for goal-directed movements.

A nonparametric statistical method for image segmentation using information theory and curve evolution.

In this paper, we present a new information-theoretic approach to image segmentation. We cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities, subject to a constraint on the total length of the region boundaries. We assume that the probability densities associated with the image pixel intensities within each region are completely unknown a priori, and we formulate the problem based on nonparametric density estimates. Due to the nonparametric structure, our method does not require the image regions to have a particular type of probability distribution and does not require the extraction and use of a particular statistic. We solve the information-theoretic optimization problem by deriving the associated gradient flows and applying curve evolution techniques. We use level-set methods to implement the resulting evolution. The experimental results based on both synthetic and real images demonstrate that the proposed technique can solve a variety of challenging image segmentation problems. Futhermore, our method, which does not require any training, performs as good as methods based on training.

An EM algorithm for shape classification based on level sets.

In this paper, we propose an expectation-maximization (EM) approach to separate a shape database into different shape classes, while simultaneously estimating the shape contours that best exemplify each of the different shape classes. We begin our formulation by employing the level set function as the shape descriptor. Next, for each shape class we assume that there exists an unknown underlying level set function whose zero level set describes the contour that best represents the shapes within that shape class. The level set function for each example shape in the database is modeled as a noisy measurement of the appropriate shape class's unknown underlying level set function. Based on this measurement model and the judicious introduction of the class labels as the hidden data, our EM formulation calculates the labels for shape classification and estimates the shape contours that best typify the different shape classes. This resulting iterative algorithm is computationally efficient, simple, and accurate. We demonstrate the utility and performance of this algorithm by applying it to two medical applications.

Statistical characterization of real-world illumination.

Although studies of vision and graphics often assume simple illumination models, real-world illumination is highly complex, with reflected light incident on a surface from almost every direction. One can capture the illumination from every direction at one point photographically using a spherical illumination map. This work illustrates, through analysis of photographically acquired, high dynamic range illumination maps, that real-world illumination possesses a high degree of statistical regularity. The marginal and joint wavelet coefficient distributions and harmonic spectra of illumination maps resemble those documented in the natural image statistics literature. However, illumination maps differ from typical photographs in that illumination maps are statistically nonstationary and may contain localized light sources that dominate their power spectra. Our work provides a foundation for statistical models of real-world illumination, thereby facilitating the understanding of human material perception, the design of robust computer vision systems, and the rendering of realistic computer graphics imagery.

A unified variational approach to denoising and bias correction in MR.

We propose a novel bias correction method for magnetic resonance (MR) imaging that uses complementary body coil and surface coil images. The former are spatially homogeneous but have low signal intensity; the latter provide excellent signal response but have large bias fields. We present a variational framework where we optimize an energy functional to estimate the bias field and the underlying image using both observed images. The energy functional contains smoothness-enforcing regularization for both the image and the bias field. We present extensions of our basic framework to a variety of imaging protocols. We solve the optimization problem using a computationally efficient numerical algorithm based on coordinate descent, preconditioned conjugate gradient, half-quadratic regularization, and multigrid techniques. We show qualitative and quantitative results demonstrating the effectiveness of the proposed method in producing debiased and denoised MR images.