Steven Haker

Bio: Steven Haker is an academic researcher from Brigham and Women's Hospital. The author has contributed to research in topics: Image segmentation & Magnetic resonance imaging. The author has an hindex of 32, co-authored 66 publications receiving 4386 citations. Previous affiliations of Steven Haker include Harvard University & Georgia Institute of Technology.

Optimal Mass Transport for Registration and Warping

Abstract: Image registration is the process of establishing a common geometric reference frame between two or more image data sets possibly taken at different times. In this paper we present a method for computing elastic registration and warping maps based on the Monge–Kantorovich theory of optimal mass transport. This mass transport method has a number of important characteristics. First, it is parameter free. Moreover, it utilizes all of the grayscale data in both images, places the two images on equal footing and is symmetrical: the optimal mapping from image A to image B being the inverse of the optimal mapping from B to A. The method does not require that landmarks be specified, and the minimizer of the distance functional involved is uniques there are no other local minimizers. Finally, optimal transport naturally takes into account changes in density that result from changes in area or volume. Although the optimal transport method is certainly not appropriate for all registration and warping problems, this mass preservation property makes the Monge–Kantorovich approach quite useful for an interesting class of warping problems, as we show in this paper. Our method for finding the registration mapping is based on a partial differential equation approach to the minimization of the L2 Kantorovich–Wasserstein or “Earth Mover's Distance” under a mass preservation constraint. We show how this approach leads to practical algorithms, and demonstrate our method with a number of examples, including those from the medical field. We also extend this method to take into account changes in intensity, and show that it is well suited for applications such as image morphing.

Differential and Numerically Invariant Signature Curves Applied to Object Recognition

Abstract: We introduce a new paradigm, the differential invariant signature curve or manifold, for the invariant recognition of visual objects A general theorem of E Cartan implies that two curves are related by a group transformation if and only if their signature curves are identical The important examples of the Euclidean and equi-affine groups are discussed in detail Secondly, we show how a new approach to the numerical approximation of differential invariants, based on suitable combination of joint invariants of the underlying group action, allows one to numerically compute differential invariant signatures in a fully group-invariant manner Applications to a variety of fundamental issues in vision, including detection of symmetries, visual tracking, and reconstruction of occlusions, are discussed

Detection of prostate cancer by integration of line-scan diffusion, T2-mapping and T2-weighted magnetic resonance imaging; a multichannel statistical classifier

Abstract: A multichannel statistical classifier for detecting prostate cancer was developed and validated by combining information from three different magnetic resonance (MR) methodologies: T2-weighted, T2-mapping, and line scan diffusion imaging (LSDI). From these MR sequences, four different sets of image intensities were obtained: T2-weighted (T2W) from T2-weighted imaging, Apparent Diffusion Coefficient (ADC) from LSDI, and proton density (PD) and T2 (T2 Map) from T2-mapping imaging. Manually segmented tumor labels from a radiologist, which were validated by biopsy results, served as tumor "ground truth." Textural features were extracted from the images using co-occurrence matrix (CM) and discrete cosine transform (DCT). Anatomical location of voxels was described by a cylindrical coordinate system. A statistical jack-knife approach was used to evaluate our classifiers. Single-channel maximum likelihood (ML) classifiers were based on 1 of the 4 basic image intensities. Our multichannel classifiers: support vector machine (SVM) and Fisher linear discriminant (FLD), utilized five different sets of derived features. Each classifier generated a summary statistical map that indicated tumor likelihood in the peripheral zone (PZ) of the prostate gland. To assess classifier accuracy, the average areas under the receiver operator characteristic (ROC) curves over all subjects were compared. Our best FLD classifier achieved an average ROC area of 0.839(+/-0.064), and our best SVM classifier achieved an average ROC area of 0.761(+/-0.043). The T2W ML classifier, our best single-channel classifier, only achieved an average ROC area of 0.599(+/-0.146). Compared to the best single-channel ML classifier, our best multichannel FLD and SVM classifiers have statistically superior ROC performance (P=0.0003 and 0.0017, respectively) from pairwise two-sided t-test. By integrating the information from multiple images and capturing the textural and anatomical features in tumor areas, summary statistical maps can potentially aid in image-guided prostate biopsy and assist in guiding and controlling delivery of localized therapy under image guidance.

Minimizing flows for the monge-kantorovich problem ∗

Abstract: In this work, we formulate a new minimizing flow for the optimal mass transport (Monge-Kantorovich) problem. We study certain properties of the flow, including weak solutions as well as short- and long-term existence. Optimal transport has found a number of applications, includ- ing econometrics, fluid dynamics, cosmology, image processing, automatic control, transportation, statistical physics, shape optimization, expert systems, and meteorology. 1. Introduction. In this paper, we derive a novel gradient descent flow for the computation of the optimal transport map (when it exists) in the Monge-Kantorovich framework. Besides being quite useful for the efficient computation of the transport map, we believe that the flow presented here is quite interesting from a theoretical point of view as well. In the present work, we undertake a study of some of its key

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Principles of Neural Science

Abstract: I have developed "tennis elbow" from lugging this book around the past four weeks, but it is worth the pain, the effort, and the aspirin. It is also worth the (relatively speaking) bargain price. Including appendixes, this book contains 894 pages of text. The entire panorama of the neural sciences is surveyed and examined, and it is comprehensive in its scope, from genomes to social behaviors. The editors explicitly state that the book is designed as "an introductory text for students of biology, behavior, and medicine," but it is hard to imagine any audience, interested in any fragment of neuroscience at any level of sophistication, that would not enjoy this book. The editors have done a masterful job of weaving together the biologic, the behavioral, and the clinical sciences into a single tapestry in which everyone from the molecular biologist to the practicing psychiatrist can find and appreciate his or

Optimal Transport: Old and New

Abstract: Couplings and changes of variables.- Three examples of coupling techniques.- The founding fathers of optimal transport.- Qualitative description of optimal transport.- Basic properties.- Cyclical monotonicity and Kantorovich duality.- The Wasserstein distances.- Displacement interpolation.- The Monge-Mather shortening principle.- Solution of the Monge problem I: global approach.- Solution of the Monge problem II: Local approach.- The Jacobian equation.- Smoothness.- Qualitative picture.- Optimal transport and Riemannian geometry.- Ricci curvature.- Otto calculus.- Displacement convexity I.- Displacement convexity II.- Volume control.- Density control and local regularity.- Infinitesimal displacement convexity.- Isoperimetric-type inequalities.- Concentration inequalities.- Gradient flows I.- Gradient flows II: Qualitative properties.- Gradient flows III: Functional inequalities.- Synthetic treatment of Ricci curvature.- Analytic and synthetic points of view.- Convergence of metric-measure spaces.- Stability of optimal transport.- Weak Ricci curvature bounds I: Definition and Stability.- Weak Ricci curvature bounds II: Geometric and analytic properties.