Keenan Crane

Bio: Keenan Crane is an academic researcher from Carnegie Mellon University. The author has contributed to research in topics: Geometry processing & Polygon mesh. The author has an hindex of 24, co-authored 48 publications receiving 2543 citations. Previous affiliations of Keenan Crane include University of Illinois at Urbana–Champaign & École Polytechnique Fédérale de Lausanne.

Geodesics in heat: A new approach to computing distance based on heat flow

Abstract: We introduce the heat method for computing the geodesic distance to a specified subset (e.g., point or curve) of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard linear elliptic problems. The resulting systems can be prefactored once and subsequently solved in near-linear time. In practice, distance is updated an order of magnitude faster than with state-of-the-art methods, while maintaining a comparable level of accuracy. The method requires only standard differential operators and can hence be applied on a wide variety of domains (grids, triangle meshes, point clouds, etc.). We provide numerical evidence that the method converges to the exact distance in the limit of refinement; we also explore smoothed approximations of distance suitable for applications where greater regularity is required.

Geodesics in Heat

Abstract: We introduce the heat method for computing the shortest geodesic distance to an arbitrary subset of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard linear elliptic problems. The resulting algorithm represents a significant breakthrough in the practical computation of distance on a wide variety of geometric domains, since these problems can be prefactored once and subsequently solved in linear time. In practice, distance can be updated via the heat method an order of magnitude faster than with state-of-the-art methods while maintaining a comparable level of accuracy. We demonstrate that the method converges to the exact geodesic distance in the limit of refinement; we also explore smoothed approximations of distance suitable for applications where differentiability is required.

Capturing and animating occluded cloth

Abstract: We capture the shape of moving cloth using a custom set of color markers printed on the surface of the cloth. The output is a sequence of triangle meshes with static connectivity and with detail at the scale of individual markers in both smooth and folded regions. We compute markers' coordinates in space using correspondence across multiple synchronized video cameras. Correspondence is determined from color information in small neighborhoods and refined using a novel strain pruning process. Final correspondence does not require neighborhood information. We use a novel data driven hole-filling technique to fill occluded regions. Our results include several challenging examples: a wrinkled shirt sleeve, a dancing pair of pants, and a rag tossed onto a cup. Finally, we demonstrate that cloth capture is reusable by animating a pair of pants using human motion capture data.

Globally optimal direction fields

Abstract: We present a method for constructing smooth n-direction fields (line fields, cross fields, etc.) on surfaces that is an order of magnitude faster than state-of-the-art methods, while still producing fields of equal or better quality. Fields produced by the method are globally optimal in the sense that they minimize a simple, well-defined quadratic smoothness energy over all possible configurations of singularities (number, location, and index). The method is fully automatic and can optionally produce fields aligned with a given guidance field such as principal curvature directions. Computationally the smoothest field is found via a sparse eigenvalue problem involving a matrix similar to the cotan-Laplacian. When a guidance field is present, finding the optimal field amounts to solving a single linear system.

Digital geometry processing with discrete exterior calculus

Abstract: An introduction to geometry processing using discrete exterior calculus (DEC), which provides a simple, flexible, and efficient framework for building a unified geometry-processing platform. The course provides essential mathematical background as well as a large array of real-world examples. It also provides a short survey of the most relevant recent developments in digital geometry processing and discrete differential geometry. Compared to previous SIGGRAPH courses, this course focuses heavily on practical aspects of DEC, with an emphasis on implementation and applications.The course begins with the core ideas from exterior calculus, in both the smooth and discrete setting. Then it shows how a large number of fundamental geometry-processing tools (smoothing, parameterization, geodesics, mesh optimization, etc.) can be implemented quickly, robustly, and efficiently within this single common framework. It concludes with a discussion of recent extensions of DEC that improve efficiency, accuracy, and versatility.The course notes grew out of the discrete differential geometry course taught over the past five years at the California Institute of Technology, for undergraduates and beginning graduate students in computer science, applied mathematics, and associated fields. The notes also provide guided exercises (both written and coding) that attendees can later use to deepen their understanding of the material.

Computer vision : a modern approach = 计算机视觉 : 一种现代的方法

Abstract: From the Publisher: The accessible presentation of this book gives both a general view of the entire computer vision enterprise and also offers sufficient detail to be able to build useful applications. Users learn techniques that have proven to be useful by first-hand experience and a wide range of mathematical methods. A CD-ROM with every copy of the text contains source code for programming practice, color images, and illustrative movies. Comprehensive and up-to-date, this book includes essential topics that either reflect practical significance or are of theoretical importance. Topics are discussed in substantial and increasing depth. Application surveys describe numerous important application areas such as image based rendering and digital libraries. Many important algorithms broken down and illustrated in pseudo code. Appropriate for use by engineers as a comprehensive reference to the computer vision enterprise.

A Survey of General-Purpose Computation on Graphics Hardware

Abstract: The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware a compelling platform for computationally demanding tasks in a wide variety of application domains. In this report, we describe, summarize, and analyze the latest research in mapping general-purpose computation to graphics hardware. We begin with the technical motivations that underlie general-purpose computation on graphics processors (GPGPU) and describe the hardware and software developments that have led to the recent interest in this field. We then aim the main body of this report at two separate audiences. First, we describe the techniques used in mapping general-purpose computation to graphics hardware. We believe these techniques will be generally useful for researchers who plan to develop the next generation of GPGPU algorithms and techniques. Second, we survey and categorize the latest developments in general-purpose application development on graphics hardware. This survey should be of particular interest to researchers who are interested in using the latest GPGPU applications in their systems of interest.

A Survey of General-Purpose Computation on Graphics Hardware.

Abstract: The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware a compelling platform for computationally demanding tasks in a wide variety of application domains. In this report, we describe, summarize, and analyze the latest research in mapping general-purpose computation to graphics hardware. We begin with the technical motivations that underlie general-purpose computation on graphics processors (GPGPU) and describe the hardware and software developments that have led to the recent interest in this field. We then aim the main body of this report at two separate audiences. First, we describe the techniques used in mapping general-purpose computation to graphics hardware. We believe these techniques will be generally useful for researchers who plan to develop the next generation of GPGPU algorithms and techniques. Second, we survey and categorize the latest developments in general-purpose application development on graphics hardware. This survey should be of particular interest to researchers who are interested in using the latest GPGPU applications in their systems of interest.

Computational Optimal Transport

Abstract: Optimal transport (OT) theory can be informally described using the words of the French mathematician Gaspard Monge (1746-1818): A worker with a shovel in hand has to move a large pile of sand lying on a construction site. The goal of the worker is to erect with all that sand a target pile with a prescribed shape (for example, that of a giant sand castle). Naturally, the worker wishes to minimize her total effort, quantified for instance as the total distance or time spent carrying shovelfuls of sand. Mathematicians interested in OT cast that problem as that of comparing two probability distributions, two different piles of sand of the same volume. They consider all of the many possible ways to morph, transport or reshape the first pile into the second, and associate a "global" cost to every such transport, using the "local" consideration of how much it costs to move a grain of sand from one place to another. Recent years have witnessed the spread of OT in several fields, thanks to the emergence of approximate solvers that can scale to sizes and dimensions that are relevant to data sciences. Thanks to this newfound scalability, OT is being increasingly used to unlock various problems in imaging sciences (such as color or texture processing), computer vision and graphics (for shape manipulation) or machine learning (for regression, classification and density fitting). This short book reviews OT with a bias toward numerical methods and their applications in data sciences, and sheds lights on the theoretical properties of OT that make it particularly useful for some of these applications.

Real-time hand-tracking with a color glove

Abstract: Articulated hand-tracking systems have been widely used in virtual reality but are rarely deployed in consumer applications due to their price and complexity. In this paper, we propose an easy-to-use and inexpensive system that facilitates 3-D articulated user-input using the hands. Our approach uses a single camera to track a hand wearing an ordinary cloth glove that is imprinted with a custom pattern. The pattern is designed to simplify the pose estimation problem, allowing us to employ a nearest-neighbor approach to track hands at interactive rates. We describe several proof-of-concept applications enabled by our system that we hope will provide a foundation for new interactions in modeling, animation control and augmented reality.