Ashok Veeraraghavan

Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing

We describe a theoretical framework for reversibly modulating 4D light fields using an attenuating mask in the optical path of a lens based camera. Based on this framework, we present a novel design to reconstruct the 4D light field from a 2D camera image without any additional refractive elements as required by previous light field cameras. The patterned mask attenuates light rays inside the camera instead of bending them, and the attenuation recoverably encodes the rays on the 2D sensor. Our mask-equipped camera focuses just as a traditional camera to capture conventional 2D photos at full sensor resolution, but the raw pixel values also hold a modulated 4D light field. The light field can be recovered by rearranging the tiles of the 2D Fourier transform of sensor values into 4D planes, and computing the inverse Fourier transform. In addition, one can also recover the full resolution image information for the in-focus parts of the scene. We also show how a broadband mask placed at the lens enables us to compute refocused images at full sensor resolution for layered Lambertian scenes. This partial encoding of 4D ray-space data enables editing of image contents by depth, yet does not require computational recovery of the complete 4D light field.

Matching shape sequences in video with applications in human movement analysis

We present an approach for comparing two sequences of deforming shapes using both parametric models and nonparametric methods. In our approach, Kendalls definition of shape is used for feature extraction. Since the shape feature rests on a non-Euclidean manifold, we propose parametric models like the autoregressive model and autoregressive moving average model on the tangent space and demonstrate the ability of these models to capture the nature of shape deformations using experiments on gait-based human recognition. The nonparametric model is based on dynamic time-warping. We suggest a modification of the dynamic time-warping algorithm to include the nature of the non-Euclidean space in which the shape deformations take place. We also show the efficacy of this algorithm by its application to gait-based human recognition. We exploit the shape deformations of a persons silhouette as a discriminating feature and provide recognition results using the nonparametric model. Our analysis leads to some interesting observations on the role of shape and kinematics in automated gait-based person authentication.

Statistical Computations on Grassmann and Stiefel Manifolds for Image and Video-Based Recognition

In this paper, we examine image and video-based recognition applications where the underlying models have a special structure-the linear subspace structure. We discuss how commonly used parametric models for videos and image sets can be described using the unified framework of Grassmann and Stiefel manifolds. We first show that the parameters of linear dynamic models are finite-dimensional linear subspaces of appropriate dimensions. Unordered image sets as samples from a finite-dimensional linear subspace naturally fall under this framework. We show that an inference over subspaces can be naturally cast as an inference problem on the Grassmann manifold. To perform recognition using subspace-based models, we need tools from the Riemannian geometry of the Grassmann manifold. This involves a study of the geometric properties of the space, appropriate definitions of Riemannian metrics, and definition of geodesics. Further, we derive statistical modeling of inter and intraclass variations that respect the geometry of the space. We apply techniques such as intrinsic and extrinsic statistics to enable maximum-likelihood classification. We also provide algorithms for unsupervised clustering derived from the geometry of the manifold. Finally, we demonstrate the improved performance of these methods in a wide variety of vision applications such as activity recognition, video-based face recognition, object recognition from image sets, and activity-based video clustering.

Recovering three-dimensional shape around a corner using ultrafast time-of-flight imaging

The recovery of objects obscured by scattering is an important goal in imaging and has been approached by exploiting, for example, coherence properties, ballistic photons or penetrating wavelengths. Common methods use scattered light transmitted through an occluding material, although these fail if the occluder is opaque. Light is scattered not only by transmission through objects, but also by multiple reflection from diffuse surfaces in a scene. This reflected light contains information about the scene that becomes mixed by the diffuse reflections before reaching the image sensor. This mixing is difficult to decode using traditional cameras. Here we report the combination of a time-of-flight technique and computational reconstruction algorithms to untangle image information mixed by diffuse reflection. We demonstrate a three-dimensional range camera able to look around a corner using diffusely reflected light that achieves sub-millimetre depth precision and centimetre lateral precision over 40 cm×40 cm×40 cm of hidden space.

The Function Space of an Activity

An activity consists of an actor performing a series of actions in a pre-defined temporal order. An action is an individual atomic unit of an activity. Different instances of the same activity may consist of varying relative speeds at which the various actions are executed, in addition to other intra- and inter- person variabilities. Most existing algorithms for activity recognition are not very robust to intra- and inter-personal changes of the same activity, and are extremely sensitive to warping of the temporal axis due to variations in speed profile. In this paper, we provide a systematic approach to learn the nature of such time warps while simultaneously allowing for the variations in descriptors for actions. For each activity we learn an ‘average’ sequence that we denote as the nominal activity trajectory. We also learn a function space of time warpings for each activity separately. The model can be used to learn individualspecific warping patterns so that it may also be used for activity based person identification. The proposed model leads us to algorithms for learning a model for each activity, clustering activity sequences and activity recognition that are robust to temporal, intra- and inter-person variations. We provide experimental results using two datasets.

Statistical analysis on Stiefel and Grassmann manifolds with applications in computer vision

Many applications in computer vision and pattern recognition involve drawing inferences on certain manifold-valued parameters. In order to develop accurate inference algorithms on these manifolds we need to a) understand the geometric structure of these manifolds b) derive appropriate distance measures and c) develop probability distribution functions (pdf) and estimation techniques that are consistent with the geometric structure of these manifolds. In this paper, we consider two related manifolds - the Stiefel manifold and the Grassmann manifold, which arise naturally in several vision applications such as spatio-temporal modeling, affine invariant shape analysis, image matching and learning theory. We show how accurate statistical characterization that reflects the geometry of these manifolds allows us to design efficient algorithms that compare favorably to the state of the art in these very different applications. In particular, we describe appropriate distance measures and parametric and non-parametric density estimators on these manifolds. These methods are then used to learn class conditional densities for applications such as activity recognition, video based face recognition and shape classification.

Fast directional chamfer matching

We study the object localization problem in images given a single hand-drawn example or a gallery of shapes as the object model. Although many shape matching algorithms have been proposed for the problem over the decades, chamfer matching remains to be the preferred method when speed and robustness are considered. In this paper, we significantly improve the accuracy of chamfer matching while reducing the computational time from linear to sublinear (shown empirically). Specifically, we incorporate edge orientation information in the matching algorithm such that the resulting cost function is piecewise smooth and the cost variation is tightly bounded. Moreover, we present a sublinear time algorithm for exact computation of the directional chamfer matching score using techniques from 3D distance transforms and directional integral images. In addition, the smooth cost function allows to bound the cost distribution of large neighborhoods and skip the bad hypotheses within. Experiments show that the proposed approach improves the speed of the original chamfer matching upto an order of 45x, and it is much faster than many state of art techniques while the accuracy is comparable.

Object Detection, Tracking and Recognition for Multiple Smart Cameras

Video cameras are among the most commonly used sensors in a large number of applications, ranging from surveillance to smart rooms for videoconferencing. There is a need to develop algorithms for tasks such as detection, tracking, and recognition of objects, specifically using distributed networks of cameras. The projective nature of imaging sensors provides ample challenges for data association across cameras. We first discuss the nature of these challenges in the context of visual sensor networks. Then, we show how real-world constraints can be favorably exploited in order to tackle these challenges. Examples of real-world constraints are (a) the presence of a world plane, (b) the presence of a three-dimiensional scene model, (c) consistency of motion across cameras, and (d) color and texture properties. In this regard, the main focus of this paper is towards highlighting the efficient use of the geometric constraints induced by the imaging devices to derive distributed algorithms for target detection, tracking, and recognition. Our discussions are supported by several examples drawn from real applications. Lastly, we also describe several potential research problems that remain to be addressed.

P2C2: Programmable pixel compressive camera for high speed imaging

We describe an imaging architecture for compressive video sensing termed programmable pixel compressive camera (P2C2). P2C2 allows us to capture fast phenomena at frame rates higher than the camera sensor. In P2C2, each pixel has an independent shutter that is modulated at a rate higher than the camera frame-rate. The observed intensity at a pixel is an integration of the incoming light modulated by its specific shutter. We propose a reconstruction algorithm that uses the data from P2C2 along with additional priors about videos to perform temporal super-resolution. We model the spatial redundancy of videos using sparse representations and the temporal redundancy using brightness constancy constraints inferred via optical flow. We show that by modeling such spatio-temporal redundancies in a video volume, one can faithfully recover the underlying high-speed video frames from the observed low speed coded video. The imaging architecture and the reconstruction algorithm allows us to achieve temporal super-resolution without loss in spatial resolution. We implement a prototype of P2C2 using an LCOS modulator and recover several videos at 200 fps using a 25 fps camera.

Role of shape and kinematics in human movement analysis

Human gait and activity analysis from video is presently attracting a lot of attention in the computer vision community. In this paper we analyze the role of two of the most important cues in human motion-shape and kinematics. We present an experimental framework whereby it is possible to evaluate the relative importance of these two cues in computer vision based recognition algorithms. In the process, we propose a new gait recognition algorithm by computing the distance between two sequences of shapes that lie on a spherical manifold. In our experiments, shape is represented using Kendalls definition of shape. Kinematics is represented using a Linear Dynamical system We place particular emphasis on human gait. Our conclusions show that shape plays a role which is more significant than kinematics in current automated gait based human identification algorithms. As a natural extension we study the role of shape and kinematics in activity recognition. Our experiments indicate that we require models that contain both shape and kinematics in order to perform accurate activity classification. These conclusions also allow us to explain the relative performance of many existing methods in computer-based human activity modeling.