Coordinate-Independent Computations on Differential Equations

This project investigates the computational representation of differentiable manifolds, with the primary goal of solving partial differential equations using multiple coordinate systems on general n- dimensional spaces. In the process, this abstraction is used to perform accurate integrations of ordinary differential equations using multiple coordinate systems. In the case of linear partial differential equations, however, unexpected difficulties arise even with the simplest equations.

Context-Based Vision System for Place and Object Recognition

While navigating in an environment, a vision system has to be able to recognize where it is and what the main objects in the scene are. In this paper we present a context-based vision system for place and object recognition. The goal is to identify familiar locations (e.g., office 610, conference room 941, Main Street), to categorize new environments (office, corridor, street) and to use that information to provide contextual priors for object recognition (e.g., table, chair, car, computer). We present a low-dimensional global image representation that provides relevant information for place recognition and categorization, and how such contextual information introduces strong priors that simplify object recognition. We have trained the system to recognize over 60 locations (indoors and outdoors) and to suggest the presence and locations of more than 20 different object types. The algorithm has been integrated into a mobile system that provides real-time feedback to the user.

Sharing visual features for multiclass and multiview object detection

We consider the problem of detecting a large number of different classes of objects in cluttered scenes. Traditional approaches require applying a battery of different classifiers to the image, at multiple locations and scales. This can be slow and can require a lot of training data, since each classifier requires the computation of many different image features. In particular, for independently trained detectors, the (run-time) computational complexity, and the (training-time) sample complexity, scales linearly with the number of classes to be detected. It seems unlikely that such an approach will scale up to allow recognition of hundreds or thousands of objects. We present a multi-class boosting procedure (joint boosting) that reduces the computational and sample complexity, by finding common features that can be shared across the classes (and/or views). The detectors for each class are trained jointly, rather than independently. For a given performance level, the total number of features required, and therefore the computational cost, is observed to scale approximately logarithmically with the number of classes. The features selected jointly are closer to edges and generic features typical of many natural structures instead of finding specific object parts. Those generic features generalize better and reduce considerably the computational cost of an algorithm for multi-class object detection.

Contextual models for object detection using boosted random fields

We seek to both detect and segment objects in images. To exploit both local image data as well as contextual information, we introduce Boosted Random Fields (BRFs), which uses Boosting to learn the graph structure and local evidence of a conditional random field (CRF). The graph structure is learned by assembling graph fragments in an additive model. The connections between individual pixels are not very informative, but by using dense graphs, we can pool information from large regions of the image; dense models also support efficient inference. We show how contextual information from other objects can improve detection performance, both in terms of accuracy and speed, by using a computational cascade. We apply our system to detect stuff and things in office and street scenes.

A Low Power Wide Dynamic Range Envelope Detector

We report a 75dB, 2.8mW, 100Hz-10kHz envelope detector in a 1.5mm 2.8V CMOS technology. The envelope detector performs input-dc-insensitive voltage-to-currentconverting rectification followed by novel nanopower current-mode peak detection. The use of a subthreshold wide- linear-range transconductor (WLR OTA) allows greater than 1.7Vpp input voltage swings. We show theoretically that this optimal performance is technology-independent for the given topology and may be improved only by spending more power. A novel circuit topology is used to perform 140nW peak detection with controllable attack and release time constants. The lower limits of envelope detection are determined by the more dominant of two effects: The first effect is caused by the inability of amplified high-frequency signals to exceed the deadzone created by exponential nonlinearities in the rectifier. The second effect is due to an output current caused by thermal noise rectification. We demonstrate good agreement of experimentally measured results with theory. The envelope detector is useful in low power bionic implants for the deaf, hearing aids, and speech-recognition front ends. Extension of the envelope detector to higher- frequency applications is straightforward if power consumption is inc

Dynamically Stable Legged Locomotion (September 1985-Septembers1989)

This report documents our work in exploring active balance for dynamic legged systems for the period from September 1985 through September 1989. The purpose of this research is to build a foundation of knowledge that can lead both to the construction of useful legged vehicles and to a better understanding of animal locomotion. In this report we focus on the control of biped locomotion, the use of terrain footholds, running at high speed, biped gymnastics, symmetry in running, and the mechanical design of articulated legs.