Spatial Reference Frames for Object Recognition: Tuning for Rotations in Depth

The inferior temporal cortex (IT) of monkeys is thought to play an essential role in visual object recognition. Inferotemporal neurons are known to respond to complex visual stimuli, including patterns like faces, hands, or other body parts. What is the role of such neurons in object recognition? The present study examines this question in combined psychophysical and electrophysiological experiments, in which monkeys learned to classify and recognize novel visual 3D objects. A population of neurons in IT were found to respond selectively to such objects that the monkeys had recently learned to recognize. A large majority of these cells discharged maximally for one view of the object, while their response fell off gradually as the object was rotated away from the neuron"s preferred view. Most neurons exhibited orientation-dependent responses also during view-plane rotations. Some neurons were found tuned around two views of the same object, while a very small number of cells responded in a view- invariant manner. For five different objects that were extensively used during the training of the animals, and for which behavioral performance became view-independent, multiple cells were found that were tuned around different views of the same object. No selective responses were ever encountered for views that the animal systematically failed to recognize. The results of our experiments suggest that neurons in this area can develop a complex receptive field organization as a consequence of extensive training in the discrimination and recognition of objects. Simple geometric features did not appear to account for the neurons" selective responses. These findings support the idea that a population of neurons -- each tuned to a different object aspect, and each showing a certain degree of invariance to image transformations -- may, as an assembly, encode complex 3D objects. In such a system, several neurons may be active for any given vantage point, with a single unit acting like a blurred template for a limited neighborhood of a single view.

Fast Pose Estimation with Parameter Sensitive Hashing

Example-based methods are effective for parameter estimation problems when the underlying system is simple or the dimensionality of the input is low. For complex and high-dimensional problems such as pose estimation, the number of required examples and the computational complexity rapidly becme prohibitively high. We introduce a new algorithm that learns a set of hashing functions that efficiently index examples relevant to a particular estimation task. Our algorithm extends a recently developed method for locality-sensitive hashing, which finds approximate neighbors in time sublinear in the number of examples. This method depends critically on the choice of hash functions; we show how to find the set of hash functions that are optimally relevant to a particular estimation problem. Experiments demonstrate that the resulting algorithm, which we call Parameter-Sensitive Hashing, can rapidly and accurately estimate the articulated pose of human figures from a large database of example images.

Parameter Estimation in Chaotic Systems

This report examines how to estimate the parameters of a chaotic system given noisy observations of the state behavior of the system. Investigating parameter estimation for chaotic systems is interesting because of possible applications for high-precision measurement and for use in other signal processing, communication, and control applications involving chaotic systems. In this report, we examine theoretical issues regarding parameter estimation in chaotic systems and develop an efficient algorithm to perform parameter estimation. We discover two properties that are helpful for performing parameter estimation on non-structurally stable systems. First, it turns out that most data in a time series of state observations contribute very little information about the underlying parameters of a system, while a few sections of data may be extraordinarily sensitive to parameter changes. Second, for one-parameter families of systems, we demonstrate that there is often a preferred direction in parameter space governing how easily trajectories of one system can "shadow'" trajectories of nearby systems. This asymmetry of shadowing behavior in parameter space is proved for certain families of maps of the interval. Numerical evidence indicates that similar results may be true for a wide variety of other systems. Using the two properties cited above, we devise an algorithm for performing parameter estimation. Standard parameter estimation techniques such as the extended Kalman filter perform poorly on chaotic systems because of divergence problems. The proposed algorithm achieves accuracies several orders of magnitude better than the Kalman filter and has good convergence properties for large data sets.

Modeling Invariances in Inferotemporal Cell Tuning

In macaque inferotemporal cortex (IT), neurons have been found to respond selectively to complex shapes while showing broad tuning ("invariance") with respect to stimulus transformations such as translation and scale changes and a limited tuning to rotation in depth. Training monkeys with novel, paperclip-like objects, Logothetis et al. could investigate whether these invariance properties are due to experience with exhaustively many transformed instances of an object or if there are mechanisms that allow the cells to show response invariance also to previously unseen instances of that object. They found object-selective cells in anterior IT which exhibited limited invariance to various transformations after training with single object views. While previous models accounted for the tuning of the cells for rotations in depth and for their selectivity to a specific object relative to a population of distractor objects, the model described here attempts to explain in a biologically plausible way the additional properties of translation and size invariance. Using the same stimuli as in the experiment, we find that model IT neurons exhibit invariance properties which closely parallel those of real neurons. Simulations show that the model is capable of unsupervised learning of view-tuned neurons. The model also allows to make experimentally testable predictions regarding novel stimulus transformations and combinations of stimuli.

Certified Rapid Solution of Parametrized Linear Elliptic Equations: Application to Parameter Estimation

We present a technique for the rapid and reliable evaluation of linear-functional output of elliptic partial differential equations with affine parameter dependence. The essential components are (i) rapidly uniformly convergent reduced-basis approximations — Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N (optimally) selected points in parameter space; (ii) a posteriori error estimation — relaxations of the residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs; and (iii) offline/online computational procedures — stratagems that exploit affine parameter dependence to de-couple the generation and projection stages of the approximation process. The operation count for the online stage — in which, given a new parameter value, we calculate the output and associated error bound — depends only on N (typically small) and the parametric complexity of the problem. The method is thus ideally suited to the many-query and real-time contexts. In this paper, based on the technique we develop a robust inverse computational method for very fast solution of inverse problems characterized by parametrized partial differential equations. The essential ideas are in three-fold: first, we apply the technique to the forward problem for the rapid certified evaluation of PDE input-output relations and associated rigorous error bounds; second, we incorporate the reduced-basis approximation and error bounds into the inverse problem formulation; and third, rather than regularize the goodness-of-fit objective, we may instead identify all (or almost all, in the probabilistic sense) system configurations consistent with the available experimental data — well-posedness is reflected in a bounded "possibility region" that furthermore shrinks as the experimental error is decreased.