Recursive Estimation of Motion and Planar Structure

A specialized formulation of Azarbayejani and Pentland's framework for recursive recovery of motion, structure and focal length from feature correspondences tracked through an image sequence is presented. The specialized formulation addresses the case where all tracked points lie on a plane. This planarity constraint reduces the dimension of the original state vector, and consequently the number of feature points needed to estimate the state. Experiments with synthetic data and real imagery illustrate the system performance. The experiments confirm that the specialized formulation provides improved accuracy, stability to observation noise, and rate of convergence in estimation for the case where the tracked points lie on a plane.

Handsignals Recognition From Video Using 3D Motion Capture Data

Hand signals are commonly used in applications such as giving instructions to a pilot for airplane take off or direction of a crane operator by a foreman on the ground. A new algorithm for recognizing hand signals from a single camera is proposed. Typically, tracked 2D feature positions of hand signals are matched to 2D training images. In contrast, our approach matches the 2D feature positions to an archive of 3D motion capture sequences. The method avoids explicit reconstruction of the 3D articulated motion from 2D image features. Instead, the matching between the 2D and 3D sequence is done by backprojecting the 3D motion capture data onto 2D. Experiments demonstrate the effectiveness of the approach in an example application: recognizing six classes of basketball referee hand signals in video.

Simultaneous Learning of Nonlinear Manifold and Dynamical Models for High-dimensional Time Series

The goal of this work is to learn a parsimonious and informative representation for high-dimensional time series. Conceptually, this comprises two distinct yet tightly coupled tasks: learning a low-dimensional manifold and modeling the dynamical process. These two tasks have a complementary relationship as the temporal constraints provide valuable neighborhood information for dimensionality reduction and conversely, the low-dimensional space allows dynamics to be learnt efficiently. Solving these two tasks simultaneously allows important information to be exchanged mutually. If nonlinear models are required to capture the rich complexity of time series, then the learning problem becomes harder as the nonlinearities in both tasks are coupled. The proposed solution approximates the nonlinear manifold and dynamics using piecewise linear models. The interactions among the linear models are captured in a graphical model. By exploiting the model structure, efficient inference and learning algorithms are obtained without oversimplifying the model of the underlying dynamical process. Evaluation of the proposed framework with competing approaches is conducted in three sets of experiments: dimensionality reduction and reconstruction using synthetic time series, video synthesis using a dynamic texture database, and human motion synthesis, classification and tracking on a benchmark data set. In all experiments, the proposed approach provides superior performance.

Simultaneous Learning of Non-Linear Manifold and Dynamical Models for High-Dimensional Time Series

The goal of this work is to learn a parsimonious and informative representation for high-dimensional time series. Conceptually, this comprises two distinct yet tightly coupled tasks: learning a low-dimensional manifold and modeling the dynamical process. These two tasks have a complementary relationship as the temporal constraints provide valuable neighborhood information for dimensionality reduction and conversely, the low-dimensional space allows dynamics to be learnt efficiently. Solving these two tasks simultaneously allows important information to be exchanged mutually. If nonlinear models are required to capture the rich complexity of time series, then the learning problem becomes harder as the nonlinearities in both tasks are coupled. The proposed solution approximates the nonlinear manifold and dynamics using piecewise linear models. The interactions among the linear models are captured in a graphical model. The model structure setup and parameter learning are done using a variational Bayesian approach, which enables automatic Bayesian model structure selection, hence solving the problem of over-fitting. By exploiting the model structure, efficient inference and learning algorithms are obtained without oversimplifying the model of the underlying dynamical process. Evaluation of the proposed framework with competing approaches is conducted in three sets of experiments: dimensionality reduction and reconstruction using synthetic time series, video synthesis using a dynamic texture database, and human motion synthesis, classification and tracking on a benchmark data set. In all experiments, the proposed approach provides superior performance.

Task-Irrelevant Perceptual Learning Specific to the Contrast Polarity of Motion Stimuli

Studies of perceptual learning have focused on aspects of learning that are related to early stages of sensory processing. However, conclusions that perceptual learning results in low-level sensory plasticity are of great controversy, largely because such learning can often be attributed to plasticity in later stages of sensory processing or in the decision processes. To address this controversy, we developed a novel random dot motion (RDM) stimulus to target motion cells selective to contrast polarity, by ensuring the motion direction information arises only from signal dot onsets and not their offsets, and used these stimuli in conjunction with the paradigm of task-irrelevant perceptual learning (TIPL). In TIPL, learning is achieved in response to a stimulus by subliminally pairing that stimulus with the targets of an unrelated training task. In this manner, we are able to probe learning for an aspect of motion processing thought to be a function of directional V1 simple cells with a learning procedure that dissociates the learned stimulus from the decision processes relevant to the training task. Our results show learning for the exposed contrast polarity and that this learning does not transfer to the unexposed contrast polarity. These results suggest that TIPL for motion stimuli may occur at the stage of directional V1 simple cells.

Neural Dynamics of Motion Perception, Recognition Learning, and Spatial Attention

Advanced Research Projects Agency (ONR N00014-92-J-4015); National Science Foundation (IRI-90-24877); Office of Naval Research (N00014-91-J-4100)

The Specialized Mappings Architecture

A probabilistic, nonlinear supervised learning model is proposed: the Specialized Mappings Architecture (SMA). The SMA employs a set of several forward mapping functions that are estimated automatically from training data. Each specialized function maps certain domains of the input space (e.g., image features) onto the output space (e.g., articulated body parameters). The SMA can model ambiguous, one-to-many mappings that may yield multiple valid output hypotheses. Once learned, the mapping functions generate a set of output hypotheses for a given input via a statistical inference procedure. The SMA inference procedure incorporates an inverse mapping or feedback function in evaluating the likelihood of each of the hypothesis. Possible feedback functions include computer graphics rendering routines that can generate images for given hypotheses. The SMA employs a variant of the Expectation-Maximization algorithm for simultaneous learning of the specialized domains along with the mapping functions, and approximate strategies for inference. The framework is demonstrated in a computer vision system that can estimate the articulated pose parameters of a human’s body or hands, given silhouettes from a single image. The accuracy and stability of the SMA are also tested using synthetic images of human bodies and hands, where ground truth is known.

Learning Euclidean Embeddings for Indexing and Classification

BoostMap is a recently proposed method for efficient approximate nearest neighbor retrieval in arbitrary non-Euclidean spaces with computationally expensive and possibly non-metric distance measures. Database and query objects are embedded into a Euclidean space, in which similarities can be rapidly measured using a weighted Manhattan distance. The key idea is formulating embedding construction as a machine learning task, where AdaBoost is used to combine simple, 1D embeddings into a multidimensional embedding that preserves a large amount of the proximity structure of the original space. This paper demonstrates that, using the machine learning formulation of BoostMap, we can optimize embeddings for indexing and classification, in ways that are not possible with existing alternatives for constructive embeddings, and without additional costs in retrieval time. First, we show how to construct embeddings that are query-sensitive, in the sense that they yield a different distance measure for different queries, so as to improve nearest neighbor retrieval accuracy for each query. Second, we show how to optimize embeddings for nearest neighbor classification tasks, by tuning them to approximate a parameter space distance measure, instead of the original feature-based distance measure.

Specialized Mappings Architecture with Applications to Vision-based Estimation of Articulated Body Pose

A fundamental task of vision systems is to infer the state of the world given some form of visual observations. From a computational perspective, this often involves facing an ill-posed problem; e.g., information is lost via projection of the 3D world into a 2D image. Solution of an ill-posed problem requires additional information, usually provided as a model of the underlying process. It is important that the model be both computationally feasible as well as theoretically well-founded. In this thesis, a probabilistic, nonlinear supervised computational learning model is proposed: the Specialized Mappings Architecture (SMA). The SMA framework is demonstrated in a computer vision system that can estimate the articulated pose parameters of a human body or human hands, given images obtained via one or more uncalibrated cameras. The SMA consists of several specialized forward mapping functions that are estimated automatically from training data, and a possibly known feedback function. Each specialized function maps certain domains of the input space (e.g., image features) onto the output space (e.g., articulated body parameters). A probabilistic model for the architecture is first formalized. Solutions to key algorithmic problems are then derived: simultaneous learning of the specialized domains along with the mapping functions, as well as performing inference given inputs and a feedback function. The SMA employs a variant of the Expectation-Maximization algorithm and approximate inference. The approach allows the use of alternative conditional independence assumptions for learning and inference, which are derived from a forward model and a feedback model. Experimental validation of the proposed approach is conducted in the task of estimating articulated body pose from image silhouettes. Accuracy and stability of the SMA framework is tested using artificial data sets, as well as synthetic and real video sequences of human bodies and hands.

Articulated Pose Estimation in a Learned Smooth Space of Feasible Solutions

A learning based framework is proposed for estimating human body pose from a single image. Given a differentiable function that maps from pose space to image feature space, the goal is to invert the process: estimate the pose given only image features. The inversion is an ill-posed problem as the inverse mapping is a one to many process. Hence multiple solutions exist, and it is desirable to restrict the solution space to a smaller subset of feasible solutions. For example, not all human body poses are feasible due to anthropometric constraints. Since the space of feasible solutions may not admit a closed form description, the proposed framework seeks to exploit machine learning techniques to learn an approximation that is smoothly parameterized over such a space. One such technique is Gaussian Process Latent Variable Modelling. Scaled conjugate gradient is then used find the best matching pose in the space of feasible solutions when given an input image. The formulation allows easy incorporation of various constraints, e.g. temporal consistency and anthropometric constraints. The performance of the proposed approach is evaluated in the task of upper-body pose estimation from silhouettes and compared with the Specialized Mapping Architecture. The estimation accuracy of the Specialized Mapping Architecture is at least one standard deviation worse than the proposed approach in the experiments with synthetic data. In experiments with real video of humans performing gestures, the proposed approach produces qualitatively better estimation results.

Learning Embeddings for Indexing, Retrieval, and Classification, with Applications to Object and Shape Recognition in Image Databases

Nearest neighbor retrieval is the task of identifying, given a database of objects and a query object, the objects in the database that are the most similar to the query. Retrieving nearest neighbors is a necessary component of many practical applications, in fields as diverse as computer vision, pattern recognition, multimedia databases, bioinformatics, and computer networks. At the same time, finding nearest neighbors accurately and efficiently can be challenging, especially when the database contains a large number of objects, and when the underlying distance measure is computationally expensive. This thesis proposes new methods for improving the efficiency and accuracy of nearest neighbor retrieval and classification in spaces with computationally expensive distance measures. The proposed methods are domain-independent, and can be applied in arbitrary spaces, including non-Euclidean and non-metric spaces. In this thesis particular emphasis is given to computer vision applications related to object and shape recognition, where expensive non-Euclidean distance measures are often needed to achieve high accuracy. The first contribution of this thesis is the BoostMap algorithm for embedding arbitrary spaces into a vector space with a computationally efficient distance measure. Using this approach, an approximate set of nearest neighbors can be retrieved efficiently - often orders of magnitude faster than retrieval using the exact distance measure in the original space. The BoostMap algorithm has two key distinguishing features with respect to existing embedding methods. First, embedding construction explicitly maximizes the amount of nearest neighbor information preserved by the embedding. Second, embedding construction is treated as a machine learning problem, in contrast to existing methods that are based on geometric considerations. The second contribution is a method for constructing query-sensitive distance measures for the purposes of nearest neighbor retrieval and classification. In high-dimensional spaces, query-sensitive distance measures allow for automatic selection of the dimensions that are the most informative for each specific query object. It is shown theoretically and experimentally that query-sensitivity increases the modeling power of embeddings, allowing embeddings to capture a larger amount of the nearest neighbor structure of the original space. The third contribution is a method for speeding up nearest neighbor classification by combining multiple embedding-based nearest neighbor classifiers in a cascade. In a cascade, computationally efficient classifiers are used to quickly classify easy cases, and classifiers that are more computationally expensive and also more accurate are only applied to objects that are harder to classify. An interesting property of the proposed cascade method is that, under certain conditions, classification time actually decreases as the size of the database increases, a behavior that is in stark contrast to the behavior of typical nearest neighbor classification systems. The proposed methods are evaluated experimentally in several different applications: hand shape recognition, off-line character recognition, online character recognition, and efficient retrieval of time series. In all datasets, the proposed methods lead to significant improvements in accuracy and efficiency compared to existing state-of-the-art methods. In some datasets, the general-purpose methods introduced in this thesis even outperform domain-specific methods that have been custom-designed for such datasets.

SOVEREIGN: A Self-Organizing, Vision, Expectation, Recognition, Emotion, Intelligent, Goal-Oriented Navigation System

Both animals and mobile robots, or animats, need adaptive control systems to guide their movements through a novel environment. Such control systems need reactive mechanisms for exploration, and learned plans to efficiently reach goal objects once the environment is familiar. How reactive and planned behaviors interact together in real time, and arc released at the appropriate times, during autonomous navigation remains a major unsolved problern. This work presents an end-to-end model to address this problem, named SOVEREIGN: A Self-Organizing, Vision, Expectation, Recognition, Emotion, Intelligent, Goal-oriented Navigation system. The model comprises several interacting subsystems, governed by systems of nonlinear differential equations. As the animat explores the environment, a vision module processes visual inputs using networks that arc sensitive to visual form and motion. Targets processed within the visual form system arc categorized by real-time incremental learning. Simultaneously, visual target position is computed with respect to the animat's body. Estimates of target position activate a motor system to initiate approach movements toward the target. Motion cues from animat locomotion can elicit orienting head or camera movements to bring a never target into view. Approach and orienting movements arc alternately performed during animat navigation. Cumulative estimates of each movement, based on both visual and proprioceptive cues, arc stored within a motor working memory. Sensory cues are stored in a parallel sensory working memory. These working memories trigger learning of sensory and motor sequence chunks, which together control planned movements. Effective chunk combinations arc selectively enhanced via reinforcement learning when the animat is rewarded. The planning chunks effect a gradual transition from reactive to planned behavior. The model can read-out different motor sequences under different motivational states and learns more efficient paths to rewarded goals as exploration proceeds. Several volitional signals automatically gate the interactions between model subsystems at appropriate times. A 3-D visual simulation environment reproduces the animat's sensory experiences as it moves through a simplified spatial environment. The SOVEREIGN model exhibits robust goal-oriented learning of sequential motor behaviors. Its biomimctic structure explicates a number of brain processes which are involved in spatial navigation.

Estimating Sensor Motion from Wide-Field Optical Flow on a Log-Dipolar Sensor

Log-polar image architectures, motivated by the structure of the human visual field, have long been investigated in computer vision for use in estimating motion parameters from an optical flow vector field. Practical problems with this approach have been: (i) dependence on assumed alignment of the visual and motion axes; (ii) sensitivity to occlusion form moving and stationary objects in the central visual field, where much of the numerical sensitivity is concentrated; and (iii) inaccuracy of the log-polar architecture (which is an approximation to the central 20°) for wide-field biological vision. In the present paper, we show that an algorithm based on generalization of the log-polar architecture; termed the log-dipolar sensor, provides a large improvement in performance relative to the usual log-polar sampling. Specifically, our algorithm: (i) is tolerant of large misalignmnet of the optical and motion axes; (ii) is insensitive to significant occlusion by objects of unknown motion; and (iii) represents a more correct analogy to the wide-field structure of human vision. Using the Helmholtz-Hodge decomposition to estimate the optical flow vector field on a log-dipolar sensor, we demonstrate these advantages, using synthetic optical flow maps as well as natural image sequences.

SOVEREIGN: An Autonomous Neural System for Incrementally Learning Planned Action Sequence to Navigate Towards a Rewarded Goal

How do reactive and planned behaviors interact in real time? How are sequences of such behaviors released at appropriate times during autonomous navigation to realize valued goals? Controllers for both animals and mobile robots, or animats, need reactive mechanisms for exploration, and learned plans to reach goal objects once an environment becomes familiar. The SOVEREIGN (Self-Organizing, Vision, Expectation, Recognition, Emotion, Intelligent, Goaloriented Navigation) animat model embodies these capabilities, and is tested in a 3D virtual reality environment. SOVEREIGN includes several interacting subsystems which model complementary properties of cortical What and Where processing streams and which clarify similarities between mechanisms for navigation and arm movement control. As the animat explores an environment, visual inputs are processed by networks that are sensitive to visual form and motion in the What and Where streams, respectively. Position-invariant and sizeinvariant recognition categories are learned by real-time incremental learning in the What stream. Estimates of target position relative to the animat are computed in the Where stream, and can activate approach movements toward the target. Motion cues from animat locomotion can elicit head-orienting movements to bring a new target into view. Approach and orienting movements are alternately performed during animat navigation. Cumulative estimates of each movement are derived from interacting proprioceptive and visual cues. Movement sequences are stored within a motor working memory. Sequences of visual categories are stored in a sensory working memory. These working memories trigger learning of sensory and motor sequence categories, or plans, which together control planned movements. Predictively effective chunk combinations are selectively enhanced via reinforcement learning when the animat is rewarded. Selected planning chunks effect a gradual transition from variable reactive exploratory movements to efficient goal-oriented planned movement sequences. Volitional signals gate interactions between model subsystems and the release of overt behaviors. The model can control different motor sequences under different motivational states and learns more efficient sequences to rewarded goals as exploration proceeds.

Cortical Learning of Recognition Categories: A Resolution of the Exemplar Vs. Prototype Debate

Do humans and animals learn exemplars or prototypes when they categorize objects and events in the world? How are different degrees of abstraction realized through learning by neurons in inferotemporal and prefrontal cortex? How do top-down expectations influence the course of learning? Thirty related human cognitive experiments (the 5-4 category structure) have been used to test competing views in the prototype-exemplar debate. In these experiments, during the test phase, subjects unlearn in a characteristic way items that they had learned to categorize perfectly in the training phase. Many cognitive models do not describe how an individual learns or forgets such categories through time. Adaptive Resonance Theory (ART) neural models provide such a description, and also clarify both psychological and neurobiological data. Matching of bottom-up signals with learned top-down expectations plays a key role in ART model learning. Here, an ART model is used to learn incrementally in response to 5-4 category structure stimuli. Simulation results agree with experimental data, achieving perfect categorization in training and a good match to the pattern of errors exhibited by human subjects in the testing phase. These results show how the model learns both prototypes and certain exemplars in the training phase. ART prototypes are, however, unlike the ones posited in the traditional prototype-exemplar debate. Rather, they are critical patterns of features to which a subject learns to pay attention based on past predictive success and the order in which exemplars are experienced. Perturbations of old memories by newly arriving test items generate a performance curve that closely matches the performance pattern of human subjects. The model also clarifies exemplar-based accounts of data concerning amnesia.