We formulate face alignment as a model-based parameter estimation problem in this paper. First, we work within a framework that combines two separate subspace models to represent frontal face patterns and pose change independently. The combined unified nonlinear model represents varying pose faces with a complex manifold. Then, we use a feature based similarity measure (FBSM) to evaluate image differences in terms of pose, and match unknown pose faces with the model image using a combined feature-feature similarity measure (FTSM). Noticeable properties of the combined FTSM include (1) its sensitivity to spatial differences between feature points in two images, which is crucial to aligning two initially faraway poses; (2) easy determination of hill-climb directions in parameter space, without computing gradients of error functions. Experimental results demonstrate that, in the absence of significant clutter, a face alignment algorithm using the combined FTSM, can reliably align varying pose faces under different lighting conditions, even when initial poses are far off.

This paper presents an automatic method for simultaneous human face detection and facial feature registration from colour video images. At the first stage, we use a skin colour Gaussian model to identify possible face locations under varying pose. Secondly, we compare image patterns with a varying pose face model in terms of shape and texture differences, using a combined feature-texture similarity measure (FTSM). False detections from the first stage are eliminated by setting an appropriate FTSM threshold. Moreover, one can also register the facial features (eyes, nose and mouth) by aligning a prototype face with the unknown pose faces. Experimental results show that the proposed method can achieve reliable face detection and feature registration under various conditions, including different poses, face appearances, and lighting conditions.

This paper describes a novel method for constructing triangle meshes from noisy and non-uniformly distributed 3D points. It consists of two steps: noise point removal uses a clustering algorithm and epipolar constraint method to identify and remove noise points from the 3D points; and a constructive polygonization algorithm interpolates cleaned 3D points to construct a triangle mesh of the object.

As databases for real-world problems increase in size, there is a need in many situations to select and keep relevant training data for efficient storage and processing reasons.Support vector machines (SVMs) reportedly exhibit certain desirable properties in selecting and preserving useful training data as support vectors.This paper attempts to quantify the extent to which SVM training behaves like a model independent example selection procedure.Using several common machine-learning training databases, we compare the prediction results obtained by different classifiers, trained with data selected by SVMs and by two other example selection methods (IB2 and random sampling).Some interesting observations are made with explanations.

With the increase in the size of real-world databases, there is an ever-increasing need to scale up inductive learning algorithms.Incremental learning techniques are one possible solution to the scalability problem.In this paper, we propose three ctiteria to evaluate the robustness and reliability of incremental learning methods, and use them to study the robustness of an incremental training method for Support Vector Machines.We provide empirical results using benchmark machine learning datasets to show that support vectors form a svccdnct and suficient set for block-by-block incremental learning.

We present an example-based learning approach for locating vertical frontal views of human faces in complex scenes. The technique models the distribution of human face patterns by means of a few view-based "face" and "nonface" model clusters. At each image location, a difference feature vector is computed between the local image pattern and the distribution-based model. A trained classifier determines, based on the difference feature vector measurements, whether or not a human face exists at the current image location. We show empirically that the distance metric we adopt for computing difference feature vectors, and the "nonface" clusters we include in our distribution-based model, are both critical for the success of our system.

Video and audio conferencing over networks is becoming increasingly popular due to the availability of video and audio I/O as standard equipment on many computer systems. So far, many algorithms have concentrated on playback only capability. This generally results in unacceptable real-time performance with respect to latency and encoder complexity. We describe a software-only system that allows full duplex video communication. For our analysis and implementation we chose a DCT based method that uses motion estimation and is modelled on the CCITT H.261 standard. We discuss the algorithm, followed by an analysis of the computational requirements for each major block. The results presented show the effect of computational simplifications on signal to noise ratio and image quality. We also examine the processing needs for full resolution coding and project when this will become available.

We develop a principled strategy to sample a function optimally for function approximation tasks within a Bayesian framework. Using ideas from optimal experiment design, we introduce an objective function (incorporating both bias and variance) to measure the de(cid:173) gree of approximation, and the potential utility of the data points towards optimizing this objective. We show how the general strat(cid:173) egy can be used to derive precise algorithms to select data for two cases: learning unit step functions and polynomial functions. In particular, we investigate whether such active algorithms can learn the target with fewer examples. We obtain theoretical and empir(cid:173) ical results to suggest that this is the case. INTRODUCTION AND MOTIVATION 1 Learning from examples is a common supervised learning paradigm that hypothe(cid:173) sizes a target concept given a stream of training examples that describes the concept. In function approximation, example-based learning can be formulated as synthesiz(cid:173) ing an approximation function for data sampled from an unknown target function (Poggio and Girosi, 1990). Active learning describes a class of example-based learning paradigms that seeks out new training examples from specific regions of the input space, instead of passively accepting examples from some data generating source. By judiciously selecting ex- 594 Kah Kay Sung, Parlha Niyogi amples instead of allowing for possible random sampling, active learning techniques can conceivably have faster learning rates and better approximation results than passive learning methods. This paper presents a Bayesian formulation for active learning within the function approximation framework. Specifically, here is the problem we want to address: Let Dn = {(Xi, Yi)li = 1, ... , n} be a set of n data points sampled from an unknown target function g, possibly in the presence of noise. Given an approximation func(cid:173) tion concept class, :F, where each f E :F has prior probability P;:-[J], one can use regularization techniques to approximate 9 from Dn (in the Bayes optimal sense) by means of a function 9 E:F. We want a strategy to determine at what input location one should sample the next data point, (XN+l, YN+d, in order to obtain the "best" possible Bayes optimal approximation of the unknown target function 9 with our concept class :F. The data sampling problem consists of two parts: 1) Defining what we mean by the "best" possible Bayes optimal ap(cid:173) proximation of an unknown target function. In this paper, we propose an optimality criterion for evaluating the "goodness" of a solution with respect to an unknown target function. 2) Formalizing precisely the task of determining where in input space to sample the next data point. We express the above mentioned optimality criterion as a cost function to be minimized, and the task of choosing the next sample as one of minimizing the cost function with respect to the input space location of the next sample point. Earlier work (Cohn, 1991; MacKay, 1992) have tried to use similar optimal experi(cid:173) ment design (Fedorov, 1972) techniques to collect data that would provide maximum information about the target function. Our work differs from theirs in several re(cid:173) spects. First, we use a different, and perhaps more general, optimality criterion for evaluating solutions to an unknown target function, based on a measure of function uncertainty that incorporates both bias and variance components of the total output generalization error. In contrast, MacKay and Cohn use only variance components in model parameter space. Second, we address the important sample complexity question, i.e., does the active strategy require fewer examples to learn the target to the same degree of uncertainty? Our results are stated in PAC-style (Valiant, 1984). After completion of this work, we learnt that Sollich (1994) had also recently developed a similar formulation to ours. His analysis is conducted in a statistical physics framework. The rest of the paper is organized as follows: Section 2, develops our active sampling paradigm. In Sections 3 and 4, we consider two classes offunctions for which active strategies are obtained, and investigate their performance both theoretically and empirically. 2 THE MATHEMATICAL FRAMEWORK In order to optimally select examples for a learning task, one should first have a clear notion of what an "ideal" learning goal is for the task. We can then measure an example's utility in terms of how well the example helps the learner achieve the Active Learning for Function Approximation 595 goal, and devise an active sampling strategy that selects examples with maximum potential utility. In this section, we propose one such learning goal - to find an approximation function g E :F that "best" estimates the unknown target function g. We then derive an example utility cost function for the goal and finally present a general procedure for selecting examples. 2.1 EVALUATING A SOLUTION TO AN UNKNOWN TARGET - THE EXPECTED INTEGRATED SQUARED DIFFERENCE Let 9 be the target function that we want to estimate by means of an approximation function 9 E :F. If the target function 9 were known, then one natural measure of how well (or badly) g approximates 9 would be the Integrated Squared Difference (ISD) of the two functions:

The authors present a novel vector ridge detector which automatically finds the right scale of a ridge even in the presence of noise, multiple steps and narrow valleys. One of the key features of the ridge detector is that it has a zero response at discontinuities. The ridge detector can be applied both to scalar and vector quantities such as color. A parallel perceptual organization scheme that works without edges and is based on the ridge detector is also presented. In addition to perceptual groups, the scheme computes potential focus of attention points at which to direct future processing. The relation to human perception and several theoretical findings supporting the scheme are presented. Results of a Connection Machine implementation of the scheme are presented for perceptual organization using color.>