Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly confront the problem of dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. The human brain confronts the same problem in everyday perception, extracting from its high-dimensional sensory inputs-30,000 auditory nerve fibers or 10(6) optic nerve fibers-a manageably small number of perceptually relevant features. Here we describe an approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set. Unlike classical techniques such as principal component analysis (PCA) and multidimensional scaling (MDS), our approach is capable of discovering the nonlinear degrees of freedom that underlie complex natural observations, such as human handwriting or images of a face under different viewing conditions. In contrast to previous algorithms for nonlinear dimensionality reduction, ours efficiently computes a globally optimal solution, and, for an important class of data manifolds, is guaranteed to converge asymptotically to the true structure.

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A global geometric framework for nonlinear dimensionality reduction.

We develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression. Taking a pattern classification approach, we consider each pixel in an image as a coordinate in a high-dimensional space. We take advantage of the observation that the images of a particular face, under varying illumination but fixed pose, lie in a 3D linear subspace of the high dimensional image space-if the face is a Lambertian surface without shadowing. However, since faces are not truly Lambertian surfaces and do indeed produce self-shadowing, images will deviate from this linear subspace. Rather than explicitly modeling this deviation, we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation. Our projection method is based on Fisher's linear discriminant and produces well separated classes in a low-dimensional subspace, even under severe variation in lighting and facial expressions. The eigenface technique, another method based on linearly projecting the image space to a low dimensional subspace, has similar computational requirements. Yet, extensive experimental results demonstrate that the proposed "Fisherface" method has error rates that are lower than those of the eigenface technique for tests on the Harvard and Yale face databases.

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Eigenfaces vs. Fisherfaces: recognition using class specific linear projection

Is perception of the whole based on perception of its parts? There is psychological and physiological evidence for parts-based representations in the brain, and certain computational theories of object recognition rely on such representations. But little is known about how brains or computers might learn the parts of objects. Here we demonstrate an algorithm for non-negative matrix factorization that is able to learn parts of faces and semantic features of text. This is in contrast to other methods, such as principal components analysis and vector quantization, that learn holistic, not parts-based, representations. Non-negative matrix factorization is distinguished from the other methods by its use of non-negativity constraints. These constraints lead to a parts-based representation because they allow only additive, not subtractive, combinations. When non-negative matrix factorization is implemented as a neural network, parts-based representations emerge by virtue of two properties: the firing rates of neurons are never negative and synaptic strengths do not change sign.

Learning the parts of objects by non-negative matrix factorization

We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models and argue that new theory from sparse signal representation offers the key to addressing this problem. Based on a sparse representation computed by C1-minimization, we propose a general classification algorithm for (image-based) object recognition. This new framework provides new insights into two crucial issues in face recognition: feature extraction and robustness to occlusion. For feature extraction, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficiently large and whether the sparse representation is correctly computed. Unconventional features such as downsampled images and random projections perform just as well as conventional features such as eigenfaces and Laplacianfaces, as long as the dimension of the feature space surpasses certain threshold, predicted by the theory of sparse representation. This framework can handle errors due to occlusion and corruption uniformly by exploiting the fact that these errors are often sparse with respect to the standard (pixel) basis. The theory of sparse representation helps predict how much occlusion the recognition algorithm can handle and how to choose the training images to maximize robustness to occlusion. We conduct extensive experiments on publicly available databases to verify the efficacy of the proposed algorithm and corroborate the above claims.

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Robust Face Recognition via Sparse Representation

Learning parts of objects by non-negative matrix factorization

We present a novel local-based face verification system whose components are analogous to those of biological systems. In the proposed system, after global registration and normalization, three eye regions are converted from the spatial to polar frequency domain by a Fourier-Bessel Transform. The resulting representations are embedded in a dissimilarity space, where each image is represented by its distance to all the other images. In this dissimilarity space a Pseudo-Fisher discriminator is built. ROC and equal error rate verification test results on the FERET database showed that the system performed at least as state-of-the-art methods and better than a system based on polar Fourier features. The local-based system is especially robust to facial expression and age variations, but sensitive to registration errors.

Face Verification in Polar Frequency Domain: a Biologically Motivated Approach

Facial expression is one of the most powerful means for people to coordinate conversation and communicate emotions and other mental, social, and physiological cues. We address two problems in facial expression recognition in this thesis: global facial expression space representation and facial expression recognition method with objective measurement. 
We propose the concept of the manifold of facial expression based on the observation that the images of all possible facial deformations of an individual make a smooth manifold embedded in a high dimensional image space. To combine the manifolds of different subjects that vary significantly and are usually hard to align, we transfer the facial deformations in all training videos to one standard model. Lipschitz embedding embeds the normalized deformation of the standard model in a low dimensional Generalized Manifold. Deformation data from different subjects complement each other for a better description of the true manifold. We learn a probabilistic expression model on the generalized manifold. There are six kinds of universally recognized facial expressions: happiness, sadness, fear, anger, disgust, and surprise, which we explicitly represent as basic expressions. In the embedded space, a complete expression sequence becomes a path on the expression manifold, emanating from a center that corresponds to the neutral expression. The transition between different expressions is represented as the evolution of the posterior probability of the six basic expressions. 
These six kinds of basic facial expressions comprise only a small subset of all visible facial deformation. To measure the facial expression recognition rate precisely in the manifold model, we developed Regional FACS (Facial Action Coding System). FACS encodes facial deformation in terms of 44 kinds of Action Units (AU). By learning the AU combinations in 9 separate facial regions, the number of combinations of regional deformations is dramatically decreased compared to the number of combinations of AUs. The manifold of each facial regional can be considered as the sub-vector of the whole manifold. The experimental results demonstrate that our system works effectively for automatic recognition of 29 AUs that cover the most frequently appearing facial deformations. The FACS recognition results also lead to high recognition accuracy of six basic expression categories. 
The main contributions of this thesis are: (1) A probabilistic model based on manifold of facial expression can represent facial expression analytically and globally; (2) The Regional FACS system provides a novel FACS recognition solution with objective measurement.

Facial expression analysis on manifolds

In its early years, the field of computer vision was largely motivated by researchers seeking computational models of biological vision and solutions to practical problems in manufacturing, defense, and medicine. For the past two decades or so, there has been an increasing interest in computer vision as an input modality in the context of human-computer interaction. Such vision-based interaction can endow interactive systems with visual capabilities similar to those important to human-human interaction, in order to perceive non-verbal cues and incorporate this information in applications such as interactive gaming, visualization, art installations, intelligent agent interaction, and various kinds of command and control tasks. Enabling this kind of rich, visual and multimodal interaction requires interactive-time solutions to problems such as detecting and recognizing faces and facial expressions, determining a person's direction of gaze and focus of attention, tracking movement of the body, and recognizing various kinds of gestures. In building technologies for vision-based interaction, there are choices to be made as to the range of possible sensors employed (e.g., single camera, stereo rig, depth camera), the precision and granularity of the desired outputs, the mobility of the solution, usability issues, etc. Practical considerations dictate that there is not a one-size-fits-all solution to the variety of interaction scenarios; however, there are principles and methodological approaches common to a wide range of problems in the domain. While new sensors such as the Microsoft Kinect are having a major influence on the research and practice of vision-based interaction in various settings, they are just a starting point for continued progress in the area. In this book, we discuss the landscape of history, opportunities, and challenges in this area of vision-based interaction; we review the state-of-the-art and seminal works in detecting and recognizing the human body and its components; we explore both static and dynamic approaches to ""looking at people"" vision problems; and we place the computer vision work in the context of other modalities and multimodal applications. Readers should gain a thorough understanding of current and future possibilities of computer vision technologies in the context of human-computer interaction.

Vision-Based Interaction

Multimodal classification is a core task in human-centric machine learning. We observe that information is highly complementary across modalities, thus unimodal information can be drastically sparsified prior to multimodal fusion without loss of accuracy. To this end, we present Sparse Fusion Transformers (SFT), a novel multimodal fusion method for transformers that performs comparably to existing state-of-the-art methods while having greatly reduced memory footprint and computation cost. Key to our idea is a sparse-pooling block that reduces unimodal token sets prior to cross-modality modeling. Evaluations are conducted on multiple multimodal benchmark datasets for a wide range of classification tasks. State-of-the-art performance is obtained on multiple benchmarks under similar experiment conditions, while reporting up to six-fold reduction in computational cost and memory requirements. Extensive ablation studies showcase our benefits of combining sparsification and multimodal learning over naive approaches. This paves the way for enabling multimodal learning on low-resource devices.

Sparse Fusion for Multimodal Transformers.

This paper pioneers a method for local color editing on stereo image pairs. We generalize the conventional edit propagation framework to stereo views by introducing recent advances in the field of image segmentation, thus allowing a user's edits in one view to be simultaneously performed in the other view. This new formulation maintains consistent editing quality in both views and avoids singularities by solving a well regularized linear system for edit propagation.

Matthew Turk

Papers

Face Verification in Polar Frequency Domain: a Biologically Motivated Approach

Facial expression analysis on manifolds

Vision-Based Interaction

Sparse Fusion for Multimodal Transformers.

High-order regularization for stereo color editing