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.

/pdf/eigenfaces-vs-fisherfaces-recognition-using-class-specific-2qyevb22n0.pdf

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.

/pdf/robust-face-recognition-via-sparse-representation-4bfqv6y74o.pdf

Robust Face Recognition via Sparse Representation

Learning parts of objects by non-negative matrix factorization

Biomechanics determines the physical range in which humans can move their bodies. Human factors research delineates a subspace in which humans can operate without experiencing musculoskeletal strai...

An Objective Measure for Postural Comfort

Years ago, it was difficult to imagine that one day the digital camera would become a standard component of mobile phones. Nowadays, smart phones have not only been equipped with camera sensors, but also various other sensors such as accelerometers, gyroscopes, and GPS receivers. The ubiquity of high quality mobile cameras with ever increasing computational capacity, packaged along with other rich sensors, is providing many new opportunities for applications of computer vision technologies, especially those that support human activities such as location-based and usercentered services.

Introduction to the Special Issue on Mobile Vision

For some time, graphical user interfaces (GUIs) have been the dominant platform for human computer interaction. The GUI-based style of interaction has made computers simpler and easier to use, especially for office productivity applications. However, as the way we use computers changes and computing becomes more pervasive and ubiquitous, GUIs will not easily support the range of interactions necessary to meet users’ needs. In order to accommodate a wider range of scenarios, tasks, users, and preferences, we need to move toward interfaces that are natural, intuitive, adaptive, and unobtrusive. The aim of a new focus in HCI, called Perceptual User Interfaces (PUIs), is to make human-computer interaction more like how people interact with each other and with the world. This paper describes the emerging PUI field and then reports on three PUI-motivated components: computer vision-based techniques to visually perceive relevant information about the user.

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Moving from GUIs to PUIs

Tracking articulated objects in dense disparity maps

Detection and description of local image features has proven to be a powerful paradigm for a variety of applications in computer vision. Often, this process includes an orientation assignment step to render the overall process invariant to in-plane rotation. In this paper, we review several different existing algorithms and propose two novel, efficient methods for orientation assignment. The first method exhibits a very good speedperformance trade-off; the second is capable of multiple orientations and performs comparable to SIFT’s orientation assignment while being significantly cheaper. Additionally, we improve one of the existing orientation assignment methods by generalizing it. All algorithms are evaluated empirically under a variety of conditions and in combination with six keypoint detectors.

/pdf/improving-keypoint-orientation-assignment-2bzyzsc70n.pdf

Matthew Turk

Papers

An Objective Measure for Postural Comfort

Introduction to the Special Issue on Mobile Vision

Moving from GUIs to PUIs

Tracking articulated objects in dense disparity maps

Improving Keypoint Orientation Assignment