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.

/pdf/a-global-geometric-framework-for-nonlinear-dimensionality-5brl02iqtj.pdf

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

We describe a novel approach to appearance-based hand pose estimation which relies on multiple cameras to improve accuracy and resolve ambiguities caused by selfocclusions. Rather than estimating 3D geometry as most previous multi-view imaging systems, our approach uses multiple views to extend current exemplar-based methods that estimate hand pose by matching a probe image with a large discrete set of labeled hand pose images. We formulate the problem in a MAP (maximum a posteriori) framework, where the information from multiple cameras is fused to provide reliable hand pose estimation. Our quantitative experimental results show that correct estimation rate is much higher using our multi-view approach than using a single-view approach.

/pdf/multi-view-appearance-based-3d-hand-pose-estimation-4t3mqk2xok.pdf

Multi-view Appearance-based 3D Hand Pose Estimation

All-in-focus imaging is a computational photography technique that produces images free of defocus blur by capturing a stack of images focused at different distances and merging them into a single sharp result. Current approaches assume that images have been captured offline, and that a reasonably powerful computer is available to process them. In contrast, we focus on the problem of how to capture such input stacks in an efficient and scene-adaptive fashion. Inspired by passive autofocus techniques, which select a single best plane of focus in the scene, we propose a method to automatically select a minimal set of images, focused at different depths, such that all objects in a given scene are in focus in at least one image. We aim to minimize both the amount of time spent metering the scene and capturing the images, and the total amount of high-resolution data that is captured. The algorithm first analyzes a set of low-resolution sharpness measurements of the scene while continuously varying the focus distance of the lens. From these measurements, we estimate the final lens positions required to capture all objects in the scene in acceptable focus. We demonstrate the use of our technique in a mobile computational photography scenario, where it is essential to minimize image capture time (as the camera is typically handheld) and processing time (as the computation and energy resources are limited).

http://ieeexplore.ieee.org/iel5/5707201/5711474/05711547.pdf

Generalized autofocus

The ability to engage in goal-oriented conversations has allowed humans to gain knowledge, reduce uncertainty, and perform tasks more efficiently. Artificial agents, however, are still far behind humans in having goal-driven conversations. In this work, we focus on the task of goal-oriented visual dialogue, aiming to automatically generate a series of questions about an image with a single objective. This task is challenging since these questions must not only be consistent with a strategy to achieve a goal, but also consider the contextual information in the image. We propose an end-to-end goal-oriented visual dialogue system, that combines reinforcement learning with regularized information gain. Unlike previous approaches that have been proposed for the task, our work is motivated by the Rational Speech Act framework, which models the process of human inquiry to reach a goal. We test the two versions of our model on the GuessWhat?! dataset, obtaining significant results that outperform the current state-of-the-art models in the task of generating questions to find an undisclosed object in an image.

/pdf/what-should-i-ask-using-conversationally-informative-rewards-59867qukay.pdf

What Should I Ask? Using Conversationally Informative Rewards for Goal-oriented Visual Dialog.

A 2D gesture annotation provides a simple way to annotate the physical world in augmented reality for a range of applications such as remote collaboration. When rendered from novel viewpoints, these annotations have previously only worked with statically positioned cameras or planar scenes. However, if the camera moves and is observing an arbitrary environment, 2D gesture annotations can easily lose their meaning when shown from novel viewpoints due to perspective effects. In this paper, we present a new approach towards solving this problem by using a gesture enhanced annotation interpretation. By first classifying which type of gesture the user drew, we show that it is possible to render the 2D annotations in 3D in a way that conforms more to the original intention of the user than with traditional methods. We first determined a generic vocabulary of important 2D gestures for an augmented reality enhanced remote collaboration scenario by running an Amazon Mechanical Turk study with 88 participants. Next, we designed a novel real-time method to automatically handle the two most common 2D gesture annotations — arrows and circles — and give a detailed analysis of the ambiguities that must be handled in each case. Arrow gestures are interpreted by identifying their anchor points and using scene surface normals for better perspective rendering. For circle gestures, we designed a novel energy function to help infer the object of interest using both 2D image cues and 3D geometric cues. Results indicate that our method outperforms previous approaches by better conveying the meaning of the original drawing from different viewpoints.

Interpreting 2D gesture annotations in 3D augmented reality

Currently, sharp discontinuities in depth and partial occlusions in multiview imaging systems pose serious challenges for many dense correspondence algorithms. However, it is important for 3D reconstruction methods to preserve depth edges as they correspond to important shape features like silhouettes which are critical for understanding the structure of a scene. In this paper, we show how active illumination algorithms can produce a rich set of feature maps that are useful in dense 3D reconstruction. We start by showing a method to compute a qualitative depth map from a single camera, which encodes object relative distances and can be used as a prior for stereo. In a multiview setup, we show that along with depth edges, binocular half-occluded pixels can also be explicitly and reliably labeled. To demonstrate the usefulness of these feature maps, we show how they can be used in two different algorithms for dense stereo correspondence. Our experimental results show that our enhanced stereo algorithms are able to extract high quality, discontinuity preserving correspondence maps from scenes that are extremely challenging for conventional stereo methods.

Matthew Turk

Papers

Multi-view Appearance-based 3D Hand Pose Estimation

Generalized autofocus

What Should I Ask? Using Conversationally Informative Rewards for Goal-oriented Visual Dialog.

Interpreting 2D gesture annotations in 3D augmented reality

Discontinuity preserving stereo with small baseline multi-flash illumination