Peter N. Belhumeur

Bio: Peter N. Belhumeur is an academic researcher from Columbia University. The author has contributed to research in topics: Rendering (computer graphics) & Lambertian reflectance. The author has an hindex of 60, co-authored 137 publications receiving 34842 citations. Previous affiliations of Peter N. Belhumeur include Nanyang Technological University & York University.

Eigenfaces vs. Fisherfaces: recognition using class specific linear projection

Abstract: 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.

From few to many: illumination cone models for face recognition under variable lighting and pose

Abstract: We present a generative appearance-based method for recognizing human faces under variation in lighting and viewpoint. Our method exploits the fact that the set of images of an object in fixed pose, but under all possible illumination conditions, is a convex cone in the space of images. Using a small number of training images of each face taken with different lighting directions, the shape and albedo of the face can be reconstructed. In turn, this reconstruction serves as a generative model that can be used to render (or synthesize) images of the face under novel poses and illumination conditions. The pose space is then sampled and, for each pose, the corresponding illumination cone is approximated by a low-dimensional linear subspace whose basis vectors are estimated using the generative model. Our recognition algorithm assigns to a test image the identity of the closest approximated illumination cone. Test results show that the method performs almost without error, except on the most extreme lighting directions.

Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection

Abstract: We develop a face recognition algorithm which is insensitive to gross 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 direction lie in a 3-D linear subspace of the high dimensional feature space — if the face is a Lambertian surface without self-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 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 significantly lower than those of the Eigenface technique when tested on the same database.

Attribute and simile classifiers for face verification

Abstract: We present two novel methods for face verification. Our first method - “attribute” classifiers - uses binary classifiers trained to recognize the presence or absence of describable aspects of visual appearance (e.g., gender, race, and age). Our second method - “simile” classifiers - removes the manual labeling required for attribute classification and instead learns the similarity of faces, or regions of faces, to specific reference people. Neither method requires costly, often brittle, alignment between image pairs; yet, both methods produce compact visual descriptions, and work on real-world images. Furthermore, both the attribute and simile classifiers improve on the current state-of-the-art for the LFW data set, reducing the error rates compared to the current best by 23.92% and 26.34%, respectively, and 31.68% when combined. For further testing across pose, illumination, and expression, we introduce a new data set - termed PubFig - of real-world images of public figures (celebrities and politicians) acquired from the internet. This data set is both larger (60,000 images) and deeper (300 images per individual) than existing data sets of its kind. Finally, we present an evaluation of human performance.

Efficient region tracking with parametric models of geometry and illumination

Abstract: As an object moves through the field of view of a camera, the images of the object may change dramatically. This is not simply due to the translation of the object across the image plane; complications arise due to the fact that the object undergoes changes in pose relative to the viewing camera, in illumination relative to light sources, and may even become partially or fully occluded. We develop an efficient general framework for object tracking, which addresses each of these complications. We first develop a computationally efficient method for handling the geometric distortions produced by changes in pose. We then combine geometry and illumination into an algorithm that tracks large image regions using no more computation than would be required to track with no accommodation for illumination changes. Finally, we augment these methods with techniques from robust statistics and treat occluded regions on the object as statistical outliers. Experimental results are given to demonstrate the effectiveness of our methods.

ImageNet Large Scale Visual Recognition Challenge

Abstract: The ImageNet Large Scale Visual Recognition Challenge is a benchmark in object category classification and detection on hundreds of object categories and millions of images. The challenge has been run annually from 2010 to present, attracting participation from more than fifty institutions. This paper describes the creation of this benchmark dataset and the advances in object recognition that have been possible as a result. We discuss the challenges of collecting large-scale ground truth annotation, highlight key breakthroughs in categorical object recognition, provide a detailed analysis of the current state of the field of large-scale image classification and object detection, and compare the state-of-the-art computer vision accuracy with human accuracy. We conclude with lessons learned in the 5 years of the challenge, and propose future directions and improvements.

Rectified Linear Units Improve Restricted Boltzmann Machines

Abstract: Restricted Boltzmann machines were developed using binary stochastic hidden units. These can be generalized by replacing each binary unit by an infinite number of copies that all have the same weights but have progressively more negative biases. The learning and inference rules for these "Stepped Sigmoid Units" are unchanged. They can be approximated efficiently by noisy, rectified linear units. Compared with binary units, these units learn features that are better for object recognition on the NORB dataset and face verification on the Labeled Faces in the Wild dataset. Unlike binary units, rectified linear units preserve information about relative intensities as information travels through multiple layers of feature detectors.

Multiple View Geometry in Computer Vision.

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Machine learning

Abstract: Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).