There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

3D Slicer as an image computing platform for the Quantitative Imaging Network.

IEEE Transactions on Pattern Analysis and Machine Intelligence

Techniques from sparse signal representation are beginning to see significant impact in computer vision, often on nontraditional applications where the goal is not just to obtain a compact high-fidelity representation of the observed signal, but also to extract semantic information. The choice of dictionary plays a key role in bridging this gap: unconventional dictionaries consisting of, or learned from, the training samples themselves provide the key to obtaining state-of-the-art results and to attaching semantic meaning to sparse signal representations. Understanding the good performance of such unconventional dictionaries in turn demands new algorithmic and analytical techniques. This review paper highlights a few representative examples of how the interaction between sparse signal representation and computer vision can enrich both fields, and raises a number of open questions for further study.

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Sparse Representation for Computer Vision and Pattern Recognition

The Alzheimer's Disease Neuroimaging Initiative (ADNI) is an ongoing, longitudinal, multicenter study designed to develop clinical, imaging, genetic, and biochemical biomarkers for the early detection and tracking of Alzheimer's disease (AD). The study aimed to enroll 400 subjects with early mild cognitive impairment (MCI), 200 subjects with early AD, and 200 normal control subjects; $67 million funding was provided by both the public and private sectors, including the National Institute on Aging, 13 pharmaceutical companies, and 2 foundations that provided support through the Foundation for the National Institutes of Health. This article reviews all papers published since the inception of the initiative and summarizes the results as of February 2011. The major accomplishments of ADNI have been as follows: (1) the development of standardized methods for clinical tests, magnetic resonance imaging (MRI), positron emission tomography (PET), and cerebrospinal fluid (CSF) biomarkers in a multicenter setting; (2) elucidation of the patterns and rates of change of imaging and CSF biomarker measurements in control subjects, MCI patients, and AD patients. CSF biomarkers are consistent with disease trajectories predicted by β-amyloid cascade (Hardy, J Alzheimers Dis 2006;9(Suppl 3):151-3) and tau-mediated neurodegeneration hypotheses for AD, whereas brain atrophy and hypometabolism levels show predicted patterns but exhibit differing rates of change depending on region and disease severity; (3) the assessment of alternative methods of diagnostic categorization. Currently, the best classifiers combine optimum features from multiple modalities, including MRI, [(18)F]-fluorodeoxyglucose-PET, CSF biomarkers, and clinical tests; (4) the development of methods for the early detection of AD. CSF biomarkers, β-amyloid 42 and tau, as well as amyloid PET may reflect the earliest steps in AD pathology in mildly symptomatic or even nonsymptomatic subjects, and are leading candidates for the detection of AD in its preclinical stages; (5) the improvement of clinical trial efficiency through the identification of subjects most likely to undergo imminent future clinical decline and the use of more sensitive outcome measures to reduce sample sizes. Baseline cognitive and/or MRI measures generally predicted future decline better than other modalities, whereas MRI measures of change were shown to be the most efficient outcome measures; (6) the confirmation of the AD risk loci CLU, CR1, and PICALM and the identification of novel candidate risk loci; (7) worldwide impact through the establishment of ADNI-like programs in Europe, Asia, and Australia; (8) understanding the biology and pathobiology of normal aging, MCI, and AD through integration of ADNI biomarker data with clinical data from ADNI to stimulate research that will resolve controversies about competing hypotheses on the etiopathogenesis of AD, thereby advancing efforts to find disease-modifying drugs for AD; and (9) the establishment of infrastructure to allow sharing of all raw and processed data without embargo to interested scientific investigators throughout the world. The ADNI study was extended by a 2-year Grand Opportunities grant in 2009 and a renewal of ADNI (ADNI-2) in October 2010 through to 2016, with enrollment of an additional 550 participants.

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The Alzheimer's Disease Neuroimaging Initiative: a review of papers published since its inception.

Watershed segmentation using prior shape and appearance knowledge

We present a face recognition method based on sparse representation for recognizing 3D face meshes under expressions using low-level geometric features. First, to enable the application of the sparse representation framework, we develop a uniform remeshing scheme to establish a consistent sampling pattern across 3D faces. To handle facial expressions, we design a feature pooling and ranking scheme to collect various types of low-level geometric features and rank them according to their sensitivities to facial expressions. By simply applying the sparse representation framework to the collected low-level features, our proposed method already achieves satisfactory recognition rates, which demonstrates the efficacy of the framework for 3D face recognition. To further improve results in the presence of severe facial expressions, we show that by choosing higher-ranked, i.e., expression-insensitive, features, the recognition rates approach those for neutral faces, without requiring an extensive set of reference faces for each individual to cover possible variations caused by expressions as proposed in previous work. We apply our face recognition method to the GavabDB and FRGC 2.0 databases and demonstrate encouraging results.

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Expression-insensitive 3D face recognition using sparse representation

Face recognition is one of the most intensively studied topics in computer vision and pattern recognition. Facial expression, which changes face geometry, usually has an adverse effect on the performance of a face recognition system. On the other hand, face geometry is a useful cue for recognition. Taking these into account, we utilize the idea of separating geometry and texture information in a face image and model the two types of information by projecting them into separate PCA spaces which are specially designed to capture the distinctive features among different individuals. Subsequently, the texture and geometry attributes are re-combined to form a classifier which is capable of recognizing faces with different expressions. Finally, by studying face geometry, we are able to determine which type of facial expression has been carried out, thus build an expression classifier. Numerical validations of the proposed method are given.

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Expression-Invariant Face Recognition with Expression Classification

We investigate the use of multiple intrinsic geometric attributes, including angles, geodesic distances, and curvatures, for 3D face recognition, where each face is represented by a triangle mesh, preprocessed to possess a uniform connectivity. As invariance to facial expressions holds the key to improving recognition performance, we propose to train for the component-wise weights to be applied to each individual attribute, as well as the weights used to combine the attributes, in order to adapt to expression variations. Using the eigenface approach based on the training results and a nearest neighbor classifier, we report recognition results on the expression-rich GavabDB face database and the well-known Notre Dame FRGC 3D database. We also perform a cross validation between the two databases.

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Adapting Geometric Attributes for Expression-Invariant 3D Face Recognition

This paper presents registration via embedded maps (REM), a deformable registration algorithm for images with varying topology. The algorithm represents 3-D images as 4-D manifolds in a Riemannian space (referred to as embedded maps). Registration is performed as a surface evolution matching one embedded map to another using a diffusion process. The approach differs from those existing in that it takes an a priori estimation of image regions where topological changes are present, for example lesions, and generates a dense vector field representing both the shape and intensity changes necessary to match the images. The algorithm outputs both a diffeomorphic deformation field and an intensity displacement which corrects the intensity difference caused by topological changes. Multiple sets of experiments are conducted on magnetic resonance imaging (MRI) with lesions from OASIS and ADNI datasets. These images are registered to either a brain template or images of healthy individuals. An exemplar case registering a template to an MRI with tumor is also given. The resulting deformation fields were compared with those obtained using diffeomorphic demons, where topological changes are not modeled. These sets of experiments demonstrate the efficacy of our proposed REM method for registration of brain MRI with severe topological differences.

Xiaoxing Li

Papers

Watershed segmentation using prior shape and appearance knowledge

Expression-insensitive 3D face recognition using sparse representation

Expression-Invariant Face Recognition with Expression Classification

Adapting Geometric Attributes for Expression-Invariant 3D Face Recognition

Registration of Images With Varying Topology Using Embedded Maps