Linear Differential Constraints for Photo-polarimetric Height Estimation

In this paper we present a differential approach to photo-polarimetric shape estimation. We propose several alternative differential constraints based on polarisation and photometric shading information and show how to express them in a unified partial differential system. Our method uses the image ratios technique to combine shading and polarisation information in order to directly reconstruct surface height, without first computing surface normal vectors. Moreover, we are able to remove the non-linearities so that the problem reduces to solving a linear differential problem. We also introduce a new method for estimating a polarisation image from multichannel data and, finally, we show it is possible to estimate the illumination directions in a two source setup, extending the method into an uncalibrated scenario. From a numerical point of view, we use a least-squares formulation of the discrete version of the problem. To the best of our knowledge, this is the first work to consider a unified differential approach to solve photo-polarimetric shape estimation directly for height. Numerical results on synthetic and real-world data confirm the effectiveness of our proposed method.Comment: To appear at International Conference on Computer Vision (ICCV), Venice, Italy, October 22-29, 201

Statistical/Geometric Techniques for Object Representation and Recognition

Object modeling and recognition are key areas of research in computer vision and graphics with wide range of applications. Though research in these areas is not new, traditionally most of it has focused on analyzing problems under controlled environments. The challenges posed by real life applications demand for more general and robust solutions. The wide variety of objects with large intra-class variability makes the task very challenging. The difficulty in modeling and matching objects also vary depending on the input modality. In addition, the easy availability of sensors and storage have resulted in tremendous increase in the amount of data that needs to be processed which requires efficient algorithms suitable for large-size databases. In this dissertation, we address some of the challenges involved in modeling and matching of objects in realistic scenarios. Object matching in images require accounting for large variability in the appearance due to changes in illumination and view point. Any real world object is characterized by its underlying shape and albedo, which unlike the image intensity are insensitive to changes in illumination conditions. We propose a stochastic filtering framework for estimating object albedo from a single intensity image by formulating the albedo estimation as an image estimation problem. We also show how this albedo estimate can be used for illumination insensitive object matching and for more accurate shape recovery from a single image using standard shape from shading formulation. We start with the simpler problem where the pose of the object is known and only the illumination varies. We then extend the proposed approach to handle unknown pose in addition to illumination variations. We also use the estimated albedo maps for another important application, which is recognizing faces across age progression. Many approaches which address the problem of modeling and recognizing objects from images assume that the underlying objects are of diffused texture. But most real world objects exhibit a combination of diffused and specular properties. We propose an approach for separating the diffused and specular reflectance from a given color image so that the algorithms proposed for objects of diffused texture become applicable to a much wider range of real world objects. Representing and matching the 2D and 3D geometry of objects is also an integral part of object matching with applications in gesture recognition, activity classification, trademark and logo recognition, etc. The challenge in matching 2D/3D shapes lies in accounting for the different rigid and non-rigid deformations, large intra-class variability, noise and outliers. In addition, since shapes are usually represented as a collection of landmark points, the shape matching algorithm also has to deal with the challenges of missing or unknown correspondence across these data points. We propose an efficient shape indexing approach where the different feature vectors representing the shape are mapped to a hash table. For a query shape, we show how the similar shapes in the database can be efficiently retrieved without the need for establishing correspondence making the algorithm extremely fast and scalable. We also propose an approach for matching and registration of 3D point cloud data across unknown or missing correspondence using an implicit surface representation. Finally, we discuss possible future directions of this research

Recovering facial shape using a statistical model of surface normal direction

In this paper, we show how a statistical model of facial shape can be embedded within a shape-from-shading algorithm. We describe how facial shape can be captured using a statistical model of variations in surface normal direction. To construct this model, we make use of the azimuthal equidistant projection to map the distribution of surface normals from the polar representation on a unit sphere to Cartesian points on a local tangent plane. The distribution of surface normal directions is captured using the covariance matrix for the projected point positions. The eigenvectors of the covariance matrix define the modes of shape-variation in the fields of transformed surface normals. We show how this model can be trained using surface normal data acquired from range images and how to fit the model to intensity images of faces using constraints on the surface normal direction provided by Lambert's law. We demonstrate that the combination of a global statistical constraint and local irradiance constraint yields an efficient and accurate approach to facial shape recovery and is capable of recovering fine local surface details. We assess the accuracy of the technique on a variety of images with ground truth and real-world images

Subspace Representations for Robust Face and Facial Expression Recognition

Analyzing human faces and modeling their variations have always been of interest to the computer vision community. Face analysis based on 2D intensity images is a challenging problem, complicated by variations in pose, lighting, blur, and non-rigid facial deformations due to facial expressions. Among the different sources of variation, facial expressions are of interest as important channels of non-verbal communication. Facial expression analysis is also affected by changes in view-point and inter-subject variations in performing different expressions. This dissertation makes an attempt to address some of the challenges involved in developing robust algorithms for face and facial expression recognition by exploiting the idea of proper subspace representations for data. Variations in the visual appearance of an object mostly arise due to changes in illumination and pose. So we first present a video-based sequential algorithm for estimating the face albedo as an illumination-insensitive signature for face recognition. We show that by knowing/estimating the pose of the face at each frame of a sequence, the albedo can be efficiently estimated using a Kalman filter. Then we extend this to the case of unknown pose by simultaneously tracking the pose as well as updating the albedo through an efficient Bayesian inference method performed using a Rao-Blackwellized particle filter. Since understanding the effects of blur, especially motion blur, is an important problem in unconstrained visual analysis, we then propose a blur-robust recognition algorithm for faces with spatially varying blur. We model a blurred face as a weighted average of geometrically transformed instances of its clean face. We then build a matrix, for each gallery face, whose column space spans the space of all the motion blurred images obtained from the clean face. This matrix representation is then used to define a proper objective function and perform blur-robust face recognition. To develop robust and generalizable models for expression analysis one needs to break the dependence of the models on the choice of the coordinate frame of the camera. To this end, we build models for expressions on the affine shape-space (Grassmann manifold), as an approximation to the projective shape-space, by using a Riemannian interpretation of deformations that facial expressions cause on different parts of the face. This representation enables us to perform various expression analysis and recognition algorithms without the need for pose normalization as a preprocessing step. There is a large degree of inter-subject variations in performing various expressions. This poses an important challenge on developing robust facial expression recognition algorithms. To address this challenge, we propose a dictionary-based approach for facial expression analysis by decomposing expressions in terms of action units (AUs). First, we construct an AU-dictionary using domain experts' knowledge of AUs. To incorporate the high-level knowledge regarding expression decomposition and AUs, we then perform structure-preserving sparse coding by imposing two layers of grouping over AU-dictionary atoms as well as over the test image matrix columns. We use the computed sparse code matrix for each expressive face to perform expression decomposition and recognition. Most of the existing methods for the recognition of faces and expressions consider either the expression-invariant face recognition problem or the identity-independent facial expression recognition problem. We propose joint face and facial expression recognition using a dictionary-based component separation algorithm (DCS). In this approach, the given expressive face is viewed as a superposition of a neutral face component with a facial expression component, which is sparse with respect to the whole image. This assumption leads to a dictionary-based component separation algorithm, which benefits from the idea of sparsity and morphological diversity. The DCS algorithm uses the data-driven dictionaries to decompose an expressive test face into its constituent components. The sparse codes we obtain as a result of this decomposition are then used for joint face and expression recognition

Face Identification and Clustering

In this thesis, we study two problems based on clustering algorithms. In the first problem, we study the role of visual attributes using an agglomerative clustering algorithm to whittle down the search area where the number of classes is high to improve the performance of clustering. We observe that as we add more attributes, the clustering performance increases overall. In the second problem, we study the role of clustering in aggregating templates in a 1:N open set protocol using multi-shot video as a probe. We observe that by increasing the number of clusters, the performance increases with respect to the baseline and reaches a peak, after which increasing the number of clusters causes the performance to degrade. Experiments are conducted using recently introduced unconstrained IARPA Janus IJB-A, CS2, and CS3 face recognition datasets

DICTIONARIES AND MANIFOLDS FOR FACE RECOGNITION ACROSS ILLUMINATION, AGING AND QUANTIZATION

During the past many decades, many face recognition algorithms have been proposed. The face recognition problem under controlled environment has been well studied and almost solved. However, in unconstrained environments, the performance of face recognition methods could still be significantly affected by factors such as illumination, pose, resolution, occlusion, aging, etc. In this thesis, we look into the problem of face recognition across these variations and quantization. We present a face recognition algorithm based on simultaneous sparse approximations under varying illumination and pose with dictionaries learned for each class. A novel test image is projected onto the span of the atoms in each learned dictionary. The resulting residual vectors are then used for classification. An image relighting technique based on pose-robust albedo estimation is used to generate multiple frontal images of the same person with variable lighting. As a result, the proposed algorithm has the ability to recognize human faces with high accuracy even when only a single or a very few images per person are provided for training. The efficiency of the proposed method is demonstrated using publicly available databases and it is shown that this method is efficient and can perform significantly better than many competitive face recognition algorithms. The problem of recognizing facial images across aging remains an open problem. We look into this problem by studying the growth in the facial shapes. Building on recent advances in landmark extraction, and statistical techniques for landmark-based shape analysis, we show that using well-defined shape spaces and its associated geometry, one can obtain significant performance improvements in face verification. Toward this end, we propose to model the facial shapes as points on a Grassmann manifold. The face verification problem is then formulated as a classification problem on this manifold. We then propose a relative craniofacial growth model which is based on the science of craniofacial anthropometry and integrate it with the Grassmann manifold and the SVM classifier. Experiments show that the proposed method is able to mitigate the variations caused by the aging progress and thus effectively improve the performance of open-set face verification across aging. In applications such as document understanding, only binary face images may be available as inputs to a face recognition algorithm. We investigate the effects of quantization on several classical face recognition algorithms. We study the performances of PCA and multiple exemplar discriminant analysis (MEDA) algorithms with quantized images and with binary images modified by distance and Box-Cox transforms. We propose a dictionary-based method for reconstructing the grey scale facial images from the quantized facial images. Two dictionaries with low mutual coherence are learned for the grey scale and quantized training images respectively using a modified KSVD method. A linear transform function between the sparse vectors of quantized images and the sparse vectors of grey scale images is estimated using the training data. In the testing stage, a grey scale image is reconstructed from the quantized image using the transform matrix and normalized dictionaries. The identities of the reconstructed grey scale images are then determined using the dictionary-based face recognition (DFR) algorithm. Experimental results show that the reconstructed images are similar to the original grey-scale images and the performance of face recognition on the quantized images is comparable to the performance on grey scale images. The online social network and social media is growing rapidly. It is interesting to study the impact of social network on computer vision algorithms. We address the problem of automated face recognition on a social network using a loopy belief propagation framework. The proposed approach propagates the identities of faces in photos across social graphs. We characterize its performance in terms of structural properties of the given social network. We propose a distance metric defined using face recognition results for detecting hidden connections. The performance of the proposed method is analyzed on graph structure networks, scalability, different degrees of nodes, labeling errors correction and hidden connections discovery. The result demonstrates that the constraints imposed by the social network have the potential to improve the performance of face recognition methods. The result also shows it is possible to discover hidden connections in a social network based on face recognition

Linear Differential Constraints for Photo-polarimetric Height Estimation

In this paper we present a differential approach to photopolarimetric shape estimation. We propose several alternative differential constraints based on polarisation and photometric shading information and show how to express them in a unified partial differential system. Our method uses the image ratios technique to combine shading and polarisation information in order to directly reconstruct surface height, without first computing surface normal vectors. Moreover, we are able to remove the non-linearities so that the problem reduces to solving a linear differential problem. We also introduce a new method for estimating a polarisation image from multichannel data and, finally, we show it is possible to estimate the illumination directions in a two source setup, extending the method into an uncalibrated scenario. From a numerical point of view, we use a least-squares formulation of the discrete version of the problem. To the best of our knowledge, this is the first work to consider a unified differential approach to solve photo-polarimetric shape estimation directly for height. Numerical results on synthetic and real-world data confirm the effectiveness of our proposed method

Optical techniques for 3D surface reconstruction in computer-assisted laparoscopic surgery

One of the main challenges for computer-assisted surgery (CAS) is to determine the intra-opera- tive morphology and motion of soft-tissues. This information is prerequisite to the registration of multi-modal patient-specific data for enhancing the surgeon’s navigation capabilites by observ- ing beyond exposed tissue surfaces and for providing intelligent control of robotic-assisted in- struments. In minimally invasive surgery (MIS), optical techniques are an increasingly attractive approach for in vivo 3D reconstruction of the soft-tissue surface geometry. This paper reviews the state-of-the-art methods for optical intra-operative 3D reconstruction in laparoscopic surgery and discusses the technical challenges and future perspectives towards clinical translation. With the recent paradigm shift of surgical practice towards MIS and new developments in 3D opti- cal imaging, this is a timely discussion about technologies that could facilitate complex CAS procedures in dynamic and deformable anatomical regions