The visual appearance of real-world surfaces is the net result of surface reflectance characteristics when exposed to illumination. Appearance models can be constructed using phenomenological models which capture surface appearance through mathematical modeling of the reflection process. This yields an integral equation, known as reflectance equation, describing the surface radiance, which depends on the interaction between the incident light field and the surface bidirectional reflectance distribution function (BRDF). The BRDF is a function defined on the cartesian product of two hemispheres corresponding to the incident and outgoing directions; the natural way to represent such a hemispherical function is to use hemispherical basis. However, due to their compactness in the frequency space, spherical harmonics (SH) have been extensively used for this purpose. In this paper, we address the geometrical compliance of hemispherical basis for representing surface BRDF. We propose a tensor product of the hemispherical harmonics (HSH) to provide a compact and efficient representation for arbitrary BRDFs, while satisfying the Helmholtz reciprocity property. We provide an analytical analysis and experimental justification that for a given approximation order, our proposed hemispherical basis provide better approximation accuracy when compared to Zernike-based basis, while avoiding the high computational complexity inherited from such polynomials. We validate our proposed Helmholtz HSH-based basis functions on Oren-Nayar and Cook-Torrance BRDF physical models.

Face and eye detection algorithms are deployed in a wide variety of applications. Unfortunately, there has been no quantitative comparison of how these detectors perform under difficult circumstances. We created a dataset of low light and long distance images which possess some of the problems encountered by face and eye detectors solving real world problems. The dataset we created is composed of reimaged images (photohead) and semi-synthetic heads imaged under varying conditions of low light, atmospheric blur, and distances of 3m, 50m, 80m, and 200m. This paper analyzes the detection and localization performance of the participating face and eye algorithms compared with the Viola Jones detector and four leading commercial face detectors. Performance is characterized under the different conditions and parameterized by per-image brightness and contrast. In localization accuracy for eyes, the groups/companies focusing on long-range face detection outperform leading commercial applications.

This paper proposes a model-based approach for 3D facial shape recovery using a small set of feature points from an input image of unknown pose and illumination. Previous model-based approaches usually require both texture (shading) and shape information from the input image in order to perform 3D facial shape recovery. However, the methods discussed here need only the 2D feature points from a single input image to reconstruct the 3D shape. Experimental results show acceptable reconstructed shapes when compared to the ground truth and previous approaches. This work has potential value in applications such face recognition at-a distance (FRAD), where the classical shape-from-X (e.g., stereo, motion and shading) algorithms are not feasible due to input image quality.

Surface irradiance signals are turned into outgoing radiance through the surface reflectance function, which can be significantly perturbed by the illumination conditions. Due to their low-frequency nature, irradiance signals can be represented using low-order basis functions, where spherical harmonics (SH) have been extensively used to provide such basis. When capturing image irradiance from a single viewpoint, the visible part of the object's surface constructs the upper hemisphere of the surface normals where the SH are no longer orthonormal. This reduced domain paves the way for even lower-dimensional approximation since full spherical representation is not needed. While harmonic basis are known to be optimal under distant light, light coming from near-by objects and indoor environments are common near light scenarios; it is essential to relax distant light assumption. Considering light source(s) distributed uniformly over the upper hemisphere, we propose the use of hemispherical harmonics (HSH) to model image irradiance of convex Lambertian objects perceived from single viewpoint under unknown near illumination. We prove analytically, and experimentally validated, that the Lambertian kernel has a more compact harmonic expansion in the hemispherical domain when compared to its spherical counterpart. We illustrate that HSH provide an efficient and accurate low-dimensional representation of image irradiance of Lambertian objects under near lighting conditions in contrast to SH.

A surface reflectance function represents the process of turning irradiance signals into outgoing radiance. Irradiance signals can be represented using low-order basis functions due to their low-frequency nature. Spherical harmonics (SH) have been used to provide such basis. However the incident light at any surface point is defined on the upper hemisphere; full spherical representation is not needed. We propose the use of hemispherical harmonics (HSH) to model images of convex Lambertian objects under distant illumination. We formulate and prove the addition theorem for HSH in order to provide an analytical expression of the reflectance function in the HSH domain. We prove that the Lambertian kernel has a more compact harmonic expansion in the HSH domain when compared to its SH counterpart. Our experiments illustrate that the 1st order HSH outperforms 1st and 2nd order SH in the process of image reconstruction as the number of light sources grows.

Bone mineral density (BMD) measurements and fracture analysis of the spine bones are restricted to the Vertebral bodies (VBs), especially the trabecular bones (TBs). In this paper, we propose a novel, fast, and robust 3D framework to segment VBs and trabecular bones in clinical computed tomography (CT) images without any user intervention. The Matched filter is employed to detect the VB region automatically. To segment the whole VB, the graph cuts method which integrates a linear combination of Gaussians (LCG) and Markov Gibbs Random Field (MGRF) is used. Then, the cortical and trabecular bones are segmented using local volume growing methods. Validity was analyzed using ground truths of data sets (expert segmentation) and the European Spine Phantom (ESP) as a known reference. Experiments on the data sets show that the proposed segmentation approach is more accurate than other known alternatives.

In this paper, we propose a new 3D framework to identify and segment VBs and TBs in clinical computed tomography (CT) images without any user intervention. The Matched filter is employed to detect the VB region automatically on axial axis. To identify the VB on coronal and sagittal axis, we use a new developed approach based on 4 points automatically placed on cortical shell. To segment the identified VB, the graph cuts method which integrates a linear combination of Gaussians (LCG) and Markov Gibbs Random Field (MGRF) are used. Then, the cortical and trabecular bones are segmented using local volume growing methods. Experiments on the data sets show that the proposed segmentation approach is more accurate than other known alternatives.

We discuss a statistical shape-from-shading framework for images of general and unknown illumination. To overcome arbitrary illumination, the framework makes use of the fact that general lighting can be expressed using low-order spherical harmonics for convex Lambertian objects. We cast the classical shape-from-shading equation as a Partial Least Squares (PLS) regression problem, which allows for the rapid computation of the solution. Results show accurate shape recovery with respect to ground truth data.

Bone mineral density (BMD) measurements and fracture analysis of the spine bones are restricted to the Vertebral bodies (VBs). In this paper, we propose a novel 3D shape based method to segment VBs in clinical computed tomography (CT) images without any user intervention. The proposed method depends on both image appearance and shape information. 3D shape information is obtained from a set of training data sets. Then, we estimate the shape variations using a distance probabilistic model which approximates the marginal densities of the VB and background in the variability region. To segment a VB, the Matched filter is used to detect the VB region automatically. We align the detected volume with 3D shape prior in order to be used in distance probabilistic model. Then, the graph cuts method which integrates the linear combination of Gaussians (LCG), Markov Gibbs Random Field (MGRF), and distance probabilistic model obtained from 3D shape prior is used. Experiments on the data sets show that the proposed segmentation approach is more accurate than other known alternatives.

This paper introduces a framework for long-distance face recognition using dense and sparse stereo reconstruction, with texture of the facial region. Two methods to determine correspondences of the stereo pair are used in this paper: (a) dense global stereo-matching using maximum-a-posteriori Markov Random Fields (MAP-MRF) algorithms and (b) Active Appearance Model (AAM) fitting of both images of the stereo pair and using the fitted AAM mesh as the sparse correspondences. Experiments are performed using combinations of different features extracted from the dense and sparse reconstructions, as well as facial texture. The cumulative rank curves (CMC), which are generated using the proposed framework, confirms the feasibility of the proposed work for long distance recognition of human faces.

We introduce a framework for face recognition at a distance based on sparse-stereo reconstruction. We develop a 3D acquisition system that consists of two CCD stereo cameras mounted on pan-tilt units with adjustable baseline. We first detect the facial region and extract its landmark points, which are used to initialize an AAM mesh fitting algorithm. The fitted mesh vertices provide point correspondences between the left and right images of a stereo pair; stereo-based reconstruction is then used to infer the 3D information of the mesh vertices. We perform experiments regarding the use of different features extracted from these vertices for face recognition. The cumulative rank curves (CMC), which are generated using the proposed framework, confirms the feasibility of the proposed work for long distance recognition of human faces with respect to the state-of-the-art [3].

We present a new statistical shape-from-shading framework for images of unknown illumination. The object (e.g., face) to be reconstructed is described by a parametric model. To deal with arbitrary illumination, the framework makes use of recent results that general lighting can be expressed using low-order spherical harmonics for convex Lambertian objects. The classical shape-from-shading equation is modified according to this framework. Results show accurate shape recovery with respect to ground truth data.