STATISTICAL SHAPE SPACES FOR 3D DATA: A REVIEW
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paper_title: Exploration of Shape Variation Using Localized Components Analysis

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Localized components analysis (LoCA) is a new method for describing surface shape variation in an ensemble of objects using a linear subspace of spatially localized shape components. In contrast to earlier methods, LoCA optimizes explicitly for localized components and allows a flexible trade-off between localized and concise representations, and the formulation of locality is flexible enough to incorporate properties such as symmetry. This paper demonstrates that LoCA can provide intuitive presentations of shape differences associated with sex, disease state, and species in a broad range of biomedical specimens, including human brain regions and monkey crania.
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paper_title: What Shape Are Dolphins? Building 3D Morphable Models from 2D Images

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3D morphable models are low-dimensional parameterizations of 3D object classes which provide a powerful means of associating 3D geometry to 2D images. However, morphable models are currently generated from 3D scans, so for general object classes such as animals they are economically and practically infeasible. We show that, given a small amount of user interaction (little more than that required to build a conventional morphable model), there is enough information in a collection of 2D pictures of certain object classes to generate a full 3D morphable model, even in the absence of surface texture. The key restriction is that the object class should not be strongly articulated, and that a very rough rigid model should be provided as an initial estimate of the “mean shape.” The model representation is a linear combination of subdivision surfaces, which we fit to image silhouettes and any identifiable key points using a novel combined continuous-discrete optimization strategy. Results are demonstrated on several natural object classes, and show that models of rather high quality can be obtained from this limited information.
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paper_title: A statistical model for synthesis of detailed facial geometry

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Detailed surface geometry contributes greatly to the visual realism of 3D face models. However, acquiring high-resolution face geometry is often tedious and expensive. Consequently, most face models used in games, virtual reality, or computer vision look unrealistically smooth. In this paper, we introduce a new statistical technique for the analysis and synthesis of small three-dimensional facial features, such as wrinkles and pores. We acquire high-resolution face geometry for people across a wide range of ages, genders, and races. For each scan, we separate the skin surface details from a smooth base mesh using displaced subdivision surfaces. Then, we analyze the resulting displacement maps using the texture analysis/synthesis framework of Heeger and Bergen, adapted to capture statistics that vary spatially across a face. Finally, we use the extracted statistics to synthesize plausible detail on face meshes of arbitrary subjects. We demonstrate the effectiveness of this method in several applications, including analysis of facial texture in subjects with different ages and genders, interpolation between high-resolution face scans, adding detail to low-resolution face scans, and adjusting the apparent age of faces. In all cases, we are able to re-produce fine geometric details consistent with those observed in high resolution scans.
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paper_title: Facial expression editing in video using a temporally-smooth factorization

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We address the problem of editing facial expression in video, such as exaggerating, attenuating or replacing the expression with a different one in some parts of the video. To achieve this we develop a tensor-based 3D face geometry reconstruction method, which fits a 3D model for each video frame, with the constraint that all models have the same identity and requiring temporal continuity of pose and expression. With the identity constraint, the differences between the underlying 3D shapes capture only changes in expression and pose. We show that various expression editing tasks in video can be achieved by combining face reordering with face warping, where the warp is induced by projecting differences in 3D face shapes into the image plane. Analogously, we show how the identity can be manipulated while fixing expression and pose. Experimental results show that our method can effectively edit expressions and identity in video in a temporally-coherent way with high fidelity.
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paper_title: Face transfer with multilinear models

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Face Transfer is a method for mapping videorecorded performances of one individual to facial animations of another. It extracts visemes (speech-related mouth articulations), expressions, and three-dimensional (3D) pose from monocular video or film footage. These parameters are then used to generate and drive a detailed 3D textured face mesh for a target identity, which can be seamlessly rendered back into target footage. The underlying face model automatically adjusts for how the target performs facial expressions and visemes. The performance data can be easily edited to change the visemes, expressions, pose, or even the identity of the target---the attributes are separably controllable. This supports a wide variety of video rewrite and puppetry applications.Face Transfer is based on a multilinear model of 3D face meshes that separably parameterizes the space of geometric variations due to different attributes (e.g., identity, expression, and viseme). Separability means that each of these attributes can be independently varied. A multilinear model can be estimated from a Cartesian product of examples (identities x expressions x visemes) with techniques from statistical analysis, but only after careful preprocessing of the geometric data set to secure one-to-one correspondence, to minimize cross-coupling artifacts, and to fill in any missing examples. Face Transfer offers new solutions to these problems and links the estimated model with a face-tracking algorithm to extract pose, expression, and viseme parameters.
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paper_title: 3D morphable face models revisited

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In this paper we revisit the process of constructing a high resolution 3D morphable model of face shape variation. We demonstrate how the statistical tools of thin-plate splines and Procrustes analysis can be used to construct a morphable model that is both more efficient and generalises to novel face surfaces more accurately than previous models. We also reformulate the probabilistic prior that the model provides on the distribution of parameter vector lengths. This distribution is determined solely by the number of model dimensions and can be used as a regularisation constraint in fitting the model to data without the need to empirically choose a parameter controlling the trade off between plausibility and quality of fit. As an example application of this improved model, we show how it may be fitted to a sparse set of 2D feature points (approximately 100). This provides a rapid means to estimate high resolution 3D face shape for a face in any pose given only a single face image. We present experimental results using ground truth data and hence provide absolute reconstruction errors. On average, the per vertex error of the reconstructed faces is less than 3.6 mm.
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paper_title: Video face replacement

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We present a method for replacing facial performances in video. Our approach accounts for differences in identity, visual appearance, speech, and timing between source and target videos. Unlike prior work, it does not require substantial manual operation or complex acquisition hardware, only single-camera video. We use a 3D multilinear model to track the facial performance in both videos. Using the corresponding 3D geometry, we warp the source to the target face and retime the source to match the target performance. We then compute an optimal seam through the video volume that maintains temporal consistency in the final composite. We showcase the use of our method on a variety of examples and present the result of a user study that suggests our results are difficult to distinguish from real video footage.
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paper_title: Expression flow for 3D-aware face component transfer

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We address the problem of correcting an undesirable expression on a face photo by transferring local facial components, such as a smiling mouth, from another face photo of the same person which has the desired expression. Direct copying and blending using existing compositing tools results in semantically unnatural composites, since expression is a global effect and the local component in one expression is often incompatible with the shape and other components of the face in another expression. To solve this problem we present Expression Flow, a 2D flow field which can warp the target face globally in a natural way, so that the warped face is compatible with the new facial component to be copied over. To do this, starting with the two input face photos, we jointly construct a pair of 3D face shapes with the same identity but different expressions. The expression flow is computed by projecting the difference between the two 3D shapes back to 2D. It describes how to warp the target face photo to match the expression of the reference photo. User studies suggest that our system is able to generate face composites with much higher fidelity than existing methods.
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paper_title: A Data-driven Approach to Human-body Cloning Using a Segmented Body Database

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We present a data-driven approach to build a human body model from a single photograph by performing Principal Component Analysis (PCA) on a database of body segments. We segment a collection of human bodies to compile the required database prior to performing the analysis. Our approach then builds a single PCA for each body segment - head, left and right arms, torso and left and right legs - yielding six PCAs in total. This strategy improves on the flexibility of conventional data-driven approaches in 3D modeling and allows our approach to take variations in ethnicity, age and body posture into account. We demonstrate our approach in practice by constructing models of a Caucasian male, an Asian male and a toddler from corresponding photographs and a Caucasian adult oriented database. We also discuss rapid consistent parameterization based on Radial Basis Functions (RBF) and non-optimization based learning systems to reduce execution time.
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paper_title: Learning shape priors for single view reconstruction

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In this paper, we aim to reconstruct free-from 3D models from a single view by learning the prior knowledge of a specific class of objects. Instead of heuristically proposing specific regularities and defining parametric models as previous research, our shape prior is learned directly from existing 3D models under a framework based on the Gaussian Process Latent Variable Model (GPLVM). The major contributions of the paper include: 1) a probabilistic framework for prior-based reconstruction we propose, which requires no heuristic of the object, and can be easily generalized to handle various categories of 3D objects, and 2) an attempt at automatic reconstruction of more complex 3D shapes, like human bodies, from 2D silhouettes only. Qualitative and quantitative experimental results on both synthetic and real data demonstrate the efficacy of our new approach.
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paper_title: The space of human body shapes: reconstruction and parameterization from range scans

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We develop a novel method for fitting high-resolution template meshes to detailed human body range scans with sparse 3D markers. We formulate an optimization problem in which the degrees of freedom are an affine transformation at each template vertex. The objective function is a weighted combination of three measures: proximity of transformed vertices to the range data, similarity between neighboring transformations, and proximity of sparse markers at corresponding locations on the template and target surface. We solve for the transformations with a non-linear optimizer, run at two resolutions to speed convergence. We demonstrate reconstruction and consistent parameterization of 250 human body models. With this parameterized set, we explore a variety of applications for human body modeling, including: morphing, texture transfer, statistical analysis of shape, model fitting from sparse markers, feature analysis to modify multiple correlated parameters (such as the weight and height of an individual), and transfer of surface detail and animation controls from a template to fitted models.
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paper_title: A statistical model of human pose and body shape

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A circuit for controlling a display panel identifying malfunctions in an engine generator receives a plurality of electrical signals from the engine generator, each of which identifies a particular trouble. The electrical signal may be produced by closing a switch. It is caused to operate a latch that lights a light associated with the particular malfunction. Indications of other malfunctions are suppressed until the circuit is reset. A manual reset tests all lights and then leaves them off ready to respond. A power-up reset does not test lights but leaves all lights off ready to respond. The circuit is rendered especially appropriate for military use by hardening against radiation and against pulses of electromagnetic interference.
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paper_title: The naked truth: Estimating body shape under clothing

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We propose a method to estimate the detailed 3D shape of a person from images of that person wearing clothing. The approach exploits a model of human body shapes that is learned from a database of over 2000 range scans. We show that the parameters of this shape model can be recovered independently of body pose. We further propose a generalization of the visual hull to account for the fact that observed silhouettes of clothed people do not provide a tight bound on the true 3D shape. With clothed subjects, different poses provide different constraints on the possible underlying 3D body shape. We consequently combine constraints across pose to more accurately estimate 3D body shape in the presence of occluding clothing. Finally we use the recovered 3D shape to estimate the gender of subjects and then employ gender-specific body models to refine our shape estimates. Results on a novel database of thousands of images of clothed and "naked" subjects, as well as sequences from the HumanEva dataset, suggest the method may be accurate enough for biometric shape analysis in video.
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paper_title: Estimating human shape and pose from a single image

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We describe a solution to the challenging problem of estimating human body shape from a single photograph or painting. Our approach computes shape and pose parameters of a 3D human body model directly from monocular image cues and advances the state of the art in several directions. First, given a user-supplied estimate of the subject's height and a few clicked points on the body we estimate an initial 3D articulated body pose and shape. Second, using this initial guess we generate a tri-map of regions inside, outside and on the boundary of the human, which is used to segment the image using graph cuts. Third, we learn a low-dimensional linear model of human shape in which variations due to height are concentrated along a single dimension, enabling height-constrained estimation of body shape. Fourth, we formulate the problem of parametric human shape from shading. We estimate the body pose, shape and reflectance as well as the scene lighting that produces a synthesized body that robustly matches the image evidence. Quantitative experiments demonstrate how smooth shading provides powerful constraints on human shape. We further demonstrate a novel application in which we extract 3D human models from archival photographs and paintings.
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paper_title: Home 3D body scans from noisy image and range data

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The 3D shape of the human body is useful for applications in fitness, games and apparel. Accurate body scanners, however, are expensive, limiting the availability of 3D body models. We present a method for human shape reconstruction from noisy monocular image and range data using a single inexpensive commodity sensor. The approach combines low-resolution image silhouettes with coarse range data to estimate a parametric model of the body. Accurate 3D shape estimates are obtained by combining multiple monocular views of a person moving in front of the sensor. To cope with varying body pose, we use a SCAPE body model which factors 3D body shape and pose variations. This enables the estimation of a single consistent shape while allowing pose to vary. Additionally, we describe a novel method to minimize the distance between the projected 3D body contour and the image silhouette that uses analytic derivatives of the objective function. We propose a simple method to estimate standard body measurements from the recovered SCAPE model and show that the accuracy of our method is competitive with commercial body scanning systems costing orders of magnitude more.
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paper_title: SCAPE: shape completion and animation of people

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We introduce the SCAPE method (Shape Completion and Animation for PEople)---a data-driven method for building a human shape model that spans variation in both subject shape and pose. The method is based on a representation that incorporates both articulated and non-rigid deformations. We learn a pose deformation model that derives the non-rigid surface deformation as a function of the pose of the articulated skeleton. We also learn a separate model of variation based on body shape. Our two models can be combined to produce 3D surface models with realistic muscle deformation for different people in different poses, when neither appear in the training set. We show how the model can be used for shape completion --- generating a complete surface mesh given a limited set of markers specifying the target shape. We present applications of shape completion to partial view completion and motion capture animation. In particular, our method is capable of constructing a high-quality animated surface model of a moving person, with realistic muscle deformation, using just a single static scan and a marker motion capture sequence of the person.
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paper_title: Tensor-Based Human Body Modeling

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In this paper, we present a novel approach to model 3D human body with variations on both human shape and pose, by exploring a tensor decomposition technique. 3D human body modeling is important for 3D reconstruction and animation of realistic human body, which can be widely used in Tele-presence and video game applications. It is challenging due to a wide range of shape variations over different people and poses. The existing SCAPE model is popular in computer vision for modeling 3D human body. However, it considers shape and pose deformations separately, which is not accurate since pose deformation is person-dependent. Our tensor-based model addresses this issue by jointly modeling shape and pose deformations. Experimental results demonstrate that our tensor-based model outperforms the SCAPE model quite significantly. We also apply our model to capture human body using Microsoft Kinect sensors with excellent results.
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paper_title: Statistical Models of Shape: Optimisation and Evaluation

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The goal of image interpretation is to convert raw image data into me- ingful information. Images are often interpreted manually. In medicine, for example, a radiologist looks at a medical image, interprets it, and tra- lates the data into a clinically useful form. Manual image interpretation is, however, a time-consuming, error-prone, and subjective process that often requires specialist knowledge. Automated methods that promise fast and - jective image interpretation have therefore stirred up much interest and have become a signi?cant area of research activity. Early work on automated interpretation used low-level operations such as edge detection and region growing to label objects in images. These can p- ducereasonableresultsonsimpleimages,butthepresenceofnoise,occlusion, andstructuralcomplexity oftenleadstoerroneouslabelling. Furthermore,- belling an object is often only the ?rst step of the interpretation process. In order to perform higher-level analysis, a priori information must be incor- rated into the interpretation process. A convenient way of achieving this is to use a ?exible model to encode information such as the expected size, shape, appearance, and position of objects in an image. The use of ?exible models was popularized by the active contour model, or snake [98]. A snake deforms so as to match image evidence (e.g., edges) whilst ensuring that it satis?es structural constraints. However, a snake lacks speci?city as it has little knowledge of the domain, limiting its value in image interpretation.
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paper_title: Fast 3d spine reconstruction of postoperative patients using a multilevel statistical model

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Severe cases of spinal deformities such as scoliosis are usually treated by a surgery where instrumentation (hooks, screws and rods) is installed to the spine to correct deformities. Even if the purpose is to obtain a normal spine curve, the result is often straighter than normal. In this paper, we propose a fast statistical reconstruction algorithm based on a general model which can deal with such instrumented spines. To this end, we present the concept of multilevel statistical model where the data are decomposed into a within-group and a between-group component. The reconstruction procedure is formulated as a second-order cone program which can be solved very fast (few tenths of a second). Reconstruction errors were evaluated on real patient data and results showed that multilevel modeling allows better 3D reconstruction than classical models.
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paper_title: A statistical parts-based appearance model of inter-subject variability

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In this article, we present a general statistical parts-based model for representing the appearance of an image set, applied to the problem of inter-subject MR brain image matching. In contrast with global image representations such as active appearance models, the parts-based model consists of a collection of localized image parts whose appearance, geometry and occurrence frequency are quantified statistically. The parts-based approach explicitly addresses the case where one-to-one correspondence does not exist between subjects due to anatomical differences, as parts are not expected to occur in all subjects. The model can be learned automatically, discovering structures that appear with statistical regularity in a large set of subject images, and can be robustly fit to new images, all in the presence of significant inter-subject variability. As parts are derived from generic scale-invariant features, the framework can be applied in a wide variety of image contexts, in order to study the commonality of anatomical parts or to group subjects according to the parts they share. Experimentation shows that a parts-based model can be learned from a large set of MR brain images, and used to determine parts that are common within the group of subjects. Preliminary results indicate that the model can be used to automatically identify distinctive features for inter-subject image registration despite large changes in appearance.
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paper_title: Principal geodesic analysis for the study of nonlinear statistics of shape

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A primary goal of statistical shape analysis is to describe the variability of a population of geometric objects. A standard technique for computing such descriptions is principal component analysis. However, principal component analysis is limited in that it only works for data lying in a Euclidean vector space. While this is certainly sufficient for geometric models that are parameterized by a set of landmarks or a dense collection of boundary points, it does not handle more complex representations of shape. We have been developing representations of geometry based on the medial axis description or m-rep. While the medial representation provides a rich language for variability in terms of bending, twisting, and widening, the medial parameters are not elements of a Euclidean vector space. They are in fact elements of a nonlinear Riemannian symmetric space. In this paper, we develop the method of principal geodesic analysis, a generalization of principal component analysis to the manifold setting. We demonstrate its use in describing the variability of medially-defined anatomical objects. Results of applying this framework on a population of hippocampi in a schizophrenia study are presented.
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paper_title: Statistical Shape Analysis

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Preliminaries: Size Measures and Shape Coordinates. Preliminaries: Planar Procrustes Analysis. Shape Space and Distance. General Procrustes Methods. Shape Models for Two Dimensional Data. Tangent Space Inference. Size--and--Shape. Distributions for Higher Dimensions. Deformations and Describing Shape Change. Shape in Images. Additional Topics. References and Author Index. Index.
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paper_title: Evaluation of 3D Correspondence Methods for Model Building

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The correspondence problem is of high relevance in the construction and use of statistical models. Statistical models are used for a variety of medical application, e.g. segmentation, registration and shape analysis. In this paper, we present comparative studies in three anatomical structures of four different correspondence establishing methods. The goal in all of the presented studies is a model-based application. We have analyzed both the direct correspondence via manually selected landmarks as well as the properties of the model implied by the correspondences, in regard to compactness, generalization and specificity. The studied methods include a manually initialized subdivision surface (MSS) method and three automatic methods that optimize the object parameterization: SPHARM, MDL and the covariance determinant (DetCov) method. In all studies, DetCov and MDL showed very similar results. The model properties of DetCov and MDL were better than SPHARM and MSS. The results suggest that for modeling purposes the best of the studied correspondence method are MDL and DetCov.
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paper_title: Generalized B-spline subdivision-surface wavelets for geometry compression

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We present a new construction of lifted biorthogonal wavelets on surfaces of arbitrary two-manifold topology for compression and multiresolution representation. Our method combines three approaches: subdivision surfaces of arbitrary topology, B-spline wavelets, and the lifting scheme for biorthogonal wavelet construction. The simple building blocks of our wavelet transform are local lifting operations performed on polygonal meshes with subdivision hierarchy. Starting with a coarse, irregular polyhedral base mesh, our transform creates a subdivision hierarchy of meshes converging to a smooth limit surface. At every subdivision level, geometric detail is expanded from wavelet coefficients and added to the surface. We present wavelet constructions for bilinear, bicubic, and biquintic B-spline subdivision. While the bilinear and bicubic constructions perform well in numerical experiments, the biquintic construction turns out to be unstable. For lossless compression, our transform is computed in integer arithmetic, mapping integer coordinates of control points to integer wavelet coefficients. Our approach provides a highly efficient and progressive representation for complex geometries of arbitrary topology.
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paper_title: Model-Guided Segmentation of 3D Neuroradiological Image Using Statistical Surface Wavelet Model

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This paper proposes a novel model-guided segmentation framework utilizing a statistical surface wavelet model as a shape prior. In the model building process, a set of training shapes are decomposed through the subdivision surface wavelet scheme. By interpreting the resultant wavelet coefficients as random variables, we compute prior probability distributions of the wavelet coefficients to model the shape variations of the training set at different scales and spatial locations. With this statistical shape model, the segmentation task is formulated as an optimization problem to best fit the statistical shape model with an input image. Due to the localization property of the wavelet shape representation both in scale and space, this multi-dimensional optimization problem can be efficiently solved in a multiscale and spatial-localized manner. We have applied our method to segment cerebral caudate nuclei from MRI images. The experimental results have been validated with segmentations obtained through human expert. These show that our method is robust, computationally efficient and achieves a high degree of segmentation accuracy.
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paper_title: Generalized B-spline subdivision-surface wavelets for geometry compression

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We present a new construction of lifted biorthogonal wavelets on surfaces of arbitrary two-manifold topology for compression and multiresolution representation. Our method combines three approaches: subdivision surfaces of arbitrary topology, B-spline wavelets, and the lifting scheme for biorthogonal wavelet construction. The simple building blocks of our wavelet transform are local lifting operations performed on polygonal meshes with subdivision hierarchy. Starting with a coarse, irregular polyhedral base mesh, our transform creates a subdivision hierarchy of meshes converging to a smooth limit surface. At every subdivision level, geometric detail is expanded from wavelet coefficients and added to the surface. We present wavelet constructions for bilinear, bicubic, and biquintic B-spline subdivision. While the bilinear and bicubic constructions perform well in numerical experiments, the biquintic construction turns out to be unstable. For lossless compression, our transform is computed in integer arithmetic, mapping integer coordinates of control points to integer wavelet coefficients. Our approach provides a highly efficient and progressive representation for complex geometries of arbitrary topology.
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paper_title: 3D face landmark labelling

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Most 3D face processing systems require feature detection and localisation, for example to crop, register, analyse or recognise faces. The three features often used in the literature are the tip of the nose, and the two inner corner of the eyes. Failure to localise these landmarks can cause the system to fail and they become very difficult to detect under large pose variations or when occlusion is present. In this paper, we present a proof-of-concept for a face labelling system capable of overcoming this problem, as a larger number of landmarks are employed. A set of points containing hand-placed landmarks is used as input data. The aim here is to retrieve the landmark's labels when some part of the face is missing. By using graph matching techniques to reduce the number of candidates, and translation and unit-quaternion clustering to determine a final correspondence, we evaluate the accuracy at which landmarks can be retrieved under changes in expression, orientation and in the presence of occlusions.
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paper_title: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography

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A new paradigm, Random Sample Consensus (RANSAC), for fitting a model to experimental data is introduced. RANSAC is capable of interpreting/smoothing data containing a significant percentage of gross errors, and is thus ideally suited for applications in automated image analysis where interpretation is based on the data provided by error-prone feature detectors. A major portion of this paper describes the application of RANSAC to the Location Determination Problem (LDP): Given an image depicting a set of landmarks with known locations, determine that point in space from which the image was obtained. In response to a RANSAC requirement, new results are derived on the minimum number of landmarks needed to obtain a solution, and algorithms are presented for computing these minimum-landmark solutions in closed form. These results provide the basis for an automatic system that can solve the LDP under difficult viewing
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paper_title: Recognizing objects by matching oriented points

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We present an approach to recognition of complex objects in cluttered 3-D scenes that does not require feature extraction or segmentation. Our object representation comprises descriptive images associated with each oriented point on the surface of an object. Using a single point basis constructed from an oriented point, the position of other points on the surface of the object can be described by two parameters. The accumulation of these parameters for many points on the surface of the object results in an image at each oriented point. These images, localized descriptions of the global shape of the object, are invariant to rigid transformations. Through correlation of images, point correspondences between a model and scene data are established and then grouped using geometric consistency. The effectiveness of our algorithm is demonstrated with results showing recognition of complex objects in cluttered scenes with occlusion.
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paper_title: A 3D facial expression database for facial behavior research

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Traditionally, human facial expressions have been studied using either 2D static images or 2D video sequences. The 2D-based analysis is incapable of handing large pose variations. Although 3D modeling techniques have been extensively used for 3D face recognition and 3D face animation, barely any research on 3D facial expression recognition using 3D range data has been reported. A primary factor for preventing such research is the lack of a publicly available 3D facial expression database. In this paper, we present a newly developed 3D facial expression database, which includes both prototypical 3D facial expression shapes and 2D facial textures of 2,500 models from 100 subjects. This is the first attempt at making a 3D facial expression database available for the research community, with the ultimate goal of fostering the research on affective computing and increasing the general understanding of facial behavior and the fine 3D structure inherent in human facial expressions. The new database can be a valuable resource for algorithm assessment, comparison and evaluation.
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paper_title: Bosphorus database for 3D face analysis

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A new 3D face database that includes a rich set of expressions, systematic variation of poses and different types of occlusions is presented in this paper. This database is unique from three aspects: i) the facial expressions are composed of judiciously selected subset of Action Units as well as the six basic emotions, and many actors/actresses are incorporated to obtain more realistic expression data; ii) a rich set of head pose variations are available; and iii) different types of face occlusions are included. Hence, this new database can be a very valuable resource for development and evaluation of algorithms on face recognition under adverse conditions and facial expression analysis as well as for facial expression synthesis.
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Title: STATISTICAL SHAPE SPACES FOR 3D DATA: A REVIEW

Section 1: Introduction
Description 1: Discuss the advancements and applications of 3D data acquisition and the importance of statistical shape models for various object classes, especially human-related structures.

Section 2: Statistical Shape Spaces
Description 2: Explain the concept of statistical shape spaces, including the formulation of statistical shape analysis and the most common techniques like PCA used for shape representation.

Section 3: Statistical Shape Spaces in Image Processing
Description 3: Review the application of statistical shape analysis in image processing, focusing on human faces, human bodies, and medical data, providing examples and methods used.

Section 4: Learning a Statistical Shape Space
Description 4: Describe the process of learning a statistical shape space, including training shape models with global PCA and wavelet PCA, and preprocessing steps like generalized Procrustes analysis.

Section 5: Evaluating a Statistical Model
Description 5: Present methods to evaluate statistical models, including metrics such as compactness, generalization, and specificity, and their impact on model performance.

Section 6: Fitting a Statistical Shape Model
Description 6: Discuss the techniques for fitting statistical shape models to ambiguous data, covering initial alignment and energy minimization in shape space.

Section 7: Experiments
Description 7: Provide experimental setups, including training and test data, error measures, and results for fitting quality and visual evaluation.

Section 8: Conclusion
Description 8: Summarize the findings of the review, emphasizing the significance of statistical shape spaces and potential areas for future research.