Automatic facial expression tracking for 4D range scans

This paper presents a fully automatic approach of spatio-temporal facial expression tracking for 4D range scans without any manual interventions (such as specifying landmarks). The approach consists of three steps: rigid registration, facial model reconstruction, and facial expression tracking. A Scaling Iterative Closest Points (SICP) algorithm is introduced to compute the optimal rigid registration between a template facial model and a range scan with consideration of the scale problem. A deformable model, physically based on thin shells, is proposed to faithfully reconstruct the facial surface and texture from that range data. And then the reconstructed facial model is used to track facial expressions presented in a sequence of range scans by the deformable model

Simultaneously continuous retraction and Bishop-Phelps-Bollob\'as type theorem

We study the existence of a retraction from the dual space $X^*$ of a (real or complex) Banach space $X$ onto its unit ball $B_{X^*}$ which is uniformly continuous in norm topology and continuous in weak-$*$ topology. Such a retraction is called a uniformly simultaneously continuous retraction. It is shown that if $X$ has a normalized unconditional Schauder basis with unconditional basis constant 1 and $X^*$ is uniformly monotone, then a uniformly simultaneously continuous retraction from $X^*$ onto $B_{X^*}$ exists. It is also shown that if $\{X_i\}$ is a family of separable Banach spaces whose duals are uniformly convex with moduli of convexity $\delta_i(\varepsilon)$ such that $\inf_i \delta_i(\varepsilon)>0$ and $X= \left[\bigoplus X_i\right]_{c_0}$ or $X=\left[\bigoplus X_i\right]_{\ell_p}$ for $1\le p<\infty$, then a uniformly simultaneously continuous retraction exists from $X^*$ onto $B_{X^*}$. The relation between the existence of a uniformly simultaneously continuous retraction and the Bishsop-Phelps-Bollob\'as property for operators is investigated and it is proved that the existence of a uniformly simultaneously continuous retraction from $X^*$ onto its unit ball implies that a pair $(X, C_0(K))$ has the Bishop-Phelps-Bollob\'as property for every locally compact Hausdorff spaces $K$. As a corollary, we prove that $(C_0(S), C_0(K))$ has the Bishop-Phelps-Bollob\'as property if $C_0(S)$ and $C_0(K)$ are the spaces of all real-valued continuous functions vanishing at infinity on locally compact metric space $S$ and locally compact Hausdorff space $K$ respectively.Comment: 15 page

Self-correction of 3D reconstruction from multi-view stereo images

We present a self-correction approach to improving the 3D reconstruction of a multi-view 3D photogrammetry system. The self-correction approach has been able to repair the reconstructed 3D surface damaged by depth discontinuities. Due to self-occlusion, multi-view range images have to be acquired and integrated into a watertight nonredundant mesh model in order to cover the extended surface of an imaged object. The integrated surface often suffers from “dent” artifacts produced by depth discontinuities in the multi-view range images. In this paper we propose a novel approach to correcting the 3D integrated surface such that the dent artifacts can be repaired automatically. We show examples of 3D reconstruction to demonstrate the improvement that can be achieved by the self-correction approach. This self-correction approach can be extended to integrate range images obtained from alternative range capture devices

The accuracy of three-dimensional prediction of soft tissue changes following the surgical correction of facial asymmetry: an innovative concept

The accuracy of three-dimensional (3D) predictions of soft tissue changes in the surgical correction of facial asymmetry was evaluated in this study. Preoperative (T1) and 6–12-month postoperative (T2) cone beam computed tomography scans of 13 patients were studied. All patients underwent surgical correction of facial asymmetry as part of a multidisciplinary treatment protocol. The magnitude of the surgical movement was measured; virtual surgery was performed on the preoperative scans using Maxilim software. The predicted soft tissue changes were compared to the actual postoperative appearance (T2). Mean (signed) distances and mean (absolute) distances between the predicted and actual 3D surface meshes for each region were calculated. The one-sample t-test was applied to test the alternative hypothesis that the mean absolute distances had a value of &lt;2.0 mm. A novel directional analysis was applied to analyse the accuracy of the prediction of soft tissue changes. The results showed that the distances between the predicted and actual postoperative soft tissue changes were less than 2.0 mm in all regions. The predicted facial morphology was narrower than the actual surgical changes in the cheek regions. 3D soft tissue prediction using Maxilim software in patients undergoing the correction of facial asymmetry is clinically acceptable

Assessment of facial asymmetry before and after the surgical repair of cleft lip in unilateral cleft lip and palate cases

This study was performed to assess facial asymmetry in patients with unilateral cleft lip and palate (UCLP) before and after primary lip repair. Three-dimensional facial images of 30 UCLP cases (mean age 3.7 ± 0.8 months) captured 1–2 days before surgery and 4 months after surgery using stereophotogrammetry were analysed. A generic mesh – a mathematical facial mask consisting of thousands of points (vertices) – was conformed on the three-dimensional images. Average preoperative and postoperative conformed facial meshes were obtained and mirrored by reflecting on the lateral plane. Facial asymmetry was assessed by measuring the distances between the corresponding vertices of the superimposed facial meshes. Asymmetries were further examined in three directions: horizontal, vertical, and anteroposterior. Preoperatively, the philtrum and bridge of the nose were deviated towards the non-cleft side. The maximum vertical asymmetry was at the upper lip. The greatest anteroposterior asymmetry was at the alar base and in the paranasal area. The overall facial asymmetry improved markedly after surgery. Residual anteroposterior asymmetry was noted at the alar base, upper lip, and cheek on the cleft slide. In conclusion, dense correspondence analysis provided an insight into the anatomical reasons for the residual dysmorphology following the surgical repair of cleft lip for future surgical consideration

Accuracy of generic mesh conformation: the future of facial morphological analysis

Three-dimensional (3D) analysis of the face is required for the assessment of changes following surgery, to monitor the progress of pathological conditions and for the evaluation of facial growth. Sophisticated methods have been applied for the evaluation of facial morphology, the most common being dense surface correspondence. The method depends on the application of a mathematical facial mask known as the generic facial mesh for the evaluation of the characteristics of facial morphology. This study evaluated the accuracy of the conformation of generic mesh to the underlying facial morphology. The study was conducted on 10 non-patient volunteers. Thirty-four 2-mm-diameter self-adhesive, non-reflective markers were placed on each face. These were readily identifiable on the captured 3D facial image, which was captured by Di3D stereophotogrammetry. The markers helped in minimising digitisation errors during the conformation process. For each case, the face was captured six times: at rest and at the maximum movements of four facial expressions. The 3D facial image of each facial expression was analysed. Euclidean distances between the 19 corresponding landmarks on the conformed mesh and on the original 3D facial model provided a measure of the accuracy of the conformation process. For all facial expressions and all corresponding landmarks, these distances were between 0.7 and 1.7 mm. The absolute mean distances ranged from 0.73 to 1.74 mm. The mean absolute error of the conformation process was 1.13 ± 0.26 mm. The conformation of the generic facial mesh is accurate enough for clinical trial proved to be accurate enough for the analysis of the captured 3D facial images

A new automated workflow for 3D character creation based on 3D scanned data

In this paper we present a new workflow allowing the creation of 3D characters in an automated way that does not require the expertise of an animator. This workflow is based of the acquisition of real human data captured by 3D body scanners, which is them processed to generate firstly animatable body meshes, secondly skinned body meshes and finally textured 3D garments

The cost and benefit of banking regulations and controls, Chinese style

The neoclassical approach focuses its attention on the prudence of individual banks. In its objective of achieving allocative efficiency, it seeks to prevent market failures caused by the operations of the banks. In this light, it is contended that China should further its market reforms in the direction of fostering the profit maximization cum risk minimization pursuit of individual banks. Meanwhile, the Keynesian-Schumpeterian-Minskyan approach focuses its attention on coping with systemic fragility. And systemic fragility is seen as endemic to the interaction between credit expansion and contraction, productive investment, and business profitability. In this light, even if it is indeed allocatively inefficient, Chinese finance can still have its advantages in terms of promoting productive efficiency

Applying mesh conformation on shape analysis with missing data

A mesh conformation approach that makes use of deformable generic meshes has been applied to establishing correspondences between 3D shapes with missing data. Given a group of shapes with correspondences, we can build up a statistical shape model by applying principal component analysis (PCA). The conformation at first globally maps the generic mesh to the 3D shape based on manually located corresponding landmarks, and then locally deforms the generic mesh to clone the 3D shape. The local deformation is constrained by minimizing the energy of an elastic model. An algorithm was also embedded in the conformation process to fill missing surface data of the shapes. Using synthetic data, we demonstrate that the conformation preserves the configuration of the generic mesh and hence it helps to establish good correspondences for shape analysis. Case studies of the principal component analysis of shapes were presented to illustrate the successes and advantages of our approach

Nonparallel support vector machines for pattern classification

We propose a novel nonparallel classifier, called nonparallel support vector machine (NPSVM), for binary classification. Our NPSVM that is fully different from the existing nonparallel classifiers, such as the generalized eigenvalue proximal support vector machine (GEPSVM) and the twin support vector machine (TWSVM), has several incomparable advantages: 1) two primal problems are constructed implementing the structural risk minimization principle; 2) the dual problems of these two primal problems have the same advantages as that of the standard SVMs, so that the kernel trick can be applied directly, while existing TWSVMs have to construct another two primal problems for nonlinear cases based on the approximate kernel-generated surfaces, furthermore, their nonlinear problems cannot degenerate to the linear case even the linear kernel is used; 3) the dual problems have the same elegant formulation with that of standard SVMs and can certainly be solved efficiently by sequential minimization optimization algorithm, while existing GEPSVM or TWSVMs are not suitable for large scale problems; 4) it has the inherent sparseness as standard SVMs; 5) existing TWSVMs are only the special cases of the NPSVM when the parameters of which are appropriately chosen. Experimental results on lots of datasets show the effectiveness of our method in both sparseness and classification accuracy, and therefore, confirm the above conclusion further. In some sense, our NPSVM is a new starting point of nonparallel classifiers