Today, computer based face recognition is a mature and reliable mechanism which is being practically utilised for many access control scenarios. As such, face recognition or authentication is predominantly performed using ‘perfect’ data of full frontal facial images. Though that may be the case, in reality, there are numerous situations where full frontal faces may not be available — the imperfect face images that often come from CCTV cameras do demonstrate the case in point. Hence, the problem of computer based face recognition using partial facial data as probes is still largely an unexplored area of research. Given that humans and computers perform face recognition and authentication inherently differently, it must be interesting as well as intriguing to understand how a computer favours various parts of the face when presented to the challenges of face recognition. In this work, we explore the question that surrounds the idea of face recognition using partial facial data. We explore it by applying novel experiments to test the performance of machine learning using partial faces and other manipulations on face images such as rotation and zooming, which we use as training and recognition cues. In particular, we study the rate of recognition subject to the various parts of the face such as the eyes, mouth, nose and the cheek. We also study the effect of face recognition subject to facial rotation as well as the effect of recognition subject to zooming out of the facial images. Our experiments are based on using the state of the art convolutional neural network based architecture along with the pre-trained VGG-Face model through which we extract features for machine learning. We then use two classifiers namely the cosine similarity and the linear support vector machines to test the recognition rates. We ran our experiments on two publicly available datasets namely, the controlled Brazilian FEI and the uncontrolled LFW dataset. Our results show that individual parts of the face such as the eyes, nose and the cheeks have low recognition rates though the rate of recognition quickly goes up when individual parts of the face in combined form are presented as probes.

This paper presents a methodology for efficient shape parametrisation for automatic design optimisation using a partial differential equation (PDE) formulation. It is shown how the choice of an elliptic PDE enables one to define and parametrise geometries corresponding to complex shapes. By using the PDE formulation it is shown how the shape definition and parametrisation can be based on a boundary value approach by which complex shapes can be created and parametrised based on the shape information at the boundaries or the character lines defining the shape. Furthermore, this approach to shape definition allows complex shapes to be parametrised intuitively using a very small set of design parameters.

The complex formation of Islamic Geometric Patterns (IGP) is one of the distinctive features in Islamic art and architecture. Many have attempted to reproduce these patterns in digital form, using various pattern generation techniques, in 2D. Shape grammars are an e ective pattern generation method, providing good aesthetic results. In this pa- per we describe a novel approach in generating 3D IGP using the shape grammar method. The particular emphasis here is to generate the motifs (repeated units with the pattern) in 3D using parameterization. These can then be manipulated within the 3D space to construct architec- tural structures. In this work we have developed two distinctive Shape Grammars in 3D namely Parameterized Shape Grammar (PSG) and Auto-Parameterized Shape Grammar (APSG). Here the PSG generates the motifs and the APSG enables construction of the structures using the generated motifs. Both grammars are practically implemented as a 3D modelling tool within Autodesk Maya. The parameterization within each grammar is the key to generate both Islamic geometric motifs and Islamic geometric motif-based structures.

This work presents an efficient and fast method for achieving cyclic animation using Partial Differential Equations (PDEs). The boundary-value nature associ- ated with elliptic PDEs offers a fast analytic solution technique for setting up a framework for this type of animation. The surface of a given character is thus cre- ated from a set of pre-determined curves, which are used as boundary conditions so that a number of PDEs can be solved. Two different approaches to cyclic ani- mation are presented here. The first consists of using attaching the set of curves to a skeletal system hold- ing the animation for cyclic motions linked to a set mathematical expressions, the second one exploits the spine associated with the analytic solution of the PDE as a driving mechanism to achieve cyclic animation, which is also manipulated mathematically. The first of these approaches is implemented within a framework related to cyclic motions inherent to human-like char- acters, whereas the spine-based approach is focused on modelling the undulatory movement observed in fish when swimming. The proposed method is fast and ac- curate. Additionally, the animation can be either used in the PDE-based surface representation of the model or transferred to the original mesh model by means of a point to point map. Thus, the user is offered with the choice of using either of these two animation repre- sentations of the same object, the selection depends on the computing resources such as storage and memory capacity associated with each particular application.

Both prominent feature points and geodesic distance are key factors for mesh segmentation. With these two factors, this paper proposes a graph cut based mesh segmentation method. The mesh is first preprocessed by Laplacian smoothing. According to the Gaussian curvature, candidate feature points are then selected by a predefined threshold. With DBSCAN (Density-Based Spatial Clustering of Application with Noise), the selected candidate points are separated into some clusters, and the points with the maximum curvature in every cluster are regarded as the final feature points. We label these feature points, and regard the faces in the mesh as nodes for graph cut. Our energy function is constructed by utilizing the ratio between the geodesic distance and the Euclidean distance of vertex pairs of the mesh. The final segmentation result is obtained by minimizing the energy function using graph cut. The proposed algorithm is pose-invariant and can robustly segment the mesh into different parts in line with the selected feature points.

One of the challenging problems in geometric modeling and computer graphics is the construction of realistic human facial geometry. Such geometry are essential for a wide range of applications, such as 3D face recognition, virtual reality applications, facial expression simulation and computer based plastic surgery application. This paper addresses a method for the construction of 3D geometry of human faces based on the use of Elliptic Partial Differential Equations (PDE). Here the geometry corresponding to a human face is treated as a set of surface patches, whereby each surface patch is represented using four boundary curves in the 3-space that formulate the appropriate boundary conditions for the chosen PDE. These boundary curves are extracted automatically using 3D data of human faces obtained using a 3D scanner. The solution of the PDE generates a continuous single surface patch describing the geometry of the original scanned data. In this study, through a number of experimental verifications we have shown the efficiency of the PDE based method for 3D facial surface reconstruction using scan data. In addition to this, we also show that our approach provides an efficient way of facial representation using a small set of parameters that could be utilized for efficient facial data storage and verification purposes.

The spine of an object is an entity that can characterise the object¿s topology and describes the object by a lower dimension. It has an intuitive appeal for supporting geometric modelling operations. The aim of this paper is to show how a spine for a PDE surface can be generated. For the purpose of the work presented here an analytic solution form for the chosen PDE is utilised. It is shown that the spine of the PDE surface is then computed as a by-product of this analytic solution. This paper also discusses how the of a PDE surface can be used to manipulate the shape. The solution technique adopted here caters for periodic surfaces with general boundary conditions allowing the possibility of the spine based shape manipulation for a wide variety of free-form PDE surface shapes.

We present an efficient method for reconstructing complex geometry using an elliptic Partial Differential Equation (PDE) formulation. The integral part of this work is the use of three-dimensional curves within the physical space which act as boundary conditions to solve the PDE. The chosen PDE is solved explicitly for a given general set of curves representing the original shape and thus making the method very efficient. In order to improve the quality of results for shape representation we utilize an automatic parameterization scheme on the chosen curves. With this formulation we discuss our methodology for shape representation using a series of practical examples.