Fast Haar Transform Based Feature Extraction for Face Representation and Recognition

Subspace learning is the process of finding a proper feature subspace and then projecting high-dimensional data onto the learned low-dimensional subspace. The projection operation requires many floating-point multiplications and additions, which makes the projection process computationally expensive. To tackle this problem, this paper proposes two simple-but-effective fast subspace learning and image projection methods, fast Haar transform (FHT) based principal component analysis and FHT based spectral regression discriminant analysis. The advantages of these two methods result from employing both the FHT for subspace learning and the integral vector for feature extraction. Experimental results on three face databases demonstrated their effectiveness and efficiency.

Phase identification in a series of liquid crystalline TPP polyethers and copolyethers having highly ordered mesophase structures. 7. Phase structures in a series of copolyethers containing odd and even numbers of methylene units of different compositions

A series of liquid crystalline copolyethers have been synthesized from 1-(4-hydroxy-4'-biphenyl)-2-(4-hydroxyphenyl)propane with 1,7-dibromoheptane and 1,12-dibromododecene [coTPPs(7/12)], which represents copolyethers containing both odd and even numbers of methylene units. The molar ratio of odd to even methylene units in this series ranges from 1/9 to 9/1. The coTPPs(7/12) exhibit multiple phase transitions during cooling and heating in differential scanning calorimetry experiments. For all these thermal transitions, a small undercooling and superheating dependence is observed upon cooling and heating at different rates. Three types of phase behaviors can be classified in coTPPs(7/12) on the basis of the structural analyses by wide-angle X-ray diffraction on powder and fiber samples and by electron diffraction experiments in transmission electron microscopy. At room temperature, highly ordered smectic and smectic crystal (SC) phases are identified in coTPPs(7/12: 1/9 and 2/8), which is similar to the homopolymer TPP(m = 12). The coTPPs(7/12: 3/7, 4/6, and 5/5) possess a hexagonal columnar (Phi(H)) phase in which the molecular and columnar axes are parallel to the fiber direction and perpendicular to the hexagonal lateral packing. The coTPPs(7/12: 6/4, 7/3, and 8/2) possess a tilted hexagonal columnar (Phi(TH)) phase with a single tilt angle which increases with the increasing composition of the seven-numbered methylene units. However, in coTPP(7/12: 9/1), a Phi(TH) phase with multiple tilt angles is found. Upon heating, phase structures in most coTPPs(7/12) involving the columnar phases enter directly into the nematic (N) phase, while the coTPP(7/12: 1/9) exhibits a highly ordered smectic F (S-F) phase before it reaches the N phase. One exception is found in coTPP(7/12: 2/8), wherein the transformation from the S-F to Phi(H) occurs prior to the N phase. Combining the copolymer phase behaviors observed with the corresponding homopolymers TPP(n = 7) and TPP(m = 12), a phase diagram describing transition temperatures with respect to the composition can be constructed.

Phase identification in a series of liquid crystalline TPP polyethers and copolyethers having highly ordered mesophase structures. 6. Structure changes from smectic to columnar phases in a series of copolyethers containing odd and even numbers of methylene units in equal molar composition

A series of liquid crystalline copolyethers has been synthesized from 1-(4-hydroxy-4'-biphenyl)-2-(4-hydroxyphenyl)propane and different alpha,omega-dibromoalkanes [coTPP(n/m)]. In this report, coTPPs having n = 5, 7, 9, 11 and m = 12 are studied, which represent copolyethers having both varying odd number and a fixed even number of methylene units. The compositions were fixed at an equal molar ratio (50/50). These coTPPs(nlm) show multiple phase transitions during cooling and heating in differential scanning calorimetry experiments. The undercooling dependence of these transitions is found to be small, indicating that these transitions are close to equilibrium, Although the coTPPs possess a high-temperature nematic (N) phase, the periodicity order along the chain direction is increasingly disturbed when the length of the odd-numbered methylene units decreases from n 11 to 5. in the coTPPs(5/12, 7/12, and 9/12), wide-angle X-ray diffraction experiments at different temperatures show that, shortly after the N phase formation during cooling, the lateral molecular packing improves toward a hexagonal lattice, as evidenced by a gradual narrowing of the scattering halo. This process represents the possible existence of an exotic N phase, which serves as a precursor to the columnar (Phi(H)) phase. A further decrease in temperature leads to a (PH phase having a long-range ordered, two-dimensional hexagonal lattice. In coTPP(11/12), the phase structures are categorized as highly ordered and tilted, smectic and smectic crystal phases, similar to homoTPPs, such as the smectic F (S-F) and smectic crystal G (SCG) phases. An interesting observation is found for coTPP(9/12), wherein a structural change from the high-temperature Phi(H) phase to the low-temperature S-F phase occurs. It can be proven that, upon heating, the well-defined layer structure disappears and the lateral packing remains hexagonal. The overall structural differences in this series of coTPPs between those of the columnar and highly ordered smectic phases are related to the disorders introduced into the layer structure by the dissimilarity of the methylene unit lengths in the comonomers.

Developing molecular identification numbers by an all-paths method

A new topological index is devised from an all-paths method. This molecular topological index has highly discriminating power for various kinds of organic compounds such as alkane trees, complex cyclic or polycyclic graphs, and structures containing heteroatoms and thus can be used as a Molecular IDentification number (MID) for chemical documentation. Some published MIDs derived from an all-paths method and their structural selectivity for alkane trees are also reviewed.

Face Recognition Under Varying Pose

While researchers in computer vision and pattern recognition have worked on automatic techniques for recognizing faces for the last 20 years, most systems specialize on frontal views of the face. We present a face recognizer that works under varying pose, the difficult part of which is to handle face rotations in depth. Building on successful template-based systems, our basic approach is to represent faces with templates from multiple model views that cover different poses from the viewing sphere. Our system has achieved a recognition rate of 98% on a data base of 62 people containing 10 testing and 15 modelling views per person.

Estimation of Pose and Illuminant Direction for Face Processing

In this paper three problems related to the analysis of facial images are addressed: the illuminant direction, the compensation of illumination effects and, finally, the recovery of the pose of the face, restricted to in-depth rotations. The solutions proposed for these problems rely on the use of computer graphics techniques to provide images of faces under different illumination and pose, starting from a database of frontal views under frontal illumination.

Face Recognition from One Example View

If we are provided a face database with only one example view per person, is it possible to recognize new views of them under a variety of different poses, especially views rotated in depth from the original example view? We investigate using prior knowledge about faces plus each single example view to generate virtual views of each person, or views of the face as seen from different poses. Prior knowledge of faces is represented in an example-based way, using 2D views of a prototype face seen rotating in depth. The synthesized virtual views are evaluated as example views in a view-based approach to pose-invariant face recognition. They are shown to improve the recognition rate over the scenario where only the single real view is used.

Vectorizing Face Images by Interpreting Shape and Texture Computations

The correspondence problem in computer vision is basically a matching task between two or more sets of features. In this paper, we introduce a vectorized image representation, which is a feature-based representation where correspondence has been established with respect to a reference image. This representation has two components: (1) shape, or (x, y) feature locations, and (2) texture, defined as the image grey levels mapped onto the standard reference image. This paper explores an automatic technique for "vectorizing" face images. Our face vectorizer alternates back and forth between computation steps for shape and texture, and a key idea is to structure the two computations so that each one uses the output of the other. A hierarchical coarse-to-fine implementation is discussed, and applications are presented to the problems of facial feature detection and registration of two arbitrary faces.

Pose-Invariant Face Recognition Using Real and Virtual Views

The problem of automatic face recognition is to visually identify a person in an input image. This task is performed by matching the input face against the faces of known people in a database of faces. Most existing work in face recognition has limited the scope of the problem, however, by dealing primarily with frontal views, neutral expressions, and fixed lighting conditions. To help generalize existing face recognition systems, we look at the problem of recognizing faces under a range of viewpoints. In particular, we consider two cases of this problem: (i) many example views are available of each person, and (ii) only one view is available per person, perhaps a driver's license or passport photograph. Ideally, we would like to address these two cases using a simple view-based approach, where a person is represented in the database by using a number of views on the viewing sphere. While the view-based approach is consistent with case (i), for case (ii) we need to augment the single real view of each person with synthetic views from other viewpoints, views we call 'virtual views'. Virtual views are generated using prior knowledge of face rotation, knowledge that is 'learned' from images of prototype faces. This prior knowledge is used to effectively rotate in depth the single real view available of each person. In this thesis, I present the view-based face recognizer, techniques for synthesizing virtual views, and experimental results using real and virtual views in the recognizer.