Marinella Cadoni

3D Face Recognition Using Joint Differential Invariants

Stemming from a sound mathematical framework dating back to the beginning of the 20th century, this paper introduces a novel approach for 3D face recognition. The proposed technique is based on joint differential invariants, projecting a 3D shape in a 9-dimensional space where the effect of rotation and translation is removed. As a consequence, the matching between two different 3D samples can be directly performed in the invariant space. Thus the matching score can be effectively used to detect surfaces or parts of surfaces characterised by similar when not identical 3D structure. The paper details an efficient procedure for the generation of the invariant signature in the 9-dimensional space, carefully discussing a number of significant implications related to the application of the mathematical framework to the discrete, non-rigid case of interest. Experimental evaluation of the proposed approach is performed over the widely known 3D_RMA database, comparing results to the well established Iterative Closest Point (ICP)-based matching approach.

Iconic Methods for Multimodal Face Recognition: A Comparative Study

When dealing with face recognition, multimodal algorithms, with their potential to capture complementary characteristics from the 2D and 3D data channels, can reach high level of efficiency and robustness. In this paper, we explore different combinations of iconic descriptors coupled with a shape descriptor and propose a fully automatic, multimodal, face recognition paradigm. Two iconic features extractors, the Scale Invariant Feature Transform (SIFT) and the Speeded-Up Robust Features (SURF), are used, in turn, to extract salient points from the images of the faces. The corresponding points on the scans are validated with Joint Differential Invariants, a 3D characterisation method based on local and global shape information. SIFT and SURF are then combined at feature level and the 3D Joint Differential Invariants used to validate them on the shape channel. The proposed method has been tested on the FRGCv2 database. Experimental results highlight the complementarity of the feature points extracted by SIFT and SURF and the effectiveness of their 3D validation.

Blending 2D and 3D Face Recognition

Over the last decade, performance of face recognition algorithms systematically improved. This is particularly impressive when considering very large or challenging datasets such as the FRGC v2 or Labelled Faces in the Wild . A better analysis of the structure of the facial texture and shape is one of the main reasons of improvement in recognition performance. Hybrid face recognition methods , combining holistic and feature-based approaches, also allowed to increase efficiency and robustness. Both photometric information and shape information allow to extract facial features which can be exploited for recognition. However, both sources, grey levels of image pixels and 3D data , are affected by several noise sources which may impair the recognition performance. One of the main difficulties in matching 3D faces is the detection and localization of distinctive and stable points in 3D scans. Moreover, the large amount of data (tens of thousands of points) to be processed make the direct one-to-one matching a very time-consuming process. On the other hand, matching algorithms based on the analysis of 2D data alone are very sensitive to variations in illumination, expression and pose. Algorithms, based on the face shape information alone, are instead relatively insensitive to these sources of noise. These mutually exclusive features of 2D- and 3D-based face recognition algorithm call for a cooperative scheme which may take advantage of the strengths of both, while coping for their weaknesses. We envisage many real and practical applications where 2D data can be used to improve 3D matching and vice versa. Towards this end, this chapter highlights both the advantages and disadvantages of 2D- and 3D-based face recognition algorithms . It also explores the advantages of blending 2D- and 3D data -based techniques, also proposing a novel approach for a fast and robust matching. Several experimental results, obtained from publicly available datasets, currently at the state of the art, demonstrate the effectiveness of the proposed approach.

Financial Crisis: A New Measure for Risk of Pension Fund Portfolios.

It has been argued that pension funds should have limitations on their asset allocation, based on the risk profile of the different financial instruments available on the financial markets. This issue proves to be highly relevant at times of market crisis, when a regulation establishing limits to risk taking for pension funds could prevent defaults. In this paper we present a framework for evaluating the risk level of a single financial instrument or a portfolio. By assuming that the log asset returns can be described by a multifractional Brownian motion, we evaluate the risk using the time dependent Hurst parameter H(t) which models volatility. To provide a measure of the risk, we model the Hurst parameter with a random variable with mixture of beta distribution. We prove the efficacy of the methodology by implementing it on different risk level financial instruments and portfolios.

From 3D faces to biometric identities

The recognition of human faces, in presence of pose and illumination variations, is intrinsically an ill-posed problem. The direct measurement of the shape for the face surface is now a feasible solution to overcome this problem and make it well-posed. This paper proposes a completely automatic algorithm for face registration and matching. The algorithm is based on the extraction of stable 3D facial features characterizing the face and the subsequent construction of a signature manifold. The facial features are extracted by performing a continuous-to-discrete scale-space analysis. Registration is driven from the matching of triplets of feature points and the registration error is computed as shape matching score. A major advantage of the proposed method is that no data pre-processing is required. Therefore all presented results have been obtained exclusively from the raw data available from the 3D acquisition device. Despite of the high dimensionality of the data (sets of 3D points, possibly with the associate texture), the signature and hence the template generated is very small. Therefore, the management of the biometric data associated to the user data, not only is very robust to environmental changes, but it is also very compact. This reduces the required storage and processing resources required to perform the identification. The method has been tested against the Bosphorus 3D face database and the performances compared to the ICP baseline algorithm. Even in presence of noise in the data, the algorithm proved to be very robust and reported identification performances in line with the current state of the art.

Large scale face identification by combined iconic features and 3D joint invariant signatures

In this paper, we present a 2D/3D multimodal face identification system. A set of iconic fiducial points and descriptors is first extracted from the images of the faces and a preliminary correspondence between the points is established on the basis of the descriptor content. Subsequently, the points are mapped on the scans and used to calculate 3D joint differential invariant vectors that define a signature of the face. Since a correspondence between the invariants is inherited from the 2D feature point matching, the signatures of the faces can be efficiently compared by evaluating the distance between corresponding vectors, thus validating the 2D matching hypothesis. This methodology guarantees an effective and fast alignment of the 3D scans, avoids iterative registration procedures and provides a simple similarity measure for face identification. Extensive tests were carried out on the FRGCv2 and on the Bosphorus databases, which both contain 3D and texture information of faces. Results show that the method is robust to expressions provided the images are of good quality, and that it is particularly suited to identification tasks in the cases of medium to large databases with multiple gallery enrolment. Indeed, in these scenarios, the performance was superior or comparable to state of the art methods, with execution times often faster by several orders of magnitude. A 2D/3D face recognition, based on SIFT-SURF and 3D joint differential invariantsCombination of SIFT and SURF descriptors in order to capture iconic information3D invariants guarantee fast and precise alignment of 3D scans.The proposed method performs well inthe case of medium-large databases.Execution times are significantly faster than most state of the art methods.

A 3D algorithm for unsupervised face identification

With the increasing availability of low-cost 3D data acquisition devices, the use of 3D face data for the recognition of individuals is becoming more appealing and computationally feasible. This paper proposes a completely automatic algorithm for face registration and matching. The algorithm is based on the extraction of stable 3D facial features characterizing the face and the subsequent construction of a signature manifold. The facial features are extracted by performing a continuous-to-discrete scale-space analysis. Registration is driven from the matching of triplets of feature points and the registration error is computed as shape matching score. Conversely to most techniques in the literature, a major advantage of the proposed method is that no data pre-processing is required. Therefore all presented results have been obtained exclusively from the raw data available from the 3D acquisition device. The method has been tested on the Bosphorus 3D face database and the performances compared to the ICP baseline algorithm. Even in presence of noise in the data, the algorithm proved to be very robust and reported identification performances which are aligned to the current state of the art, but without requiring any pre-processing of the raw data.

Interpreting 3D faces for augmented human-computer interaction

Human-machine interaction requires the ability to analyze and discern human faces. Due to the nature of the 3D to 2D projection, the recognition of human faces from 2D images, in presence of pose and illumination variations, is intrinsically an ill-posed problem. The direct measurement of the shape for the face surface is now a feasible solution to overcome this problem and make it well-posed. This paper proposes a completely automatic algorithm for 3D face registration and matching based on the extraction of stable 3D facial features characterizing the face and the subsequent construction of a signature manifold. The facial features are extracted by performing a continuous-to-discrete scale-space analysis. Registration is driven from the matching of triplets of feature points and the registration error is computed as shape matching score. A major advantage of the proposed method is that no data pre-processing is required. Despite of the high dimensionality of the data (sets of 3D points, possibly with the associate texture), the signature and hence the template generated is very small. Therefore, the management of the biometric data associated to the user data, not only is very robust to environmental changes, but it is also very compact. The method has been tested against the Bosphorus 3D face database and the performances compared to the ICP baseline algorithm. Even in presence of noise in the data, the algorithm proved to be very robust and reported identification performances in line with the current state of the art.