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Geometry considerations in face recognition technology

SPIE
: 11 December, 2008 (Technical Article) 

Michael Bronstein of the Technion Israel Institute of Technology explains the advanced geometric factors being used to push forward the latest advancements in 3D face biometrics 

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Face recognition is one of the classical and still unsolved problems that has kept computer vision scientists busy since the early 1970s. Though a routine task for humans, identifying a face is a far greater challenge for machines. One of the main problems is the vast number of degrees of freedom in the appearance of a human face. External factors such as variations in illumination and head pose can make the same subject look completely different. For this reason, most of today's facerecognition technologies work only in controlled environments, where the influence of such factors on face perception is moderate.
We believe that a major sticking point in face recognition is that it is approached as a problem in 2D image analysis, whereas in practice the human face is a 3D object. Recent research has shown that taking into account the geometry of a face as well as its pose could reduce the sensitivity of identification systems to the environmental context. At the same time, acquiring facial geometry is more painstaking than simply capturing a pose, and typically involves using a multicamera setup to record the face from multiple viewpoints. Our two eyes are a good example of this approach in that the binocular system gives us the ability to perceive depth.
In regards to the recognition task itself, however, technology deviates from nature. Human visual perception relies mostly on analyzing how an object appears rather than its geometric structure. Machines, on the other hand, treat human faces as 3D surfaces and compare them using relevant shape analysis methods. Unfortunately, human faces are nonrigid, and the variability of different shapes a deformable object can assume is immense. For instance, when we smile, our facial surface moves in a way that dramatically changes its geometry. As a consequence, 3D facerecognition methods have been struggling with the problem of sensitivity to facial expressions.
It is admittedly very difficult to model the deformations of the facial surface as a result of different expressions. Computer graphics experts routinely encounter this challenge in producing 3D animation movies. What is easier is to characterize the geometric properties of the surface that remain unaltered or invariant under such transformations. We found that most facial expressions have little effect on the intrinsic geometry, that is, the structure of distances measured on the facial surface. In differential geometry, such distances are called geodesic, a notion that derives from mapmaking applications. This can be illustrated intuitively as follows. Take a piece of paper and draw a line between a pair of points. If you now bend the paper, the position of the points in space can change, but the length of the path connecting them (which is no more a straight line since the paper is curved) remains unchanged. Similarly, facial expressions are deformations that approximately preserve the geodesic distances, and for this reason are called isometries. Consequently, comparing two faces requires examining their geodesic distance structures. Since the structures are isometryinvariant, and expressions are modeled as isometries, the comparison is tantamount to expressioninvariant face recognition.
Having found a way to capture the expressioninvariant characteristic of the face in terms of the geodesic distances, we still have to answer the question of how to compare two sets of geodesic distances describing two faces. The solution lies in analytical techniques used for visualizing multidimensional data. The method we borrowed from these applications is called multidimensional scaling (MDS), and it allows visualizing a complicated distance structure in a lowdimensional Euclidean space. Applying MDS to our geodesic distances, we obtain lowdimensional representations (introduced by Elad and Kimmel and referred to as canonical forms). These forms are a single way of representing all the possible surfaces that have the given geodesic distances (i.e., all the expressions of the face), thus, in a sense, undoing them.
Based on this approach, face recognition is performed by 'canonizing' faces, followed by comparing the forms as rigid objects. This technique involves two numerical stages of computing the geodesic distances and performing MDS. Both can be performed very efficiently, allowing for a realtime facerecognition system. We tested this method on a database of faces with extreme facial expressions and obtained very high recognition performance. We were even able to distinguish between identical twins.
In followup studies, we showed that the distance structures capturing the expressioninvariant characteristics of the faces can be compared directly without using canonical forms. For illustration, think of stretching a rubber mask to fit your face. The more similar the mask is to your face, the less you need to stretch it. Considering a facial surface as such a mask, we can measure its similarity to another face by quantifying the amount of stretching we have to introduce. This approach has a profound relation to the socalled GromovHausdorff distance, another powerful tool in metric geometry. We believe that borrowing such tools from theoretical geometry and applying them to computer vision problems could create important practical applications in face recognition. At this point, we are beyond feasibility testing, proven by a lab prototype. Currently, we are working on developing a commercial prototype based on our 3D facerecognition technology.
















