Finite element surface registration incorporating curvature, volume preservation, and statistical model information

We present a novel method for nonrigid registration of 3D surfaces and images. The method can be used to register surfaces by means of their distance images, or to register medical images directly. It is formulated as a minimization problem of a sum of several terms representing the desired properties of a registration result: smoothness, volume preservation, matching of the surface, its curvature, and possible other feature images, as well as consistency with previous registration results of similar objects, represented by a statistical deformation model. While most of these concepts are already known, we present a coherent continuous formulation of these constraints, including the statistical deformation model. This continuous formulation renders the registration method independent of its discretization. The finite element discretization we present is, while independent of the registration functional, the second main contribution of this paper. The local discontinuous Galerkin method has not previously been used in image registration, and it provides an efficient and general framework to discretize each of the terms of our functional. Computational efficiency and modest memory consumption are achieved thanks to parallelization and locally adaptive mesh refinement. This allows for the first time the use of otherwise prohibitively large 3D statistical deformation models

Conformal Invariance and Renormalization Group in Quantum Gravity Near Two Dimensions

We study quantum gravity in $2+\epsilon$ dimensions in such a way to preserve the volume preserving diffeomorphism invariance. In such a formulation, we prove the following trinity: the general covariance, the conformal invariance and the renormalization group flow to Einstein theory at long distance. We emphasize that the consistent and macroscopic universes like our own can only exist for matter central charge $0<c<25$. We show that the spacetime singularity at the big bang is resolved by the renormalization effect and universes are found to bounce back from the big crunch. Our formulation may be viewed as a Ginzburg-Landau theory which can describe both the broken and the unbroken phase of quantum gravity and the phase transition between them.Comment: 32 pages, TIT-HEP-256, KEK-TH-395, YITP/U-94-1

Supermembranes and Super Matrix Models

We review recent developments in the theory of supermembranes and their relation to matrix models.Comment: Invited lecture presented at the Corfu Workshop, September 20 - 26, 1998, of the TMR Project "Quantum Aspects of Gauge Theories, Supersymmetry and Unification" (ERBFMRXCT96-0045), to appear in the proceedings. Latex 41 p

Decodability Attack against the Fuzzy Commitment Scheme with Public Feature Transforms

The fuzzy commitment scheme is a cryptographic primitive that can be used to store biometric templates being encoded as fixed-length feature vectors protected. If multiple related records generated from the same biometric instance can be intercepted, their correspondence can be determined using the decodability attack. In 2011, Kelkboom et al. proposed to pass the feature vectors through a record-specific but public permutation process in order to prevent this attack. In this paper, it is shown that this countermeasure enables another attack also analyzed by Simoens et al. in 2009 which can even ease an adversary to fully break two related records. The attack may only be feasible if the protected feature vectors have a reasonably small Hamming distance; yet, implementations and security analyses must account for this risk. This paper furthermore discusses that by means of a public transformation, the attack cannot be prevented in a binary fuzzy commitment scheme based on linear codes. Fortunately, such transformations can be generated for the non-binary case. In order to still be able to protect binary feature vectors, one may consider to use the improved fuzzy vault scheme by Dodis et al. which may be secured against linkability attacks using observations made by Merkle and Tams