Martins Bruveris

Yuanwei Li, Elizaveta Ivanova, Martins Bruveris

Automatic image anomaly detection is important for quality inspection in the manufacturing industry. The usual unsupervised anomaly detection approach is to train a model for each object class using a dataset of normal samples. However, a more realistic problem is zero-/few-shot anomaly detection where zero or only a few normal samples are available. This makes the training of object-specific models challenging. Recently, large foundation vision-language models have shown strong zero-shot performance in various downstream tasks. While these models have learned complex relationships between vision and language, they are not specifically designed for the tasks of anomaly detection. In this paper, we propose the Few-shot/zero-shot Anomaly Detection Engine (FADE) which leverages the vision-language CLIP model and adjusts it for the purpose of industrial anomaly detection. Specifically, we improve language-guided anomaly segmentation 1) by adapting CLIP to extract multi-scale image patch embeddings that are better aligned with language and 2) by automatically generating an ensemble of text prompts related to industrial anomaly detection. 3) We use additional vision-based guidance from the query and reference images to further improve both zero-shot and few-shot anomaly detection. On the MVTec-AD (and VisA) dataset, FADE outperforms other state-of-the-art methods in anomaly segmentation with pixel-AUROC of 89.6% (91.5%) in zero-shot and 95.4% (97.5%) in 1-normal-shot. Code is available at https://github.com/BMVC-FADE/BMVC-FADE.

Martin Bauer, Martins Bruveris, Peter W. Michor

We study reparametrization invariant Sobolev metrics on spaces of regular curves. We discuss their completeness properties and the resulting usability for applications in shape analysis. In particular, we will argue, that the development of efficient numerical methods for higher order Sobolev type metrics is an extremely desirable goal.

Martin Bauer, Martins Bruveris, Stephen Marsland et al.

Metrics on shape space are used to describe deformations that take one shape to another, and to determine a distance between them. We study a family of metrics on the space of curves, that includes several recently proposed metrics, for which the metrics are characterised by mappings into vector spaces where geodesics can be easily computed. This family consists of Sobolev-type Riemannian metrics of order one on the space $\text{Imm}(S^1,\mathbb R^2)$ of parametrized plane curves and the quotient space $\text{Imm}(S^1,\mathbb R^2)/\text{Diff}(S^1)$ of unparametrized curves. For the space of open parametrized curves we find an explicit formula for the geodesic distance and show that the sectional curvatures vanish on the space of parametrized and are non-negative on the space of unparametrized open curves. For the metric, which is induced by the "R-transform", we provide a numerical algorithm that computes geodesics between unparameterised, closed curves, making use of a constrained formulation that is implemented numerically using the RATTLE algorithm. We illustrate the algorithm with some numerical tests that demonstrate it's efficiency and robustness.

Martins Bruveris, Laurent Risser, François-Xavier Vialard

In the framework of large deformation diffeomorphic metric mapping (LDDMM), we develop a multi-scale theory for the diffeomorphism group based on previous works. The purpose of the paper is (1) to develop in details a variational approach for multi-scale analysis of diffeomorphisms, (2) to generalise to several scales the semidirect product representation and (3) to illustrate the resulting diffeomorphic decomposition on synthetic and real images. We also show that the approaches presented in other papers and the mixture of kernels are equivalent.

Martin Bauer, Martins Bruveris

We present a new approach for matching regular surfaces in a Riemannian setting. We use a Sobolev type metric on deformation vector fields which form the tangent bundle to the space of surfaces. In this article we compare our approach with the diffeomorphic matching framework. In the latter approach a deformation is prescribed on the ambient space, which then drags along an embedded surface. In contrast our metric is defined directly on the deformation vector field and can therefore be called an inner metric. We also show how to discretize the corresponding geodesic equation and compute the gradient of the cost functional using finite elements.

Martin Bauer, Martins Bruveris, Philipp Harms et al.

Statistical shape analysis can be done in a Riemannian framework by endowing the set of shapes with a Riemannian metric. Sobolev metrics of order two and higher on shape spaces of parametrized or unparametrized curves have several desirable properties not present in lower order metrics, but their discretization is still largely missing. In this paper, we present algorithms to numerically solve the geodesic initial and boundary value problems for these metrics. The combination of these algorithms enables one to compute Karcher means in a Riemannian gradient-based optimization scheme and perform principal component analysis and clustering. Our framework is sufficiently general to be applicable to a wide class of metrics. We demonstrate the effectiveness of our approach by analyzing a collection of shapes representing HeLa cell nuclei.

Martins Bruveris, Jochem Gietema, Pouria Mortazavian et al.

As face recognition algorithms become more accurate and get deployed more widely, it becomes increasingly important to ensure that the algorithms work equally well for everyone. We study the geographic performance differentials-differences in false acceptance and false rejection rates across different countries-when comparing selfies against photos from ID documents. We show how to mitigate geographic performance differentials using sampling strategies despite large imbalances in the dataset. Using vanilla domain adaptation strategies to fine-tune a face recognition CNN on domain-specific doc-selfie data improves the performance of the model on such data, but, in the presence of imbalanced training data, also significantly increases the demographic bias. We then show how to mitigate this effect by employing sampling strategies to balance the training procedure.

Martin Bauer, Martins Bruveris, Nicolas Charon et al.

In this paper we study a class of Riemannian metrics on the space of unparametrized curves and develop a method to compute geodesics with given boundary conditions. It extends previous works on this topic in several important ways. The model and resulting matching algorithm integrate within one common setting both the family of $H^2$-metrics with constant coefficients and scale-invariant $H^2$-metrics on both open and closed immersed curves. These families include as particular cases the class of first-order elastic metrics. An essential difference with prior approaches is the way that boundary constraints are dealt with. By leveraging varifold-based similarity metrics we propose a relaxed variational formulation for the matching problem that avoids the necessity of optimizing over the reparametrization group. Furthermore, we show that we can also quotient out finite-dimensional similarity groups such as translation, rotation and scaling groups. The different properties and advantages are illustrated through numerical examples in which we also provide a comparison with related diffeomorphic methods used in shape registration.

Martins Bauer, Martins Bruveris, Nicolas Charon et al.

Second order Sobolev metrics are a useful tool in the shape analysis of curves. In this paper we combine these metrics with varifold-based inexact matching to explore a new strategy of computing geodesics between unparametrized curves. We describe the numerical method used for solving the inexact matching problem, apply it to study the shape of mosquito wings and compare our method to curve matching in the LDDMM framework.

Martin Bauer, Martins Bruveris, Philipp Harms et al.

Second order Sobolev metrics on the space of regular unparametrized planar curves have several desirable completeness properties not present in lower order metrics, but numerics are still largely missing. In this paper, we present algorithms to numerically solve the initial and boundary value problems for geodesics. The combination of these algorithms allows to compute Karcher means in a Riemannian gradient-based optimization scheme. Our framework has the advantage that the constants determining the weights of the zero, first, and second order terms of the metric can be chosen freely. Moreover, due to its generality, it could be applied to more general spaces of mapping. We demonstrate the effectiveness of our approach by analyzing a collection of shapes representing physical objects.

Martin Bauer, Martins Bruveris, Philipp Harms et al.

In the recent years, Riemannian shape analysis of curves and surfaces has found several applications in medical image analysis. In this paper we present a numerical discretization of second order Sobolev metrics on the space of regular curves in Euclidean space. This class of metrics has several desirable mathematical properties. We propose numerical solutions for the initial and boundary value problems of finding geodesics. These two methods are combined in a Riemannian gradient-based optimization scheme to compute the Karcher mean. We apply this to a study of the shape variation in HeLa cell nuclei and cycles of cardiac deformations, by computing means and principal modes of variations.