In image processing, classical methods minimize a suitable functional that balances between computational feasibility (convexity of the functional is ideal) and suitable penalties reflecting the desired image decomposition. The fact that algorithms derived from such minimization problems can be used to construct (deep) learning architectures has spurred the development of algorithms that can be trained for a specifically desired image decomposition, e.g., into cartoon and texture. While many such methods are very successful, theoretical guarantees are only scarcely available. To this end, in this contribution, we formalize a general class of intersection point problems encompassing a wide range of (learned) image decomposition models, and we give an existence result for a large subclass of such problems, i.e., giving the existence of a fixed point of the corresponding algorithm. This class generalizes classical model-based variational problems, such as the TV-$\ell^2$-model or the more general TV-Hilbert model. To illustrate the potential for learned algorithms, novel (nonlearned) choices within our class show comparable results in denoising and texture removal.

Automated biometric identification systems are inherently challenged to optimize false (non-)match rates. This can be addressed either by directly improving comparison subsystems, or indirectly by allowing only “good quality” biometric queries to be compared. We are interested in the latter, where the challenge lies in relating the “good quality” of a query to its utility with respect to a comparison subsystem. First, we propose a new general robust biometric quality validation scheme (RBQ VS) that, mimicking the use-case, robustly quantifies comparison improvement obtained by employing a specific quality estimator. For this purpose, we robustify an existing validation scheme by repeated random subsampling cross-validation. Second, specifically for the task of fingerprint comparison, we propose a novel biometric feature for quality estimation. Since comparison subsystems based on fingerprint minutiae, which are ridge endings and bifurcations, appear to miss minutiae or detect spurious minutiae, especially in the presence of smudge noise, we propose an algorithm aiming at measuring corruption by smudge. To this end, we employ a recently developed three parts image-decomposition and link our new smudge noise quality estimator (SNoQE) to the structure of the texture part found. At last, using the FVC databases and an NIST database, we compare the SNoQE with the popular NFIQ 2.0 estimator, and its predecessor. Experimental results show that the single-feature SNoQE can compete with the multi-feature NFIQ 2.0 and, in fact, adds new information not sufficiently reproduced by the NFIQ 2.0. Indeed, a simple combination of SNoQE and NFIQ 2.0 tends to outperform on all databases included in the comparison study. An implementation of the RBQ VS and the SNoQE can be found online.

Synthetic fingerprint generation has two major advantages. First, it is possible to create arbitrarily large databases for research purposes e.g. of a million or a billion fingerprints at virtually no cost and without legal constraints. Secondly, together with the generated fingerprint images comes additional ground truth information for free such as e.g. the corresponding minutiae template. However, recently it has been shown that existing methods in the literature synthesize images with unrealistic minutiae configurations, usually not visible to the naked eye of an expert. In this paper, we propose an algorithm called Realistic Fingerprint Creator (RFC) for the generation realistic synthetic fingerprint images, which, as a core ingredient, involves a selection procedure how to choose the most `realistic' synthetic fingerprints to build a database. We have performed a test of realness comparing prints synthesized by RFC and real fingerprints, and we have observed that the proposed RFC is the first method which produces artificial fingerprints that pass this test due to their realistic minutiae configuration.

We propose an intrinsic multifactorial model for data on Riemannian manifolds that typically occur in the statistical analysis of shape. Due to the lack of a linear structure, linear models cannot be defined in general; to date only one-way MANOVA is available. For a general multifactorial model, we assume that variation not explained by the model is concentrated near elements defining the effects. By determining the asymptotic distributions of respective sample covariances under parallel transport, we show that they can be compared by standard MANOVA. Often in applications manifolds are only implicitly given as quotients, where the bottom space parallel transport can be expressed through a differential equation. For Kendall's space of planar shapes, we provide an explicit solution. We illustrate our method by an intrinsic two-way MANOVA for a set of leaf shapes. While biologists can identify genotype effects by sight, we can detect height effects that are otherwise not identifiable.

Quadratic differentials naturally define analytic orientation fields on planar surfaces. We propose to model orientation fields of fingerprints by specifying quadratic differentials. Models for all fingerprint classes such as arches, loops and whorls are laid out. These models are parametrised by few, geometrically interpretable parameters which are invariant under Euclidean motions. We demonstrate their ability in adapting to given, observed orientation fields, and we compare them to existing models using the fingerprint images of the NIST Special Database 4. We also illustrate that these model allow for extrapolation into unobserved regions. This goes beyond the scope of earlier models for the orientation field as those are restricted to the observed planar fingerprint region. Within the framework of quadratic differentials we are able to verify analytically Penrose's formula for the singularities on a palm. Potential applications of these models are the use of their parameters as indices of large fingerprint databases, as well as the definition of intrinsic coordinates for single fingerprint images.