Abstract In many image processing applications (e.g. computational anatomy) a groupwise registration is performed on a sample of images and a template image is simultaneously generated. From the template alone it is in general unclear to which extent the registered images are still misaligned. The local spatial variation left after registration may be seen as the resolution of the resulting template. In this sense we develop the first template resolution measure (TRM) quantifying the misalignment at each location of the template. The TRM is based on the key insight that the size of such misalignments can be determined as the amount of smoothing required to bring the registered images in agreement. This relationship is mathematically derived from characteristic examples in one dimension. This way, the TRM quantifies the remaining spatial variation in the template’s units of length. Furthermore we propose to enhance the template by an effective visualization of its resolution measure. Finally we demonstrate the TRM’s applicability and validate its interpretability for example datasets in two and three dimensions. The corresponding code is publicly available on GitHub.

Real-time surveillance is a crucial element in the response to infectious disease outbreaks. However, the interpretation of incidence data is often hampered by delays occurring at various stages of data gathering and reporting. As a result, recent values are biased downward, which obscures current trends. Statistical nowcasting techniques can be employed to correct these biases, allowing for accurate characterization of recent developments and thus enhancing situational awareness. In this paper, we present a preregistered real-time assessment of eight nowcasting approaches, applied by independent research teams to German 7-day hospitalization incidences during the COVID-19 pandemic. This indicator played an important role in the management of the outbreak in Germany and was linked to levels of non-pharmaceutical interventions via certain thresholds. Due to its definition, in which hospitalization counts are aggregated by the date of case report rather than admission, German hospitalization incidences are particularly affected by delays and can take several weeks or months to fully stabilize. For this study, all methods were applied from 22 November 2021 to 29 April 2022, with probabilistic nowcasts produced each day for the current and 28 preceding days. Nowcasts at the national, state, and age-group levels were collected in the form of quantiles in a public repository and displayed in a dashboard. Moreover, a mean and a median ensemble nowcast were generated. We find that overall, the compared methods were able to remove a large part of the biases introduced by delays. Most participating teams underestimated the importance of very long delays, though, resulting in nowcasts with a slight downward bias. The accompanying prediction intervals were also too narrow for almost all methods. Averaged over all nowcast horizons, the best performance was achieved by a model using case incidences as a covariate and taking into account longer delays than the other approaches. For the most recent days, which are often considered the most relevant in practice, a mean ensemble of the submitted nowcasts performed best. We conclude by providing some lessons learned on the definition of nowcasting targets and practical challenges.

We study the problem of direction of arrival estimation for arbitrary antenna arrays. We formulate it as a continuous line spectral estimation problem and solve it under a sparsity prior without any gridding assumptions. Moreover, we incorporate the array's beampattern in form of the Effective Aperture Distribution Function (EADF), which allows to use arbitrary (synthetic as well as measured) antenna arrays. This generalizes known atomic norm based grid-free DOA estimation methods (that have so far been limited to uniformly spaced arrays) to arbitrary antenna arrays. In addition, our formulation allows to incorporate compressed sensing in form of special linear combinations of the antennas' output ports. We provide conditions for the successful reconstruction of a certain number of targets depending on the amount of compression and the EADF of the antenna array. Our results are applicable to measurement matrices from any sub-Gaussian distribution.

MOTIVATION: DNA segmentation, i.e. the partitioning of DNA in compositionally homogeneous segments, is a basic task in bioinformatics. Different algorithms have been proposed for various partitioning criteria such as Guanine/Cytosine (GC) content, local ancestry in population genetics or copy number variation. A critical component of any such method is the choice of an appropriate number of segments. Some methods use model selection criteria and do not provide a suitable error control. Other methods that are based on simulating a statistic under a null model provide suitable error control only if the correct null model is chosen. RESULTS: Here, we focus on partitioning with respect to GC content and propose a new approach that provides statistical error control: as in statistical hypothesis testing, it guarantees with a user-specified probability [Formula: see text] that the number of identified segments does not exceed the number of actually present segments. The method is based on a statistical multiscale criterion, rendering this as a segmentation method that searches segments of any length (on all scales) simultaneously. It is also accurate in localizing segments: under benchmark scenarios, our approach leads to a segmentation that is more accurate than the approaches discussed in the comparative review of Elhaik et al. In our real data examples, we find segments that often correspond well to features taken from standard University of California at Santa Cruz (UCSC) genome annotation tracks. AVAILABILITY AND IMPLEMENTATION: Our method is implemented in function smuceR of the R-package stepR available at http://www.stochastik.math.uni-goettingen.de/smuce.

We study the effect of growth on the fingerprints of adolescents, based on which we suggest a simple method to adjust for growth when trying to recover a juvenile's fingerprint in a database years later. Based on longitudinal data sets in juveniles' criminal records, we show that growth essentially leads to an isotropic rescaling, so that we can use the strong correlation between growth in stature and limbs to model the growth of fingerprints proportional to stature growth as documented in growth charts. The proposed rescaling leads to a 72% reduction of the distances between corresponding minutiae for the data set analyzed. These findings were corroborated by several verification tests. In an identification test on a database containing 3.25 million right index fingers at the Federal Criminal Police Office of Germany, the number of identification errors was reduced from 10 errors in 48 identification attempts to 1 in 48 by rescaling. The presented method is of striking simplicity and can easily be integrated into existing automated fingerprint identification systems.

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.