arXiv subjects

Dominik Eckert

Publications and source records attributed to Dominik Eckert.

6 recordsLinked to original sources

arXiv2026

Soft-Argmax for the Projective Plane via the Veronese Embedding

From horizon detection to fibre structures in X-ray imaging, many vision tasks recover lines via peak detection in Hough space $H=S^1\times\mathbb{R}$, the domain of orientation-offset pairs $(\theta,\rho)$. Differentiable pipelines extract coordinates via \emph{soft-argmax}, a probability-weighted average that is only meaningful in a globally linear space. However, $(\theta,\rho)$ and $(\theta+\pi,-\rho)$ describe the same undirected line, so $H$ double-covers the space of undirected lines $H/\mathbb{Z}_2$: a M\"obius strip, obtained by identifying each pair under $\mathbb{Z}_2$ action. Soft-argmax operates on the cover $H$, but since $H/\mathbb{Z}_2$ admits no linear structure, it tears geometrically adjacent lines apart. Thus we need a $\mathbb{Z}_2$-invariant embedding of lines into a linear space, on which soft-argmax is well-defined. We achieve this by parametrising lines via unit-norm homogeneous vectors $\ell=(1+\rho^2)^{-1/2}(\cos\theta,\sin\theta,-\rho)^{\top}\in\mathbb{R}^3$ and applying the Veronese map $v_2(\ell)=\ell\ell^{\top}$ that satisfies $v_2(\ell)=v_2(-\ell)$. This descends continuously to an embedding of the quotient $H/\mathbb{Z}_2$ into the linear space $\mathrm{Sym}^2(\mathbb{R}^3)$, where the antipodal ambiguity vanishes. Line extraction becomes a barycentre in $\mathrm{Sym}^2(\mathbb{R}^3)$, projected back via its leading eigenvector. We validate our \emph{Veronese soft-argmax} in a Hough transform-based network across all resolvable lines, confirming uniform and seam-free recovery. We further derive that the $L_2$-loss on isometrically weighted Veronese embeddings equals the squared chordal distance between lines in projective space, enabling a geometrically precise training objective.

cs.CV↗

arXiv2025

From Lines to Shapes: Geometric-Constrained Segmentation of X-Ray Collimators via Hough Transform

Collimation in X-ray imaging restricts exposure to the region-of-interest (ROI) and minimizes the radiation dose applied to the patient. The detection of collimator shadows is an essential image-based preprocessing step in digital radiography posing a challenge when edges get obscured by scattered X-ray radiation. Regardless, the prior knowledge that collimation forms polygonal-shaped shadows is evident. For this reason, we introduce a deep learning-based segmentation that is inherently constrained to its geometry. We achieve this by incorporating a differentiable Hough transform-based network to detect the collimation borders and enhance its capability to extract the information about the ROI center. During inference, we combine the information of both tasks to enable the generation of refined, line-constrained segmentation masks. We demonstrate robust reconstruction of collimated regions achieving median Hausdorff distances of 4.3-5.0mm on diverse test sets of real Xray images. While this application involves at most four shadow borders, our method is not fundamentally limited by a specific number of edges.

cs.CV↗

arXiv2024

A Realistic Collimated X-Ray Image Simulation Pipeline

Collimator detection remains a challenging task in X-ray systems with unreliable or non-available information about the detectors position relative to the source. This paper presents a physically motivated image processing pipeline for simulating the characteristics of collimator shadows in X-ray images. By generating randomized labels for collimator shapes and locations, incorporating scattered radiation simulation, and including Poisson noise, the pipeline enables the expansion of limited datasets for training deep neural networks. We validate the proposed pipeline by a qualitative and quantitative comparison against real collimator shadows. Furthermore, it is demonstrated that utilizing simulated data within our deep learning framework not only serves as a suitable substitute for actual collimators but also enhances the generalization performance when applied to real-world data.

cs.CV↗

arXiv2024

An Interpretable X-ray Style Transfer via Trainable Local Laplacian Filter

Radiologists have preferred visual impressions or 'styles' of X-ray images that are manually adjusted to their needs to support their diagnostic performance. In this work, we propose an automatic and interpretable X-ray style transfer by introducing a trainable version of the Local Laplacian Filter (LLF). From the shape of the LLF's optimized remap function, the characteristics of the style transfer can be inferred and reliability of the algorithm can be ensured. Moreover, we enable the LLF to capture complex X-ray style features by replacing the remap function with a Multi-Layer Perceptron (MLP) and adding a trainable normalization layer. We demonstrate the effectiveness of the proposed method by transforming unprocessed mammographic X-ray images into images that match the style of target mammograms and achieve a Structural Similarity Index (SSIM) of 0.94 compared to 0.82 of the baseline LLF style transfer method from Aubry et al.

cs.CV↗

arXiv2024

StyleX: A Trainable Metric for X-ray Style Distances

The progression of X-ray technology introduces diverse image styles that need to be adapted to the preferences of radiologists. To support this task, we introduce a novel deep learning-based metric that quantifies style differences of non-matching image pairs. At the heart of our metric is an encoder capable of generating X-ray image style representations. This encoder is trained without any explicit knowledge of style distances by exploiting Simple Siamese learning. During inference, the style representations produced by the encoder are used to calculate a distance metric for non-matching image pairs. Our experiments investigate the proposed concept for a disclosed reproducible and a proprietary image processing pipeline along two dimensions: First, we use a t-distributed stochastic neighbor embedding (t-SNE) analysis to illustrate that the encoder outputs provide meaningful and discriminative style representations. Second, the proposed metric calculated from the encoder outputs is shown to quantify style distances for non-matching pairs in good alignment with the human perception. These results confirm that our proposed method is a promising technique to quantify style differences, which can be used for guided style selection as well as automatic optimization of image pipeline parameters.

cs.CV↗

arXiv2019

Deep Learning-based Denoising of Mammographic Images using Physics-driven Data Augmentation

Mammography is using low-energy X-rays to screen the human breast and is utilized by radiologists to detect breast cancer. Typically radiologists require a mammogram with impeccable image quality for an accurate diagnosis. In this study, we propose a deep learning method based on Convolutional Neural Networks (CNNs) for mammogram denoising to improve the image quality. We first enhance the noise level and employ Anscombe Transformation (AT) to transform Poisson noise to white Gaussian noise. With this data augmentation, a deep residual network is trained to learn the noise map of the noisy images. We show, that the proposed method can remove not only simulated but also real noise. Furthermore, we also compare our results with state-of-the-art denoising methods, such as BM3D and DNCNN. In an early investigation, we achieved qualitatively better mammogram denoising results.

eess.IV↗