Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2503.20907

Generalized Ray Tracing with Basis functions for Tomographic Projections

Youssef Haouchat·Sepand Kashani·Philippe Thévenaz·Michael Unser
View original source ↗Read source document ↗Export metadata ↓

Abstract

This work aims at the precise and efficient computation of the x-ray projection of an image represented by a linear combination of general shifted basis functions that typically overlap. We achieve this with a suitable adaptation of ray tracing, which is one of the most efficient methods to compute line integrals. In our work, the cases in which the image is expressed as a spline are of particular relevance. The proposed implementation is applicable to any projection geometry as it computes the forward and backward operators over a collection of arbitrary lines. We validate our work with experiments in the context of inverse problems for image reconstruction and maximize the image quality for a given resolution of the reconstruction grid.

Explore related subjects

eess.IV

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Youssef Haouchat, Sepand Kashani, Philippe Thévenaz, Michael Unser. 2025-03-26. Generalized Ray Tracing with Basis functions for Tomographic Projections. https://arxiv.org/abs/2503.20907

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Exponential Pixelating Integral transform with dual fractal features for enhanced chest X-ray abnormality detection

The heightened prevalence of respiratory disorders, particularly exacerbated by a significant upswing in fatalities due to the novel coronavirus, underscores the critical need for early detection and timely intervention. This imperative is paramount, possessing the potential to profoundly impact and safeguard numerous lives. Medically, chest radiography stands out as an essential and economically viable medical imaging approach for diagnosing and assessing the severity of diverse Respiratory Disorders. However, their detection in Chest X-Rays is a cumbersome task even for well-trained radiologists owing to low contrast issues, overlapping of the tissue structures, subjective variability, and the presence of noise. To address these issues, a novel analytical model termed Exponential Pixelating Integral is introduced for the automatic detection of infections in Chest X-Rays in this work. Initially, the presented Exponential Pixelating Integral enhances the pixel intensities to overcome the low-contrast issues that are then polar-transformed followed by their representation using the locally invariant Mandelbrot and Julia fractal geometries for effective distinction of structural features. The collated features labeled Exponential Pixelating Integral with dually characterized fractal features are then classified by the non-parametric multivariate adaptive regression splines to establish an ensemble model between each pair of classes for effective diagnosis of diverse diseases. Rigorous analysis of the proposed classification framework on large medical benchmarked datasets showcases its superiority over its peers by registering a higher classification accuracy and F1 scores ranging from 98.46 to 99.45% and 96.53-98.10% respectively, making it a precise and interpretable automated system for diagnosing respiratory disorders.

eess.IV↗
arXiv2026

Myocardial Strain Drift Correction in Deep Learning Based Ultrasound Tracking

Myocardial strain from echocardiography is a key biomarker for cardiac function. Recent deep learning methods show strong performance for myocardial motion tracking but often lack physiological constraints, leading to temporal drift across the cardiac cycle. Consequently, tracked points may not return to their relative initial positions at the end of each cardiac cycle, producing inaccurate strain estimates and even divergence in some cases. We propose a deep learning framework that compensates for drift during myocardial tracking. We extend a state-of-the-art echocardiographic tracking method (TAS-Net) with persistent memory tokens that share information across sliding windows over full cardiac cycles. A teacher-student fine-tuning strategy on real echocardiographic data then enforces physiologically consistent cyclic motion while preserving tracking accuracy. Experiments show reduced global and regional strain drift, improved agreement with clinical references, and better test-retest reproducibility, supporting more reliable myocardial strain estimation in clinical practice.

eess.IV↗
arXiv2026

Morphological Decoupling-Based Skeletal Classification for Clinical Assessment of Malocclusion

Malocclusion skeletal grading is a fundamental task in orthodontics, critical for diagnosis and treatment planning. Traditionally, cone-beam computed tomography (CBCT) is used for visual measurement, and the reconstructed lateral cephalograms are handed over to expert dentists for diagnosis. However, manual review is time-consuming, labor-intensive, and subject to inter-operator variability. Therefore, an automatic CBCT-based system is needed for reliable malocclusion skeletal grading. In this case, we develop TeethGNN, a novel graph-based framework designed to combine CBCT image features with morphological information for accurate and efficient malocclusion grading. TeethGNN utilizes a decoupled learnable decoder to directly predict key morphological indicators from CBCT images, eliminating the need for manual measurements. These morphological features are then fused with image features using a graph neural network (GNN), which effectively models the relationships between the modalities. To further enhance robustness and calibration, we introduce a collaborative calibration strategy. This strategy combines multi-scale graph adversarial perturbation for explicit calibration and nonlinear topological graph calibration for implicit confidence adjustment. Extensive experiments and ablation studies on our collected clinical dataset demonstrate that our malocclusion measurement system achieves 77.08\% in accuracy and 89.61\% in AUC, outperforming the compared state-of-the-art methods. These results validate the effectiveness of graph-based multimodal fusion and collaborative calibration in improving malocclusion grading performance. Our system shows strong potential for advancing computer-aided orthodontic diagnosis, providing an accurate and reliable solution for vision-based clinical measurement and diagnosis.

eess.IV↗