Searcharxiv⌕ Search

SEARCH · Searcharxiv

Results for “math.CT”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

972 recordsLinked to original sources
arXiv2026

A categorical formulation of Kraus' paradox

We give a categorical formulation of Kraus' "magic trick" for recovering information from truncated types. Rather than type theory, we work in Van den Berg-Moerdijk path categories with a univalent universe, and rather than propositional truncation we work with arbitrary cofibrations, which includes truncation as a special case. We show, using Kraus' argument that any cofibration with homogeneous domain is a monomorphism. We give some simple concrete examples in groupoids to illustrate the interaction between homogeneous types, cofibrations and univalent fibrations.

math.CT↗
arXiv2026

Override and Update in Restriction Categories

We study the override and update operators on partial functions from the perspective of restriction categories. We propose a definition of override restriction categories, in which both of the operators in question exist. We prove a number of results concerning these operators and their relationship to the structure of the ambient restriction category, as well as relating them to the existing literature on the override and update operators. We provide various examples of override restriction categories and in particular show that every classical restriction category is an override restriction category.

math.CT↗
arXiv2026

Coexact completion of profinite Heyting algebras and uniform interpolation

This paper shows that the sheaf representation of finitely generated free Heyting algebras constructed by Ghilardi and Zawadowski can be factored as the profinite completion of Heyting algebras, followed by identifying the dual category of profinite Heyting algebras as a full subcategory of a sheaf topos. We show that the dual category of profinite Heyting algebras is an infinitary extensive regular category, and its ex/reg-completion is exactly the aforementioned sheaf topos, which we refer to as the K-topos. We show how certain properties of uniform interpolation can be generalised to the context of arbitrary profinite Heyting algebras, and that they are consequences of the internal logic of the K-topos. Along the way we also establish various topos-theoretic properties of the K-topos.

math.LO↗
arXiv2026

Categorical algebra of conditional probability

In the field of categorical probability, one uses concepts and techniques from category theory, such as monads and monoidal categories, to study the structures of probability and statistics. In this paper, we connect some ideas from categorical algebra, namely weakly cartesian functors and natural transformations, to the idea of conditioning in probability theory, using Markov categories and probability monads. First of all, we show that under some conditions, the monad associated to a Markov category with conditionals has a weakly cartesian functor and weakly cartesian multiplication. In particular, we show that this is the case for the Giry monad on standard Borel spaces. We then connect this theory to existing results on statistical experiments. We show that for deterministic statistical experiments, the so-called standard measure construction (which can be seen as a generalization of the ``hypernormalizations'' introduced by Jacobs) satisfies a universal property, allowing an equivalent definition which does not rely on the existence of conditionals.

math.CT↗
arXiv2026

Essential Unitarity for Higher-Order Quantum Computation

We develop a boundary-centric semantic framework for higher-order quantum computation, building on the Kelly-Laplaza description of compact closure and Abramsky's execution account. In the semantic carrier Perm(C), morphisms are complex-linear combinations of polarized boundary linkings, composed by execution. Finite-family addresses provide coherent control over finite-level quantum registers (qudits) while retaining the multiplicative boundary structure. We identify essential unitarity, a boundary condition extending ordinary unitarity to higher-order interfaces. On positive qudit registers it coincides with ordinary matrix unitarity; at higher order it expresses preservation of information across the full polarized boundary. We define a unit-free coherent quantum core generated by multiplicative wiring, unitary gates on positive qudit registers, and contextual coherent control, and prove that every one of its morphisms is essentially unitary. The framework realizes an applied coherent quantum switch and the unitary stages of equal-ratio one-slot supermap dilations with explicit memory. An extended abstract of this work was accepted for QPL 2026 and is forthcoming in its proceedings.

quant-ph↗
arXiv2026

On Left Adjoints Preserving Colimits in Homotopy Type Theory

We examine how the standard proof that left adjoints preserve colimits behaves in the setting of wild categories, a natural setting for synthetic homotopy theory inside homotopy type theory. We show that the proof may fail for adjunctions between wild categories and even produce a wild left adjoint that fails to preserve colimits. Our core contribution, however, is a sufficient condition on the left adjoint for the proof to go through. The condition, which we call 2-coherence, expresses that the naturality structure of the hom-isomorphism commutes with composition of morphisms. We present two useful examples of this condition in action. First, we use it, along with a new version of a known trick for homogeneous types, to show that the suspension functor, as well as a generalization thereof, preserves graph-indexed colimits. Second, we show that every modality, viewed as a functor on coslices of a type universe, is 2-coherent as a left adjoint to the forgetful functor from the subcategory of modal types, thereby proving this subcategory is cocomplete. We have formalized our main results in Agda.

cs.LO↗
arXiv2026

ARC-CT: Anatomy-Routed Contrastive Vision-Language Learning for 3D Chest CT

Contrastive vision-language learning uses paired chest CT volumes and radiology reports to learn abnormality classifiers without manually annotated labels. However, two characteristics of chest CT challenge conventional global contrastive learning. First, many critical abnormalities are small or anatomically localized, and pooling an en- tire volume into a single embedding may dilute their visual evidence. Second, the standard contrastive objective treats every other scan in a batch as a negative. Because many chest CTs share abnormalities, this objective incorrectly pushes co-positive pairs apart. We propose Anatomy-Routed Contrastive Learning for 3D Chest CT (ARC-CT), a region-aware framework that addresses these limitations using only la- bels extracted from reports by an LLM, with no manual annotations or bounding boxes. ARC-CT combines three components: (1) an Anato- myQFormer localizing evidence via queries constrained by automatically generated organ masks; (2) a label-Jaccard soft InfoNCE objective in- tegrating the standard one-hot target with the label-set overlap of each pair, which reduces false-negative penalties between studies that share clinical findings; and (3) an organ-level alignment loss connecting mask- pooled visual features to organ-specific report text extracted offline with a large language model. ARC-CT achieves a 0.86 mask-free macro AUC across 18 abnormalities using a compact 3D ResNet-18 backbone. Over- all, ARC-CT outperforms both comparable efficient baselines and sev- eral larger transformer models. Our code and weights are available at https://github.com/arc-ct/arc-ct.

cs.CV↗
arXiv2026

MetaStructAtlas: A Grounded 3D Vision-Language Dataset and Benchmark for Functional and Structural Reasoning in Whole-Body PET/CT

The joint interpretation of metabolic function and anatomical structure is essential for clinical diagnosis in whole-body PET/CT. Although recent advances in 3D medical vision-language models have demonstrated remarkable progress, current efforts are limited to regional CT imaging, leaving a critical void in comprehensive whole-body PET/CT analysis. In this work, we introduce MetaStructAtlas, a large-scale dataset for grounded whole-body PET/CT interpretation that synthesizes multimodal imaging with integrated anatomical, metabolic, and semantic annotations. MetaStructAtlas provides 490 co-registered 3D PET and CT volumes with 50,470 organ-level segmentation masks and grounded radiology reports. To facilitate interactive reasoning, we further developed MetaStructVQA, a standardized 3D grounded visual question-answering benchmark containing 100,565 QA pairs. This framework explicitly links diagnostic queries to visual evidence across modalities, encompassing anatomical, morphological, and metabolic characteristics. Finally, we evaluate state-of-the-art 3D medical VLMs on MetaStructVQA, establishing a robust foundation for multimodal representation learning and integrated whole-body reasoning in nuclear medicine.

cs.CV↗
arXiv2026

Conditional Diffusion Posterior Alignment for Sparse-View CT Reconstruction

Computed Tomography (CT) is a widely used imaging modality in medical and industrial applications. To limit radiation exposure and measurement time, there is a growing interest in sparse-view CT, where the number of projection views is significantly reduced. Deep neural networks have shown great promise in improving reconstruction quality in sparse-view CT, especially generative diffusion models. However, these methods struggle to scale to large 3D volumes due to several reasons: (i) the high memory and computational requirements of 3D models, (ii) the lack of large 3D training datasets, and (iii) the inconsistencies across slices when using 2D models independently on each slice. We overcome these limitations and scale diffusion-based sparse-view CT reconstruction to large 3D volumes by combining conditional diffusion with explicit data consistency. We propose Conditional Diffusion Posterior Alignment (CDPA) to enable scalable 3D sparse-view CT reconstruction. A 2D U-Net diffusion model is conditioned on an initial 3D reconstruction to improve inter-slice consistency, combined with data-consistency alignment to match measured projections. Experiments on synthetic and real Cone Beam CT (CBCT) data show state-of-the-art performance, with ablations that confirm the synergistic effects of the proposed pipeline. Finally, we show that the same principles also strengthen fast denoising U-Nets, yielding near-diffusion quality at a fraction of the computational cost.

eess.IV↗
arXiv2026

Artifact Reduction in Undersampled 3D Cone-Beam CTs using a Hybrid 2D-3D CNN Framework

Undersampled CT volumes minimize acquisition time and radiation exposure but introduce artifacts degrading image quality and diagnostic utility. Reducing these artifacts is critical for high-quality imaging. We propose a computationally efficient hybrid deep-learning framework that combines the strengths of 2D and 3D models. First, a 2D U-Net operates on individual slices of undersampled CT volumes to extract feature maps. These slice-wise feature maps are then stacked across the volume and used as input to a 3D decoder, which utilizes contextual information across slices to predict an artifact-free 3D CT volume. The proposed two-stage approach balances the computational efficiency of 2D processing with the volumetric consistency provided by 3D modeling. The results show substantial improvements in inter-slice consistency in coronal and sagittal direction with low computational overhead. This hybrid framework presents a robust and efficient solution for high-quality 3D CT image post-processing. The code of this project can be found on github: https://github.com/J-3TO/2D-3DCNN_sparseview/.

cs.CV↗
arXiv2026

Mamba-driven MRI-to-CT Synthesis for MRI-only Radiotherapy Planning

Radiotherapy workflows for oncological patients increasingly rely on multi-modal medical imaging, commonly involving both Magnetic Resonance Imaging (MRI) and Computed Tomography (CT). MRI-only treatment planning has emerged as an attractive alternative, as it reduces patient exposure to ionizing radiation and avoids errors introduced by inter-modality registration. While nnU-Net-based frameworks are predominantly used for MRI-to-CT synthesis, we explore Mamba-based architectures for this task to investigate the applicability of state-space modeling for cross-modality medical image translation and assess its performance relative to established convolutional architectures. Specifically, we adapt the SegMamba architecture, originally proposed for segmentation, to perform image-to-image generation. Our 3D Mamba architecture effectively captures complex volumetric features and long-range dependencies, thus allowing accurate CT synthesis while maintaining a relatively low parameter count. Experiments were conducted on a subset of SynthRAD2025 dataset, comprising registered single-channel MRI-CT volume pairs across three anatomical regions. Quantitative evaluation is performed via a combination of image similarity metrics computed in Hounsfield Units (HU) and segmentation-based metrics obtained from TotalSegmentator to ensure geometric consistency is preserved. The findings pave the way for the integration of state-space models into radiotherapy workflows.

cs.CV↗
arXiv2026

Physics-Guided Flow Matching for CT Image Reconstruction

Deep generative models have recently emerged as powerful priors for solving ill-posed inverse problems in CT, with diffusion-based approaches achieving state-of-the-art reconstruction performance. However, diffusion models typically rely on stochastic sampling procedures, long inference trajectories, and carefully tuned noise schedules, which can limit computational efficiency and numerical stability, especially at high spatial resolutions. In this work, we investigate Flow Matching as an alternative generative prior for CT reconstruction. We train a high-resolution Rectified Flow Matching model on 256x256 chest images from the Mayo Clinic Low-Dose CT dataset. To mitigate overfitting and limited anatomical variability, we employ a two-stage training strategy consisting of an initial phase with strong, anatomically informed data augmentation, followed by a fine-tuning phase with reduced or no augmentation to refine structural fidelity. The resulting model is capable of generating high-quality and anatomically coherent CT-like images, serving as a strong learned prior. We then evaluate multiple reconstruction methods specifically designed for Flow Matching models, including Plug-and-Play Flow, FlowDPS, Flower, and Flow-Priors (ICTM), and compare them against state-of-the-art diffusion-based reconstruction algorithms such as DDRM, DPS, and DiffPIR. Experimental results across several CT inverse problem settings show that Flow Matching-based approaches consistently outperform diffusion-based methods in terms of PSNR, SSIM, and perceptual quality, while requiring fewer sampling steps. Finally, we publicly release the trained Flow Matching model and accompanying code to facilitate reproducibility and future research. Overall, this work demonstrates that Flow Matching provides a stable, efficient, and effective alternative to diffusion models for high-resolution CT image reconstruction.

cs.AI↗
arXiv2026

Patient-Specific Articulated Digital Twins from a Single Full-Body CT Scan

Patient-specific anatomical models provide individualized context for surgical planning, image-guided intervention, and algorithm development. However, most CT-derived models are static: they preserve the body configuration captured at scan time, but cannot represent how the same anatomy would appear after patient repositioning. This limitation is especially important for radiographic imaging, where appearance depends jointly on imaging geometry and patient pose. We present a proof-of-concept for constructing a patient-specific \emph{articulated} digital twin from a single full-body CT scan. The method fits a parametric human body model (SMPL) to obtain a patient-aligned kinematic scaffold, binds segmented bones and organs to an anatomy-aware rig, and retargets body-pose changes while preserving skeletal geometry. Using full-body CT scans from three subjects, the fitted scaffold achieved 15.8 $\pm$ 4.0 mm chamfer distance and 95.9 $\pm$ 1.8\% skeletal enclosure. Recomposition at the acquisition pose preserved major radiographic structure, with overall SSIM of 0.872 $\pm$ 0.016 and PSNR of 18.5 $\pm$ 1.4 dB across paired DRRs. Across unseen target poses, the resulting twins enabled articulation while maintaining high skeletal enclosure (94.4 $\pm$ 0.4\%). As a feasibility demonstration, we render the articulated twin as pose-dependent DRRs. These results suggest the feasibility of extending static, view-controllable CT simulation toward pose-controllable anatomical twins for future synthetic imaging and positioning studies.

cs.CV↗
arXiv2026

Coronary Mask Guided Registration for Continuous Time 4D Cardiac CT Dataset Construction

Objective: Clinical cardiac CT multiphase reconstructions generally provide acceptable image quality in end-diastole (ED) or end-systole (ES) phases, but in other phases may exhibit motion artifacts, especially in the right coronary artery (RCA). This limits ground-truth availability in 4D cardiac CT imaging research. We aim to construct a 4D cardiac CT dataset that is generally suitable to serve as pseudo ground truth. Methods: We propose Coronary Mask Guided Registration (CMGR) to produce a motion-preserved, artifact-reduced, and continuous-time 4D cardiac CT sequence from the clinical multiphase reconstruction of each patient. For artifact reduction, CMGR uses the ED or ES phase as the reference phase and warps the reference volume with deformation fields to produce the sequence. For motion preservation, CMGR registers the reference phase to each non-reference phase of the multiphase reconstruction. To capture the motion of both the RCA and other cardiac structures in each registration, CMGR regularizes RCA masks and incorporates them into image-domain registration. Time-continuity is achieved by interpolating the deformation fields for non-reference phases to arbitrary times. Results: CMGR outperformed representative image-domain registration methods in capturing RCA motion and providing reasonable RCA shape, and showed competitive performance in capturing whole-heart motion. Additionally, CMGR reduced motion artifacts from clinical multiphase reconstructions, and intermediate CMGR frames generally provided plausible transitions between discrete cardiac phases. Conclusion: CMGR provides an effective approach for constructing continuous-time 4D cardiac CT datasets. Significance: The dataset can be used in system design simulations and in reconstruction algorithm development, thereby facilitating advances in cardiac CT imaging.

eess.IV↗
arXiv2026

Accurate Reconstruction of Gas Turbine Blade Geometry Using 3D/2D Rigid Registration and CT View Optimization

Non-destructive X-ray and computed tomography (CT) testing are essential for ensuring the dimensional accuracy of manufactured components with complex internal structures, such as the cooling channels in gas turbine blades, which directly affect thermal performance and service life. This study presents a multipart 3D-2D rigid registration approach for aligning CAD models with X-ray projections as an alternative to CT reconstruction for part inspection and measurement. A greedy registration algorithm sequentially aligns the blade's exterior before registering its internal components by maximizing the mutual information between simulated and acquired X-ray images. This stepwise approach reduces problem complexity and improves alignment accuracy. View angles are optimized using a greedy method that iteratively selects angles to minimize dimensional measurement errors. The results indicate that a small number of oblique views provides the best accuracy, although a broad range of angles yields acceptable results. The method achieves subpixel registration accuracy, with errors below one-fifth of the magnified detector-pixel pitch. Image noise and defects reduce registration precision, but direct registration in projection space mitigates these effects compared with CT reconstruction. Appropriate view selection can therefore preserve acceptable subpixel accuracy in the presence of image noise and defects.

cs.CV↗
arXiv2026

CT-$Δ$Bench: A Benchmark for Longitudinal 3D Medical Imaging Difference Reporting with Vision-Language Models

In medical imaging, the clinical value of Computed Tomography (CT) lies not only in depicting current disease status, but crucially in enabling longitudinal comparison of serial scans to determine disease evolution, a process that underpins response assessment, recurrence detection, and ongoing patient management. Yet, despite this central role of temporal comparison in clinical decision-making, existing medical foundation models remain largely confined to single-study understanding, leaving temporally grounded cross-examination insufficiently addressed. To address this gap, we study longitudinal imaging difference reporting, a task in which a model takes two temporally separated scans from the same patient and generates a clinically meaningful report describing interval changes between them. We introduce CT-$Δ$Bench, a dedicated benchmark for this task with patient-level splitting to prevent information leakage. To better evaluate this task beyond surface-level text similarity, we further develop change-aware metrics specifically designed to capture clinically meaningful longitudinal changes, and conduct an independent physician validation to assess the reliability of the synthesized references and event extraction pipeline. We also compare direct paired-CT reasoning with an indirect two-stage pipeline that first generates single-timepoint reports and then performs textual differencing. Finally, we propose DeltaMed, a baseline model for direct paired-CT difference reporting, and train it on the benchmark training set. Together, these contributions lay the groundwork for temporally aware medical foundation models that better reflect real-world longitudinal clinical reasoning.

cs.CL↗
arXiv2026

CARDINAL Predicts Cardiovascular Risk From Non-contrast Cardiac CT

Cardiovascular risk prediction remains limited by incomplete clinical data and imaging biomarkers that reduce computed tomography (CT) to a small number of handcrafted features. We developed CARDINAL (Cardiovascular Assessment via Representation learning from Deep Imaging with Nested Anatomical Latent embeddings), a clinically grounded framework that learns compact representations from routine non-contrast cardiac CT for major adverse cardiovascular event (MACE) prediction. In 17,659 patients, CARDINAL was evaluated for 1-, 3-, 5-, and 10-year MACE prediction against American Heart Association (AHA) pooled cohort equations (PCE), AHA predicting risk of cardiovascular disease events (PREVENT), coronary artery calcium (CAC), segmentation-derived CT biomarkers, and 70-feature structural radiomics. Gains were largest at longer horizons. At 10 years, CARDINAL (joint) achieved an area under the receiver operating characteristic curve (AUROC) of 0.866 $\pm$ 0.020 and an area under the precision-recall curve (AUPRC) of 0.890 $\pm$ 0.015, compared with an AUROC of 0.826 $\pm$ 0.023 and an AUPRC of 0.826 $\pm$ 0.022 for structural radiomics, the strongest baseline. CARDINAL also achieved the highest survival concordance index (C-index), 0.753 $\pm$ 0.015, and high-versus-low risk-tertile hazard ratio, 10.78 $\pm$ 3.16, with favorable reclassification and exploratory calibration. These findings suggest that non-contrast cardiac CT contains prognostic information beyond conventional risk equations, CAC scoring, and engineered imaging biomarkers.

eess.IV↗
arXiv2026

BS: Take the Hint - Interactive Multitracer PET/CT Lesion Segmentation with a Scribble-Conditioned ResEnc U-Net

Automated lesion segmentation in whole-body PET/CT is complicated by the variety of physiological tracer uptake patterns and by the differing appearance of lesions across tracers. The autoPET/CT V challenge addresses this by making segmentation interactive: user scribbles marking foreground and background are supplied alongside the image, and the algorithm is expected to exploit them. We present our submission, a scribble-conditioned residual encoder U-Net operating on four input channels: CT, PET, and a sparse scribble map for each of foreground and background. The network is initialised from the autoPET-III winning weights and extended from two to four input channels, with the two scribble channels zero-initialised so that the pretrained representation is preserved exactly at initialisation. Every model is fine-tuned per fold from the corresponding autoPET-III fold checkpoint, so that no validation case is seen during pretraining. PET intensities are normalised against a per-scan aorta blood-pool reference derived from a CT segmentation, which removes tracer- and centre-specific scaling without requiring lesion labels. At inference the five fold models are ensembled by averaging their softmax outputs per sliding-window patch, before Gaussian-weighted stitching. On the challenge's five-fold split, with each fold evaluated on its own validation cases, mean Dice is 0.554 and mean lesion-level F1 is 0.528 without scribbles, rising to 0.751 and 0.733 after five correction rounds. About 85% of that gain follows the first scribble, and the spread between fold models narrows five-fold over the same rounds, so interaction largely compensates for how well or badly a given model segments unaided.

cs.CV↗