Meeting on Tomography and Applications

Discrete Tomography, Neuroscience
and Image Reconstruction

19^th Edition

May 5, 2025 – May 7, 2025

 

Mathematics Department-6° Floor
Politecnico di Milano

 

Paolo Dulio - Politecnico di Milano

Paolo Finotelli – Université de Caen Normandie

Andrea Frosini - Università degli Studi di Firenze

Silvia Pagani - Università Cattolica del Sacro Cuore

 

 

Titles and abstracts of the talks will be progressively uploaded once submitted by the speakers

 

Edoardo Nicolò Aiello Neuropsychological disorders in neurodegenerative conditions: a clinical overview of diagnostic procedures

Abstract. Cognitive and behavioural disorders of a neurodegenerative etiology are increasing in incidence and prevalence worldwide and represent a major public health challenge. Hence, in the view of treatment planning, a timely diagnosis of these conditions is pivotal. Neuropsychological assessment – i.e., the standardized assessment of cognition, behaviour and functional independence – is a core step for diagnosing such disorders.

The current presentation will focus on the semiology and the diagnostics of neuropsychological disorders in the context of some of the most prevalent/incident neurodegenerative conditions – namely Alzheimer’s disease, Lewy body and Parkinson’s disease and frontotemporal lobar degenerations; a focus will be also placed on the neuroradiological and fluid biomarkers of these disturbances.

Andreas Alpers   Anisotropic Power Diagrams: From Descartes and Voronoi to Superpixels and Tomography

Abstract.From Descartes’ early investigations into polyhedral space division to Kepler’s conjectures on optimal sphere packings and Voronoi’s foundational work on metric partitions, the problem of decomposing space into meaningful regions has long fascinated geometers. This talk traces a conceptual lineage from these classical constructions to anisotropic power diagrams — a modern generalization of Voronoi diagrams that incorporates directional and weighted information via ellipsoidal norms defining local distances.

I will then discuss recent developments and applications of anisotropic power diagrams, with a particular focus on their use in tomography for imaging polycrystalline structures, as well as in superpixel generation and image segmentation, the latter of which is joint work with Ke Chen and Jisui Huang.

Michela Ascolese   Reconstruction of gray-scale images with no ambiguities

Abstract The main challenge in the field of Discrete Tomography is to develop techniques leading to the reconstruction with no ambiguities of an unknown object, starting from the knowledge of its projections collected by means of X-rays along a certain set of directions. The problem is ill-posed in general, meaning that, for a given set of directions, different images having the same projections along them exist. When looking for binary solutions, uniqueness of reconstruction can be reached by properly choosing the set of directions along which the projections are collected; the result has been recently implemented in the algorithm e-BRA (2024), that allows unambiguous reconstruction in the binary case. In this talk, we present some experiments we performed on binary phantoms using different sets of directions as input of the algorithm, and consider possible extensions of the results known in the literature to the general case of gray-scale images. Even if a theoretical result is still missing, our experiments suggest that e-BRA could be extended  to the case of gray-scale solutions, and encourage us to follow the same research line to solve the reconstruction problem in the general case.

Alberto Bravin Phase Contrast microCT and spectral imaging with laboratory sources: novel tools in preclinical diagnostics

Abstract  The Anthem project (AdvaNced Technology for Human centEred Medicine) aims at developing devices, tools, and strategies for monitoring and improving the outcome of a portfolio of diseases. Within Anthem, we are developing two complementary X-ray laboratories for realizing Virtual Histology of tissues. Virtual Histology is a novel technique able to non-destructively analyse tissues in 3D, at the (sub)microscopic scale, to complement the diagnostic significance of conventional histology. It profits from the improved image contrast provided by the phase contrast imaging techniques, which exploit the tiny refraction of X-rays occurring within samples.

One of the laboratories, equipped with a Zeiss X-Radia Versa microscope, is presently under delivery at the University of Milano-Bicocca: it will analyse sequences of biopsies using the most advanced commercial CT instrument equipped with the Phase contrast imaging capability.

A second laboratory is presently under construction at the University of Bergamo. It will be equipped with multiple phase contrast imaging techniques (propagation, edge illumination, speckle) to perform advanced clinically-oriented research. The X-ray setup will also foresee a novel spectral imaging detector which permits the simultaneous acquisition of images formed, respectively, by the low- and high-energy tails of the X-ray spectrum impinging on the sample. Using suitable contrast agents, it will provide a higher tissue discrimination of the internal features. The scope and the implementation of the project will be here presented and discussed.

Niccolò Di Marco  Maximizing influence in network structures

Abstract. Maximizing influence in network structures is a fundamental problem in various domains, including graph theory, social science and epidemiology.Theoretically, given a graph G=(V,E), the goal is to identify a subset of seed nodes that maximizes influence, which can be measured in various ways (e.g., node degree, expected number of infected nodes, etc.). Since this problem is, in the general case, NP-hard, in this talk we will focus on influence maximization within directed tree structures, where nodes are labeled with a binary state (indicating the belonging to the seed subset), and influence is quantified by the number of affected neighbors from one class to another. We will discuss strategies to deal both with the unconstrained problem -where the number of seed nodes is not specified- and the constrained one -where the seed nodes must be exactly k. Finally, we will explore real-world use cases of our algorithms.

One notable application involves assessing the impact of coordinated inauthentic behavior—groups of accounts that collaborate to spread misleading or inaccurate information on social media. By applying our strategies to real data from information cascades reconstructed from Twitter/X, we provide a bounded estimate of their influence, offering valuable insights into the reach and effectiveness of such coordinated efforts.

Azzurra Di Palma  Remembering Like a Brain: A Modular HH Network for Associative Memory

Abstract. Associative memory is one of the key functions of neural systems, allowing the retrieval of stored information based on partial or noisy inputs. Among these models, Hopfield-type neural networks have been extensively studied as simplified representations of the learning and memory processes based on Hodgkin-Huxley (HH) model. By incorporating both chemical and electrical synapses, as well as structured block-based connectivity, we have defined a model that enhances storage capacity and retrieval efficiency. The network consists of modular groups of HH neurons, including excitatory (IB, RSA) and inhibitory (FS) units, which interact via dynamic synapses regulated by the Willshaw rule and lateral inhibition. This organization reduces interference between stored patterns, improving pattern segregation. Furthermore, it captures key features of biological neural systems, including the balance of excitation and inhibition, noise suppression, and the importance of temporal precision in coding and retrieval.
For input without noise, our model performs efficiently in high-fidelity memory recall under optimal conditions. When noise is introduced, the model successfully recognizes patterns at high frequencies, but struggles at lower frequencies.
The framework can be further extended to incorporate additional neuronal types, synaptic mechanisms, and network structures, allowing for broader applications.

Guglielmo Fadabini Applications of tomography in art

Abstract. In this short talk, I will explain how it is possible, thanks to the underlying principles of tomography, to create artistic representations using the method of algorithmic stringArt. I will then show how, with the help of a robot, kilometers of thread are woven onto a frame, bringing digital images to life in the physical world.

Paolo Finotelli Collective memories formation and evolution: A geometrical interpretation

Abstract. In this talk, I will describe a way of modeling the formation and evolution of collective memories. To form collective memories within a group, four conditions must be met: 1) memories must be transmitted through a communication network, 2) they must be shaped by interactions with others, 3) they must converge to a common form within the group, and 4) this representation must stabilize over time, a process we call dynamic stability. While formalizing these conditions mathematically is crucial for defining the formation and evolution of collective memory—a task still to be fully explored—this paper presents a theoretical model to address it. We use concepts from geometry, linear algebra, sociology, and psychology to define the formation, evolution, and dynamic stability of collective memories. Our approach incorporates both individual memories and group interactions, illustrating how collective memory can be modeled by means of an orthogonal matrix and a hypersphere in R^D space, where D represents the number of questions in an evaluation questionnaire.

Ivan Fumagalli Computational modeling of brain clearance and vascular-cerebrospinal fluid coupling

Abstract. Brain clearance relies on the coordinated action of multiple physical processes, including cerebrospinal fluid flow, blood perfusion, tissue deformation, and solute transport, whose impairment is associated with neurodegenerative diseases. We present a computational framework encompassing Multiple-network Poro-Elasticity (MPE) for perfusion and protein transport, Stokes flow for CSF dynamics, and reduced models of blood circulation. Anatomical information is reconstructed from magnetic resonance imaging, enabling personalized simulations. The numerical discretization relies on a high-order PolyDG method on polytopal meshes, tailored to address complex geometries. This method achieves both accuracy and computational efficiency, as demonstrated by benchmark tests. We further discuss the challenges in model calibration and in bridging image reconstruction with simulation-based inference. This research is a joint work with P. Antonietti, M. Corti, N. Parolini, R. Petrucci, and the BraiNum project, and it is part of the activities of "Dipartimento di Eccellenza 2023-2027".

Yan Gerard Shadok Heuristics for Geometric Optimization

Abstract. Since 2019, the Shadoks team has regularly participated in geometric optimization competitions such as CG:SHOP (Computational Geometry: Solving Hard Optimization Problems https://cgshop.ibr.cs.tu-bs.de/ and others (League of Robot Runners). For CG:SHOP 2019, the problem was a variant of the Traveling Salesman Problem.
    CG:SHOP 2020 focused on a convex partitioning problem.
    CG:SHOP 2021 was the critical Multi-Agent Path Finding -MAPF- problem involving moving a fleet of robots while avoiding collisions.
    CG:SHOP 2022 was a segment intersection graph coloring problem.
    CG:SHOP 2023 was a convex covering problem.
    CG:SHOP 2024 was a 2-dimensional knapsack problem, i.e., packing.
The Shadok's record includes three first-place finishes (2021/2022/2024) and two second-place finishes (2019/2023). The goal of the talk is to present the competitive optimization strategies implemented by the Shadoks, with a focus on the conflict-based optimization meta-heuristic developed in 2021 and successfully reused in 2022.
[the composition of Shadoks varied with Aldo Gonzalez-Lorenzo (3 editions of CG:SHOP), Luc Libralesso (2021), Loïc Crombez (4 editions), Pascal Lafourcade (2021), Yan Gerard (5 editions) and Guilherme Da Fonseca (6 editions)]

Maria Hernandez Cifre Successive radii of convex bodies

Abstract. For a convex body $K$ of the $n$-dimensional Euclidean space, we define the successive outer and inner radii, denoted respectively by $R_i(K)$ and $r_i(K)$, $i=1,\dots,n$, in the following way: $R_i(K)$ is the smallest radius of a solid cylinder with $i$-dimensional spherical cross section containing $K$, whereas $r_i(K)$ is the radius of the greatest $i$-dimensional ball contained in $K$.

These measures generalize the well-known functionals diameter, minimal width, circumradius and inradius of $K$, and can be also defined via the circumradius/inradius of suitable projections/sections of the convex body $K$.

Our aim in this talk is to present the known results as well as some extensions and recent developments about them. Furthermore, the relation between the different successive radii with other relevant geometric measures will be also pointed out, and the determination of certain convex bodies via these properties, highlighted.

This is a joint work with Lidia Gordo, from the University of Murcia.

Jaques-Olivier Lachaud Around global and local convexity in digital spaces

Abstract. This talk presents several aspects of convexity in digital spaces Z^d. We first examine the geometry of the digitization of convex shapes and, more precisely determine how the convex hull of these lattice points is close to the geometry of the convex shape before digitization. Under some smoothness properties, we establish that the convex hull is Hausdorff close to the original shape proportionnaly to the digitization gridstep h. Convex hull vertices are shown to be much closer to the shape than expected (proportional to h^(2d/(d+1))). This explains why the convex hull is an appealing reconstruction of digital convex objects. We then show that the normal vector to the convex hull facets converges to the normal vectors of the smooth convex shape with a speed proportional to sqrt(h), and the bound is tight. Secondly we study how we can define the notion of local convexity without recourse to differential geometry. The problem is decomposed into two stages:

(i) identification of locally extremal points using a plane-probingvariant,

(ii) joining pairs of extremal points whenever the straight

segment between them stays sufficiently close to the input surface without crossing it (visibility). Finally, convex and concave polyhedral approximations are computed from the previously obtained soup of candidate edges. The method output is exactly the convex hull of the input surface if it is digitally convex and is composed of polyhedral approximations of the convex and concave parts otherwise.

Maurizio Santini Assessments on diffusion coefficient of biological materials

Abstract. Formalin fixation and paraffin embedding (FFPE) are widely used to preserve resections for clinical histopathological examination and the techniques comprises several steps in which knowing the diffusion coefficients in porous media is predominant for the timing. Used processing protocols often rely on empirical assumptions of different nature because most are multicompartmental heterogeneous porous media.

An experimental method for determining the diffusion coefficient in biological tissues is presented based on the solution of an inverse problem: the infiltration of any fluid through the porous medium (resected in quasi-cylindrical symmetry) is based on an analytical solution of the three-dimensional diffusion equation in cylindrical coordinates, solved by a general solution with a zero-order Bessel function of the first kind. Combining it with Beer's law (evaluating the attenuation of X-ray intensity by radiographs since it is proportional to the variation of fluid concentration over time) it is possible to calculate the diffusion coefficient.

Tommaso Traetta From near alternating sign matrices to Heffter arrays

Abstract.  A near alternating sign matrix (NASM) is an array with entries from $\{0, \pm1\}$ such that, ignoring $0$s, the $+1$s and $-1$s alternate in each row and each column; in addition, we require such a matrix to have arbitrarily prescribed weights for each row and column. These arrays, which generalize alternating sign matrices, were studied for the first time by Brualdi and Kim, although they focused on constructing them, leaving out the weights, but with arbitrarily prescribed first and last nonzero entries in each row and column. It is well known that these matrices have connections with partitions, tilings, and statistical physics.

In this talk, we describe some constructive methods and show an application of NASMs to build (generalized) Heffter arrays that satisfy further properties, thus obtaining orthogonal cycle decompositions and biembeddings of Cayley graphs.

 

 

PROGRAM 

 

Monday 5		Tuesday 6		Wednesday 7
13:45 - 14:00	Opening	10:00 - 10:55	M. Hernandez Cifre	10:00 - 10:55	J-O. Lachaud
14:00 – 14:55	A. Alpers	11:00 - 11:55	A. Bravin - M. Santini	11:00 - 11:30	Coffee Break
15:00 – 15:25	Coffee Break	12:00 - 12:20	G. Fadabini	11:30 - 12:25	Y. Gerard
15:30 - 16:25	T. Traetta	12:30 - 14:00	Lunch Break	12:30  - 12:55	N. Di Marco
16:30 - 17:00	M. Ascolese	14:00 - 14:55	E. Aiello	13:00 -14:30	Farewell Aperitif
		15:00 - 15:25	A. di Palma
		15:30 -15:55	Coffee Break
		16:00 - 16:55	I. Fumagalli
		17:00 - 17:30	P. Finotelli
		20:00	Social Dinner

 

Conference place

Conference room - 7° floor
Building 14 
Via Bonardi n. 9  
20133 Milano - Italy

 

How to reach Milano Leonardo Campus (Conference venue)

Subway: Line 2 (MM2 green line), stop: PIOLA. Then 50 meters on walk.

From Linate Airport: Bus n. 91, stop: ROMAGNA-PIOLA, or n. 93, stop: PONZIO-CELORIA. Then 5 minutes walking.

From Malpensa Airport Terminal 1: Train Malpensa Express to Milano Cadorna - Subway Line 2.

From Malpensa Airport Terminal 2: Shuttle service to Terminal 1 - Train Malpensa Express to Milano Cadorna - Subway Line 2.

From Orio al Serio Airport: Orio Shuttle (or other companies) to Milano Centrale – Subway Line 2.