Proceedings of the First International Workshop on Mathematical Foundations of Computational Anatomy (MFCA'06) - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceNon-linear registration and shape analysis are well developed research topic in the medical image analysis community. There is nowadays a growing number of methods that can faithfully deal with the underlying biomechanical behaviour of intra-subject shape deformations. However, it is more difficult to relate the anatomical shape of different subjects. The goal of computational anatomy is to analyse and to statistically model this specific type of geometrical information. In the absence of any justified physical model, a natural attitude is to explore very general mathematical methods, for instance diffeomorphisms. However, working with such infinite dimensional space raises some deep computational and mathematical problems. In particular, one of the key problem is to do statistics. Likewise, modelling the variability of surfaces leads to rely on shape spaces that are much more complex than for curves. To cope with these, different methodological and computational frameworks have been proposed. The goal of the workshop was to foster interactions between researchers investigating the combination of geometry and statistics for modelling biological shape variability from image and surfaces. A special emphasis was put on theoretical developments, applications and results being welcomed as illustrations. Contributions were solicited in the following areas: * Riemannian and group theoretical methods on non-linear transformation spaces * Advanced statistics on deformations and shapes * Metrics for computational anatomy * Geometry and statistics of surfaces 26 submissions of very high quality were recieved and were reviewed by two members of the programm committee. 12 papers were finally selected for oral presentations and 8 for poster presentations. 16 of these papers are published in these proceedings, and 4 papers are published in the proceedings of MICCAI'06 (for copyright reasons, only extended abstracts are provided here)

Tracking human motion with multiple cameras using articulated ICP with hard constraints

Questa tesi propone un nuovo algoritmo basato su ICP per il tracking di un modello scheletrico articolato di un corpo umano. L\u2019algoritmo proposto prende in input immagini calibrate di un soggetto, calcola la ricostruzione volumetrica e la linea mediale del corpo e quindi posiziona in modo adeguato il modello, composto di segmenti, in ogni frame usando una versione di ICP modificata (versione che usa una strategia di attraversamento alberi gerarchica che mantiene connessi tutti i segmenti del modello nei giunti relativi). L\u2019approccio proposto usa limiti cinematica per i giunti e un filtro di Kalman esteso per fare il tracking del modello. Il primo contributo originale di questa tesi \ue8 l\u2019algoritmo per trovare i punti sullo scheletro di un volume tridimensionale. L\u2019algoritmo, usando una tecnica di slicing trova l\u2019asse mediale di un volume 3D in modo veloce utilizzando il processore della scheda grafica e le texture units della scheda stessa. Questo algoritmo produce ottimi risultati per quanto riguarda la qualit\ue0 e le prestazioni se comparato con altri algoritmi in letteratura. Un altro contributo originale \ue8 l\u2019introduzione di una nuova strategia di tracking basata su un approccio gerarchico dell\u2019algoritmo ICP, utilizzato per trovare le congruenze tra un modello di corpo umano composto da soli segmenti e un insieme di punti 3D. L\u2019algoritmo usa una versione di ICP dove tutti i punti 3D sono pesati in funzione del segmento del corpo preso in considerazione dall\u2019algoritmo in quel momento. L\u2019applicazione di queste tecniche dimostra la bont\ue0 del metodo e le prestazioni ottenute in termini di qualit\ue0 della stima della posa sono comparabili con altri lavori in letteratura. I risultati presentati nella tesi dimostrano la fattibilit\ue0 dell\u2019approccio generale, che si intende utilizzare in un sistema completo per il tracking di corpi umani senza l\u2019uso di marcatori. In futuro il lavoro pu\uf2 essere esteso ottimizzando l\u2019implementazione e la codifica in modo da poter ottenere prestazioni real-time.This thesis proposed a new ICP-based algorithm for tracking articulated skeletal model of a human body. The proposed algorithm takes as input multiple calibrated views of the subject, computes a volumetric reconstruction and the centerlines of the body and fits the skeletal body model in each frame using a hierarchic tree traversal version of the ICP algorithm that preserves the connection of the segments at the joints. The proposed approach uses the kinematic constraints and an Extended Kalman Filter to track the body pose. The first contribution is a new algorithm to find the skeletal points of a 3D volume. The algorithm using a slicing technique find the medial axis of a volume in a fast way using the graphic card processor and the texture units. This algorithm produce good results in quality and performance compared to other works in literature. Another contribution is the introduction of a new tracking strategy based on a hierarchical application of the ICP standard algorithm to find the match between a stick body model and a set of 3D points. The algorithm use a traversing version of ICP where also all the 3D points are weighted in such a way every limbs of the model can best fit on the right portion of the body. The application of these techniques shown the feasibility of the method and the performances obtained in terms of quality of estimate pose are comparable with other works in literature. The results presented here demonstrate the feasibility of the approach, which is is intended to be used in complete system for vision-based markerless human body tracking. Future work will aimed at optimizing the implementation, in order to achieve real-time performances

Digital Interaction and Machine Intelligence

This book is open access, which means that you have free and unlimited access. This book presents the Proceedings of the 9th Machine Intelligence and Digital Interaction Conference. Significant progress in the development of artificial intelligence (AI) and its wider use in many interactive products are quickly transforming further areas of our life, which results in the emergence of various new social phenomena. Many countries have been making efforts to understand these phenomena and find answers on how to put the development of artificial intelligence on the right track to support the common good of people and societies. These attempts require interdisciplinary actions, covering not only science disciplines involved in the development of artificial intelligence and human-computer interaction but also close cooperation between researchers and practitioners. For this reason, the main goal of the MIDI conference held on 9-10.12.2021 as a virtual event is to integrate two, until recently, independent fields of research in computer science: broadly understood artificial intelligence and human-technology interaction

Digital Restoration of Damaged Historical Parchment

In this thesis we describe the development of a pipeline for digitally restoring damaged historical parchment. The work was carried out in collaboration with London Metropolitan Archives (LMA), who are in possession of an extremely valuable 17th century document called The Great Parchment Book. This book served as the focus of our project and throughout this thesis we demonstrate our methods on its folios. Our aim was to expose the content of the book in a legible form so that it can be properly catalogued and studied. Our approach begins by acquiring an accurate digitisation of the pages. We have developed our own 3D reconstruction pipeline detailed in Chapter 5 in which each parchment is imaged using a hand-held digital-SLR camera, and the resulting image set is used to generate a high-resolution textured 3D reconstruction of each parchment. Investigation into methods for flatting the parchments demonstrated an analogy with surface parametrization. Flattening the entire parchment globally with various existing parametrization algorithms is problematic, as discussed in Chapters 4, 6, and 7, since this approach is blind to the distortion undergone by the parchment. We propose two complementary approaches to deal with this issue. Firstly, exploiting the fact that a reader will only ever inspect a small area of the folio at a given time, we proposed a method for performing local undistortion of the parchments inside an interactive viewer application. The application, described in Chapter 6, allows a user to browse a parchment folio as the application un-distorts in real-time the area of the parchment currently under inspection. It also allows the user to refer back to the original image set of the parchment to help with resolving ambiguities in the reconstruction and to deal with issues of provenance. Secondly, we proposed a method for estimating the actual deformation undergone by each parchment when it was damaged by using cues in the text. Since the text was originally written in straight lines and in a roughly uniform script size, we can detect the the variation in text orientation and size and use this information to estimate the deformation. in Chapter 7 we then show how this deformation can be inverted by posing the problem as a Poisson mesh deformation, and solving it in a way that guarantees local injectivity, to generate a globally flattened and undistorted image of each folio. We also show how these images can optionally be colour corrected to remove the shading cues baked into the reconstruction texture, and the discolourations in the parchment itself, to further improve legibility and give a more complete impression that the parchment has been restored. The methods we have developed have been very well received by London Metropolitan Archives, as well the the larger archival community. We have used the methods to digitise the entire Great Parchment Book, and have demonstrated our global flattening method on eight folios. As of the time of writing of this thesis, our methods are being used to virtually restore all of the remaining folios of the Great Parchment Book. Staff at LMA are also investigating potential future directions by experimenting with other interesting documents in their collections, and are exploring the possibility of setting up a service which would give access to our methods to other archival institutions with similarly damaged documents

Point-set manifold processing for computational mechanics: thin shells, reduced order modeling, cell motility and molecular conformations

In many applications, one would like to perform calculations on smooth manifolds of dimension d embedded in a high-dimensional space of dimension D. Often, a continuous description of such manifold is not known, and instead it is sampled by a set of scattered points in high dimensions. This poses a serious challenge. In this thesis, we approximate the point-set manifold as an overlapping set of smooth parametric descriptions, whose geometric structure is revealed by statistical learning methods, and then parametrized by meshfree methods. This approach avoids any global parameterization, and hence is applicable to manifolds of any genus and complex geometry. It combines four ingredients: (1) partitioning of the point set into subregions of trivial topology, (2) the automatic detection of the local geometric structure of the manifold by nonlinear dimensionality reduction techniques, (3) the local parameterization of the manifold using smooth meshfree (here local maximum-entropy) approximants, and (4) patching together the local representations by means of a partition of unity. In this thesis we show the generality, flexibility, and accuracy of the method in four different problems. First, we exercise it in the context of Kirchhoff-Love thin shells, (d=2, D=3). We test our methodology against classical linear and non linear benchmarks in thin-shell analysis, and highlight its ability to handle point-set surfaces of complex topology and geometry. We then tackle problems of much higher dimensionality. We perform reduced order modeling in the context of finite deformation elastodynamics, considering a nonlinear reduced configuration space, in contrast with classical linear approaches based on Principal Component Analysis (d=2, D=10000's). We further quantitatively unveil the geometric structure of the motility strategy of a family of micro-organisms called Euglenids from experimental videos (d=1, D~30000's). Finally, in the context of enhanced sampling in molecular dynamics, we automatically construct collective variables for the molecular conformational dynamics (d=1...6, D~30,1000's)

Three Dimensional Data Acquisition and The Registration Problem

The use of 3D scanners for capturing three dimensional data give rise to many interesting mathematical problems. The main problem we consider is known as the registration problem. When we have two images, i.e. visualizations of some sort, of the same object taken at different viewpoints, or at different times, these will in general not be in the same coordinate system. The problem is in essence, how to bring the images together in a common coordinate system. We will consider the problem in the context of scans of rigid body objects, captured by 3D scanners. This means that we will study registration where the objects are not allowed to undergo deformations, i.e. we focus on non-elastic registration

Computational Modeling of Facial Response for Detecting Differential Traits in Autism Spectrum Disorders

This dissertation proposes novel computational modeling and computer vision methods for the analysis and discovery of differential traits in subjects with Autism Spectrum Disorders (ASD) using video and three-dimensional (3D) images of face and facial expressions. ASD is a neurodevelopmental disorder that impairs an individual’s nonverbal communication skills. This work studies ASD from the pathophysiology of facial expressions which may manifest atypical responses in the face. State-of-the-art psychophysical studies mostly employ na¨ıve human raters to visually score atypical facial responses of individuals with ASD, which may be subjective, tedious, and error prone. A few quantitative studies use intrusive sensors on the face of the subjects with ASD, which in turn, may inhibit or bias the natural facial responses of these subjects. This dissertation proposes non-intrusive computer vision methods to alleviate these limitations in the investigation for differential traits from the spontaneous facial responses of individuals with ASD. Two IRB-approved psychophysical studies are performed involving two groups of age-matched subjects: one for subjects diagnosed with ASD and the other for subjects who are typically-developing (TD). The facial responses of the subjects are computed from their facial images using the proposed computational models and then statistically analyzed to infer about the differential traits for the group with ASD. A novel computational model is proposed to represent the large volume of 3D facial data in a small pose-invariant Frenet frame-based feature space. The inherent pose-invariant property of the proposed features alleviates the need for an expensive 3D face registration in the pre-processing step. The proposed modeling framework is not only computationally efficient but also offers competitive performance in 3D face and facial expression recognition tasks when compared with that of the state-ofthe-art methods. This computational model is applied in the first experiment to quantify subtle facial muscle response from the geometry of 3D facial data. Results show a statistically significant asymmetry in specific pair of facial muscle activation (p\u3c0.05) for the group with ASD, which suggests the presence of a psychophysical trait (also known as an ’oddity’) in the facial expressions. For the first time in the ASD literature, the facial action coding system (FACS) is employed to classify the spontaneous facial responses based on facial action units (FAUs). Statistical analyses reveal significantly (p\u3c0.01) higher prevalence of smile expression (FAU 12) for the ASD group when compared with the TD group. The high prevalence of smile has co-occurred with significantly averted gaze (p\u3c0.05) in the group with ASD, which is indicative of an impaired reciprocal communication. The metric associated with incongruent facial and visual responses suggests a behavioral biomarker for ASD. The second experiment shows a higher prevalence of mouth frown (FAU 15) and significantly lower correlations between the activation of several FAU pairs (p\u3c0.05) in the group with ASD when compared with the TD group. The proposed computational modeling in this dissertation offers promising biomarkers, which may aid in early detection of subtle ASD-related traits, and thus enable an effective intervention strategy in the future

Gaze-Based Human-Robot Interaction by the Brunswick Model

We present a new paradigm for human-robot interaction based on social signal processing, and in particular on the Brunswick model. Originally, the Brunswick model copes with face-to-face dyadic interaction, assuming that the interactants are communicating through a continuous exchange of non verbal social signals, in addition to the spoken messages. Social signals have to be interpreted, thanks to a proper recognition phase that considers visual and audio information. The Brunswick model allows to quantitatively evaluate the quality of the interaction using statistical tools which measure how effective is the recognition phase. In this paper we cast this theory when one of the interactants is a robot; in this case, the recognition phase performed by the robot and the human have to be revised w.r.t. the original model. The model is applied to Berrick, a recent open-source low-cost robotic head platform, where the gazing is the social signal to be considered