1,720,966 research outputs found
A meshless strategy for shape diameter analysis
No full textAn approach to computing an intuitive local thickness from surface meshes was introduced with the
shape diameter function (SDF) in Shapira et al. (Vis Comput 24(4):249–259, 2008). In this paper, we present a new
dynamic approach to the computation of the SDF for a cloud of points on the boundary of a volumetric object.We employ
a particle flow driven by a simple collision test. The resulting SDF scalar field can be naturally exploited as a shape property for the volume-oriented object decomposition. Experimental results show the effectiveness and efficiency of our proposals
Sparsity-inducing variational shape partitioning
No full textAbstract. We propose a sparsity-inducing multi-channel multiple region model for the efficient partitioning
of a mesh into salient parts. Our approach is based on rewriting the Mumford-Shah models in terms of piece-wise
smooth/constant functionals that incorporate a non-convex regularizer for minimizing the boundary lengths. The
solution of this optimization problem, obtained by an efficient proximal forward backward algorithm, is used by a
simple thresholding/clusterization procedure to segment the shape into the required number of parts. Therefore, it is
not necessary to further solve the optimization problem for a different number of partitioning regions. Experimental
results show the effectiveness and efficiency of our proposals when applied to both single- and multi-channel (shape
characterizing) functions
Variational Methods and Numerical Algorithms for Geometry Processing
Full text linkIn questo lavoro affrontiamo il problema della partizione delle forme il cui scopo è la decomposizione di un oggetto di topologia arbitraria in parti più piccole e meglio gestibili chiamate partizioni. Svariate applicazioni in Computer Aided Design (CAD), Computer Aided Manufactury (CAM) e Finite Element Analysis (FEA) sfruttano tali decomposizioni in quanto forniscono un’informazione globale sulla forma. In particolare, siamo interessati al partizionamento di varietà topologiche di dimensioni 2, in quanto il bordo di oggetti fisici tangibili può essere definito matematicamente da varietà bidimensionali immerse nello spazio euclideo tridimensionale. A tale scopo, viene eseguita un’analisi preliminare sulla forma che fa uso di diverse funzioni scalari/vettoriali definite sulla varietà. Il processo di partizionamento si può affrontare da due punti di vista: uno basato sulla percezione visiva umana e un altro basato sullo spessore delle componenti della forma in esame. In particolare, ci concentriamo sulla funzione ’Diametro di forma’ che recupera informazioni volumetriche dalla superficie, fornendo così un naturale legame tra il volume dell’oggetto e il suo bordo; inoltre studiamo la decomposizione spettrale di opportune matrici di affinità che fornisce coordinate spettrali multidimensionali caratterizzanti la forma dell’oggetto; infine introduciamo una nuova base, denominata Lp Compressed Manifold Modes, di quasi-autofunzioni sparse e localizzate dell’operatore Laplace-Beltrami.
Il problema di partizionamento può essere considerato un particolare problema inverso, pertanto è fomulato come un problema di regolarizzazione variazionale che ha come soluzione la cosiddetta funzione di partizionamento. Il funzionale da minimizzare è somma di un termine di fedeltà a un determinato set di dati e di un termine di regolarizzazione che promuove la sparsità, come ad esempio la norma Lp con p ∈ (0, 1) o altre funzioni di penalizzazione non convesse e parametrizzate, con parametro positivo, che controlla il grado di non convessità.
I metodi proposti per ottenere la funzione di partizione, ispirati ai modelli variazionali di Mumford-Shah di funzionali costanti o smooth a tratti, incorporano un regolarizzatore non convesso per ridurre al minimo le lunghezze del contorno delle partizioni. Per la soluzione dei problemi di ottimizzazione non convessi e non smooth si propongono metodi numerici basati su Proximal Forward-Backward Splitting, Alternating Directions Method of Multipliers e strategie Convex Non-Convex.
Inoltre, studiamo un’applicazione del partizionamento di forma nell’ambito della patchbased surface quadrangulation. A questo scopo la varietà viene prima suddivisa in patch di genere zero che catturano la topologia arbitraria dell’oggetto, quindi per ogni patch viene creata una superficie minima ad elementi quadrilateri che si evolve secondo un modello differenziale alle derivate parziali, seguendo un approccio Lagrangiano per ottenere una rappresentazione a griglie quadrilatere semi-regolari. L’evoluzione è supervisionata da una ridistribuzione tangenziale uniforme dell’area-asintotica dei quadrilateri
A forward-backward strategy for handling non-linearity in Electrical Impedence Tomography
No full textElectrical Impedance Tomography (EIT) is known
to be a nonlinear and ill-posed inverse problem. Conventional
penalty-based regularization methods rely on the linearized
model of the nonlinear forward operator. However, the linearized
problem is only a rough approximation of the real situation,
where the measurements can further contain unavoidable noise.
The proposed reconstruction variational framework allows to
turn the complete nonlinear ill-posed EIT problem into a sequence
of regularized linear least squares optimization problems
via a forward-backward splitting strategy, thus converting the ill-posed
problem to a well-posed one. The framework can easily integrate
suitable penalties to enforce smooth or piecewise-constant
conductivity reconstructions depending on prior information.
Numerical experiments validate the effectiveness and feasibility
of the proposed approach
Convex non-convex segmentation of scalar fields over arbitrary triangulated surfaces
Full text linkAn extension of the Mumford–Shah model for image segmentation is introduced to segment real-valued functions having values on a complete, connected, 2-manifold embedded in R3. The proposed approach consists of three stages: first, a multi-phase piecewise smooth partition function is computed, then its values are clustered and, finally, the curve tracking is computed on the segmented boundaries. The first stage, which constitutes the key novelty behind our proposal, relies on a Convex Non-Convex variational model where an ad-hoc non-convex regularization term coupled with a space-variant regularization parameter allows to effectively deal with both the boundaries and the inner parts of the segments. The cost functional is minimized by means of an efficient numerical scheme based on the Alternating Directions Methods of Multipliers. Experimental results are presented which demonstrate the effectiveness of the proposed three-stage segmentation approach
A Variational Approach to Additive Image Decomposition into Structure, Harmonic, and Oscillatory Components
Full text linkWe propose a nonconvex variational decomposition model which separates a given image into piecewise-constant, smooth, and oscillatory components. This decomposition is motivated not only by image denoising and structure separation, but also by shadow and spot light removal. The proposed model clearly separates the piecewise-constant structure and smoothly varying harmonic part, thanks to having a separated oscillatory component. The piecewise-constant part is captured by TV-like nonconvex regularization, harmonic term via second-order regularization, and oscillatory (noise and texture) term via a H^{-1}-norm penalty. There are interesting interactions between these three regularization terms. We explore the effects of each regularization and the choice of parameters carefully. We propose an efficient alternating direction method of multipliers based minimization for fast numerical computation of the optimization problem. Various experiments are presented to show the robustness against a high level of noise, applications to soft spotlight and shadow removal, and the comparisons with other methods
Convex non-convex segmentation over surfaces
No full textThe paper addresses the segmentation of real-valued functions having values on a complete, connected, 2-manifold embedded in R3. We present a three-stage segmentation algorithm that first computes a piecewise smooth multi-phase partition function, then applies clusterization on its values, and finally tracks the boundary curves to obtain the segmentation on the manifold. The proposed formulation is based on the minimization of a Convex Non-Convex functional where an ad-hoc non-convex regularization term improves the treatment of the boundary lengths handled by the L1 norm in [2]. An appropriate numerical scheme based on the Alternating Directions Methods of Multipliers procedure is proposed to efficiently solve the nonlinear optimization problem. Experimental results show the effectiveness of this three-stage procedure
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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