Structuring 3D Medial Skeletons: A Comparative Study

International audienceMedial skeletons provide an effective alternative to boundary or volumetric representations for applications that focus on shape structure. This capability is provided by the skeletal structure, i.e., the curves and surfaces computed from centers of maximally inscribed balls by a process called structuration. Many several structuration methods exist, all having various challenges in terms of delivering a high-quality medial skeleton. This paper provides a first overview of existing structuration methods. We formally define the skeletal structure by giving its theoretical properties, and use these properties to propose quality criteria for structurations. We next review existing structuration methods and compare them using the established criteria. The obtained insights help both practitioners in choosing a suitable structuration method and researchers in further perfecting such methods

Spiking neurons in 3D growing self-organising maps

In Kohonen’s Self-Organising Maps (SOM) learning, preserving the map topology to simulate the actual input features appears to be a significant process. Misinterpretation of the training samples can lead to failure in identifying the important features that may affect the outcomes generated by the SOM model. Nonetheless, it is a challenging task as most of the real problems are composed of complex and insufficient data. Spiking Neural Network (SNN) is the third generation of Artificial Neural Network (ANN), in which information can be transferred from one neuron to another using spike, processed, and trigger response as output. This study, hence, embedded spiking neurons for SOM learning in order to enhance the learning process. The proposed method was divided into five main phases. Phase 1 investigated issues related to SOM learning algorithm, while in Phase 2; datasets were collected for analyses carried out in Phase 3, wherein neural coding scheme for data representation process was implemented in the classification task. Next, in Phase 4, the spiking SOM model was designed, developed, and evaluated using classification accuracy rate and quantisation error. The outcomes showed that the proposed model had successfully attained exceptional classification accuracy rate with low quantisation error to preserve the quality of the generated map based on original input data. Lastly, in the final phase, a Spiking 3D Growing SOM is proposed to address the surface reconstruction issue by enhancing the spiking SOM using 3D map structure in SOM algorithm with a growing grid mechanism. The application of spiking neurons to enhance the performance of SOM is relevant in this study due to its ability to spike and to send a reaction when special features are identified based on its learning of the presented datasets. The study outcomes contribute to the enhancement of SOM in learning the patterns of the datasets, as well as in proposing a better tool for data analysis

Medialness and the Perception of Visual Art

In this article we explore the practical use of medialness informed by perception studies as a representation and processing layer for describing a class of works of visual art. Our focus is towards the description of 2D objects in visual art, such as found in drawings, paintings, calligraphy, graffiti writing, where approximate boundaries or lines delimit regions associated to recognizable objects or their constitutive parts. We motivate this exploration on the one hand by considering how ideas emerging from the visual arts, cartoon animation and general drawing practice point towards the likely importance of medialness in guiding the interaction of the traditionally trained artist with the artifact. On the other hand, we also consider recent studies and results in cognitive science which point in similar directions in emphasizing the likely importance of medialness, an extension of the abstract mathematical representation known as ‘medial axis’ or ‘Voronoi graphs’, as a core feature used by humans in perceiving shapes in static or dynamic scenarios.We illustrate the use of medialness in computations performed with finished artworks as well as artworks in the process of being created, modified, or evolved through iterations. Such computations may be used to guide an artificial arm in duplicating the human creative performance or used to study in greater depth the finished artworks. Our implementations represent a prototyping of such applications of computing to art analysis and creation and remain exploratory. Our method also provides a possible framework to compare similar artworks or to study iterations in the process of producing a final preferred depiction, as selected by the artist

Surface reconstruction from point clouds by transforming the medial scaffold

We propose an algorithm for surface reconstruction from unorganized points based on a view of the sampling process as a deformation from the original surface. In the course of this deformation the Medial Scaffold(MS) — a graph representation of the 3D Medial Axis(MA) — of the original surface undergoes abrupt topological changes (transitions) such that the MS of the unorganized point set is significantly different from that of the original surface. The algorithm seeks a sequence of transformations of the MS to invert this process. Specifically, some MS curves (junctions of 3 MA sheets) correspond to triplets of points on the surface and represent candidates for generating a (Delaunay) triangle to mesh that portion of the surface. We devise a greedy algorithm that iteratively transforms the MS by “removing” suitable candidate MS curves (gap transform) from a rank-ordered list sorted by a combination of properties of the MS curve and its neighborhood context. This approach is general and applicable to surfaces which are: non-closed (with boundaries), non-orientable, non-uniformly sampled, non-manifold (with self-intersections), non-smooth (with sharp features: seams, ridges). In addition, the method is comparable in speed and complexity to current popular Voronoi/Delaunay-based algorithms, and is applicable to very large datasets

Skeletonization methods for image and volume inpainting

Image and shape restoration techniques are increasingly important in computer graphics. Many types of restoration techniques have been proposed in the 2D image-processing and according to our knowledge only one to volumetric data. Well-known examples of such techniques include digital inpainting, denoising, and morphological gap filling. However efficient and effective, such methods have several limitations with respect to the shape, size, distribution, and nature of the defects they can find and eliminate. We start by studying the use of 2D skeletons for the restoration of two-dimensional images. To this end, we show that skeletons are useful and efficient for volumetric data reconstruction. To explore our hypothesis in the 3D case, we first overview the existing state-of-the-art in 3D skeletonization methods, and conclude that no such method provides us with the features required by efficient and effective practical usage. We next propose a novel method for 3D skeletonization, and show how it complies with our desired quality requirements, which makes it thereby suitable for volumetric data reconstruction context. The joint results of our study show that skeletons are indeed effective tools to design a variety of shape restoration methods. Separately, our results show that suitable algorithms and implementations can be conceived to yield high end-to-end performance and quality of skeleton-based restoration methods. Finally, our practical applications can generate competitive results when compared to application areas such as digital hair removal and wire artifact removal

Shape segmentation and retrieval based on the skeleton cut space

3D vormverzamelingen groeien snel in veel toepassingsgebieden. Om deze effectief te kunnen gebruiken bij modelleren, simuleren, of 3D contentontwikkeling moet men 3D vormen verwerken. Voorbeelden hiervan zijn het snijden van een vorm in zijn natuurlijke onderdelen (ook bekend als segmentatie), en het vinden van vormen die lijken op een gegeven model in een grote vormverzameling (ook bekend als opvraging). Dit proefschrift presenteert nieuwe methodes voor 3D vormsegmentatie en vormopvraging die gebaseerd zijn op het zogenaamde oppervlakskelet van een 3D vorm. Hoewel allang bekend, dergelijke skeletten kunnen alleen sinds kort snel, robuust, en bijna automatisch berekend worden. Deze ontwikkelingen stellen ons in staat om oppervlakskeletten te gebruiken om vormen te karakteriseren en analyseren zodat operaties zoals segmentatie en opvraging snel en automatisch gedaan kunnen worden. We vergelijken onze nieuwe methodes met moderne methodes voor dezelfde doeleinden en laten zien dat ons aanpak kwalitatief betere resultaten kan produceren. Ten slotte presenteren wij een nieuwe methode om oppervlakskeletten te extraheren die is veel simpeler dan, en heeft vergelijkbare snelheid met, de beste technieken in zijn klasse. Samenvattend, dit proefschrift laat zien hoe men een complete workflow kan implementeren voor het segmenteren en opvragen van 3D vormen gebruik makend van oppervlakskeletten alleen

Explanatory visualization of multidimensional projections

Het verkrijgen van inzicht in grote gegevensverzalelingen (tegenwoording bekend als ‘big data’) kan gedaan worden door ze visueel af te beelden en deze visualisaties vervolgens interactief exploreren. Toch kunnen beide het aantal datapunten of metingen, en ook het aantal dimensies die elke meting beschrijven, zeer groot zijn – zoals een table met veel rijen en kolommen. Het visualiseren van dergelijke zogenaamde hoog-dimensionale datasets is zeer uitdagend. Een manier om dit te doen is door het maken van een laag (twee of drie) dimensionale afbeelding, waarin men dan zoekt naar interessante datapatronen in plaats van deze te zoeken in de oorspronkelijke hoog-dimensionale data. Technieken die dit scenario ondersteunen, de zogenaamde projecties, hebben verschillende voordelen – ze zijn visueel schaalbaar, ze werken robuust met ruizige data, en ze zijn snel. Toch is het gebruik van projecties ernstig beperkt door het feit dat ze moeilijk te interpreteren zijn. We benaderen dit problem door verschillende technieken te ontwikkelen die de interpretative vergemakkelijken, zoals het weergeven van projectiefouten en het uitleggen van projecties door middel van de oorpronkelijke hoge dimensies. Onze technieken zijn makkelijk te leren, snel te rekenen, en makkelijk toe te voegen aan elke dataexploratiescenario dat gebruik maakt van elke projectie. We demonstreren onze oplossingen met verschillende toepassingen en data van metingen, wetenschappelijke simulaties, software-engineering, en netwerken