Point clouds provide a flexible geometric representation suitable for countless applications in computer graphics; they also comprise the raw output of most 3D data acquisition devices. While hand-designed features on point clouds have long been proposed in graphics and vision, however, the recent overwhelming success of convolutional neural networks (CNNs) for image analysis suggests the value of adapting insight from CNN to the point cloud world. Point clouds inherently lack topological information, so designing a model to recover topology can enrich the representation power of point clouds. To this end, we propose a new neural network module dubbed EdgeConv suitable for CNN-based high-level tasks on point clouds, including classification and segmentation. EdgeConv acts on graphs dynamically computed in each layer of the network. It is differentiable and can be plugged into existing architectures. Compared to existing modules operating in extrinsic space or treating each point independently, EdgeConv has several appealing properties: It incorporates local neighborhood information; it can be stacked applied to learn global shape properties; and in multi-layer systems affinity in feature space captures semantic characteristics over potentially long distances in the original embedding. We show the performance of our model on standard benchmarks, including ModelNet40, ShapeNetPart, and S3DIS.

/pdf/dynamic-graph-cnn-for-learning-on-point-clouds-20wlcru9tg.pdf

Dynamic Graph CNN for Learning on Point Clouds

Many scientific fields study data with an underlying structure that is non-Euclidean. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions) and are natural targets for machine-learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural-language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure and in cases where the invariances of these structures are built into networks used to model them.

Geometric Deep Learning: Going beyond Euclidean data

The unprecedented growth in the tourism industry during the last fifty years has created major challenges in tourism marketing. As more and more areas of the world are developed for tourism, the destination choices available to consumers continue to expand. Furthermore, today's consumers, facilitated by increased leisure time, rising levels of disposable income and more efficient transportation networks, have the means to choose from among this much larger variety of destinations. As a result, tourism marketers are now faced with influencing consumer decision making in an increasingly complex and competitive global marketplace.

The meaning and measurement of destination image.

コンピュータ・サイエンス : ACM computing surveys

Point clouds provide a flexible geometric representation suitable for countless applications in computer graphics; they also comprise the raw output of most 3D data acquisition devices. While hand-designed features on point clouds have long been proposed in graphics and vision, however, the recent overwhelming success of convolutional neural networks (CNNs) for image analysis suggests the value of adapting insight from CNN to the point cloud world. Point clouds inherently lack topological information so designing a model to recover topology can enrich the representation power of point clouds. To this end, we propose a new neural network module dubbed EdgeConv suitable for CNN-based high-level tasks on point clouds including classification and segmentation. EdgeConv acts on graphs dynamically computed in each layer of the network. It is differentiable and can be plugged into existing architectures. Compared to existing modules operating in extrinsic space or treating each point independently, EdgeConv has several appealing properties: It incorporates local neighborhood information; it can be stacked applied to learn global shape properties; and in multi-layer systems affinity in feature space captures semantic characteristics over potentially long distances in the original embedding. We show the performance of our model on standard benchmarks including ModelNet40, ShapeNetPart, and S3DIS.

http://reuter.mit.edu/papers/reuter-smi09.pdf

Technical Section: Discrete Laplace-Beltrami operators for shape analysis and segmentation

Reeb graphs for shape analysis and applications

Differential topology, and specifically Morse theory, provide a suitable setting for formalizing and solving several problems related to shape analysis The fundamental idea behind Morse theory is that of combining the topological exploration of a shape with quantitative measurement of geometrical properties provided by a real function defined on the shape The added value of approaches based on Morse theory is in the possibility of adopting different functions as shape descriptors according to the properties and invariants that one wishes to analyze In this sense, Morse theory allows one to construct a general framework for shape characterization, parametrized with respect to the mapping function used, and possibly the space associated with the shape The mapping function plays the role of a lens through which we look at the properties of the shape, and different functions provide different insightsIn the last decade, an increasing number of methods that are rooted in Morse theory and make use of properties of real-valued functions for describing shapes have been proposed in the literature The methods proposed range from approaches which use the configuration of contours for encoding topographic surfaces to more recent work on size theory and persistent homology All these have been developed over the years with a specific target domain and it is not trivial to systematize this work and understand the links, similarities, and differences among the different methods Moreover, different terms have been used to denote the same mathematical constructs, which often overwhelm the understanding of the underlying common frameworkThe aim of this survey is to provide a clear vision of what has been developed so far, focusing on methods that make use of theoretical frameworks that are developed for classes of real functions rather than for a single function, even if they are applied in a restricted manner The term geometrical-topological used in the title is meant to underline that both levels of information content are relevant for the applications of shape descriptions: geometrical, or metrical, properties and attributes are crucial for characterizing specific instances of features, while topological properties are necessary to abstract and classify shapes according to invariant aspects of their geometry The approaches surveyed will be discussed in detail, with respect to theory, computation, and application Several properties of the shape descriptors will be analyzed and compared We believe this is a crucial step to exploit fully the potential of such approaches in many applications, as well as to identify important areas of future research

/pdf/describing-shapes-by-geometrical-topological-properties-of-3eispojr71.pdf

Describing shapes by geometrical-topological properties of real functions

There are many possible 2D views of a given 3D object and most people would agree that some views are more aesthetic and/or more “informative” than others. Thus, it would be very useful, in many applications, to be able to automatically compute these “best” views. Although all measures of the quality of a view will ultimately be subjective, hence difficult to quantify, we propose some general principles which may be used to address this challenge. In particular, we describe a number of different ways to measure the goodness of a view, and show how to optimize these measures by reducing the size of the search space.

What’s in an image?

To fully exploit the valuable knowledge embedded in repositories of digital models, it is crucial to devise search engines capable of expressing high-level and advanced queries, which can effectively support the re-use of CAD models. The retrieval mechanism should be able to return not only global similarity measures among objects, but it should also be coupled with methods for the automatic identification of similar sub-parts in the query and retrieved models, possibly highlighting automatically the object differences. This paper describes a method for partial shape-matching able to recognize similar sub-parts of objects represented as 3D polygonal meshes. The geometry and the structure of the shapes are coupled in a descriptor that provides a flexible coding, grounded on solid mathematical theories, and that can be adapted to the user’s needs and to the context of applications. The matching framework for sub-part correspondence is achieved through a graph-matching technique, which builds the common sub-graphs between the two shapes and highlights the maximal sub-parts having similar structure and similar space distribution.

Silvia Biasotti

Papers

Technical Section: Discrete Laplace-Beltrami operators for shape analysis and segmentation

Reeb graphs for shape analysis and applications

Describing shapes by geometrical-topological properties of real functions

What’s in an image?

Sub-part correspondence by structural descriptors of 3D shapes