Spatial learning with perceptually grounded representations

The goal of this paper is to develop the foundation for a spatial navigation without objective representations. Rather than building the spatial representations on a Euclidean space, a weaker conception of space is used. A type of spatial representation is described that uses perceptual information directly to define the regions in space. By combining such regions, it is possible to derive a number of useful spatial representations such as place-fields, paths and topological maps. Compared to other methods, the representations of the present approach have the advantage that they are always grounded in the perceptual abilities of the robot.     

Infused design. I. Theory

The paper introduces infused design: an approach for establishing effective collaboration between designers from different engineering fields. In infused design, the design problem representation is brought up to a mathematical meta-level, which is common to all engineering disciplines. The reasoning about the problem is then done by using mathematical terminology and tools that, due to their generality, are the same for all engineers, disregarding their background. This gives engineers an opportunity to infuse their work with knowledge, methods, and solutions shared by specialists from other engineering fields. When these knowledge, methods, and solutions cross disciplinary boundaries, they are provably relevant to any problem in another domain to which it can be transformed. The suggested meta-level consists of general discrete mathematical models, called combinatorial representations (CR). Specific mathematical basis for the combinatorial representations chosen in this paper is graph theory although other representations are possible. We explain the theory of infused design and carefully contrast it with other approaches. This comparison clearly demonstrates the advantages of infused design and its potential. We conclude with several practical issues related to the introduction of infused design into practice and briefly discuss the role of information systems in infused design. A companion paper includes several examples that demonstrate the details of infused design.

Auto- and allo-confrontation as tools for reflective activities

This paper presents a methodology of assistance to reflective activity, based on confronting participants with the video recording of their own activity or that of others. A typology of the various forms of use of confrontation is proposed and illustrated from a study based on the construction of technical procedures. Two categories of results are highlighted. On the one hand, individual auto-confrontation (confronting participants with their own activity) reveals the cognitive processes underlying the activity. On the other hand, individual allo-confrontation (confronting participants with an activity they practice but which is performed by someone else, without the latter being present) allows participants to develop their knowledge by getting aware of other types of representations.     

Free-Sets: A Condensed Representation of Boolean Data for the Approximation of Frequency Queries

Given a large collection of transactions containing items, a basic common data mining problem is to extract the so-called frequent itemsets (i.e., sets of items appearing in at least a given number of transactions). In this paper, we propose a structure called free-sets, from which we can approximate any itemset support (i.e., the number of transactions containing the itemset) and we formalize this notion in the framework of -adequate representations (H. Mannila and H. Toivonen, 1996. In Proc. of the Second International Conference on Knowledge Discovery and Data Mining (KDD'96), pp. 189–194). We show that frequent free-sets can be efficiently extracted using pruning strategies developed for frequent itemset discovery, and that they can be used to approximate the support of any frequent itemset. Experiments on real dense data sets show a significant reduction of the size of the output when compared with standard frequent itemset extraction. Furthermore, the experiments show that the extraction of frequent free-sets is still possible when the extraction of frequent itemsets becomes intractable, and that the supports of the frequent free-sets can be used to approximate very closely the supports of the frequent itemsets. Finally, we consider the effect of this approximation on association rules (a popular kind of patterns that can be derived from frequent itemsets) and show that the corresponding errors remain very low in practice.     

Volume Preservation of Multiresolution Meshes

Geometric constraints have proved to be efficient for enhancing the realism of shape animation. The present paper addresses the computation and the preservation of the volume enclosed by multiresolution meshes. A wavelet based representation allows the mesh to be handled at any level of resolution. The key contribution is the calculation of the volume as a trilinear form with respect to the multiresolution coefficients. Efficiency is reached thanks to the pre-processing of a sparse 3D data structure involving the transposition of the filters while represented as a lifting scheme. A versatile and interactive method for preserving the volume during a deformation process is then proposed. It is based on a quadratic minimization subject to a linearization of the volume constraint. A closed form of the solution is derived.     

An Efficient Algorithm for Determining an Aesthetic Shape Connecting Unorganized 2D Points

We present anefficient algorithm for determining an aesthetically pleasing shape boundary connecting all the points in a given unorganized set of 2D points, with no other information than point coordinates. By posing shape construction as a minimisation problem which follows the Gestalt laws, our desired shape is non‐intersecting, interpolates all points and minimizes a criterion related to these laws. The basis for our algorithm is an initial graph, an extension of the Euclidean minimum spanning tree but with no leaf nodes, called as the minimum boundary complex . and can be expressed similarly by parametrizing a topological constraint. A close approximation of , termed can be computed fast using a greedy algorithm. is then transformed into a closed interpolating boundary in two steps to satisfy ’s topological and minimization requirements. Computing exactly is an NP (Non‐Polynomial)‐hard problem, whereas is computed in linearithmic time. We present many examples showing considerable improvement over previous techniques, especially for shapes with sharp corners. Source code is available online.     

Surface Patches from Unorganized Space Curves

Recent 3D sketch tools produce networks of three‐space curves that suggest the contours of shapes. The shapes may be non‐manifold, closed three‐dimensional, open two‐dimensional, or mixed. We describe a system that automatically generates intuitively appealing piecewise‐smooth surfaces from such a curve network, and an intelligent user interface for modifying the automatically chosen surface patches. Both the automatic and the semi‐automatic parts of the system use a linear algebra representation of the set of surface patches to track the topology. On complicated inputs from ILoveSketch [ [BBS08] ], our system allows the user to build the desired surface with just a few mouse‐clicks.     

G2 Tensor Product Splines over Extraordinary Vertices

We present a second order smooth filling of an n‐valent Catmull‐Clark spline ring with n biseptic patches. While an underdetermined biseptic solution to this problem has appeared previously, we make several advances in this paper. Most notably, we cast the problem as a constrained minimization and introduce a novel quadratic energy functional whose absolute minimum of zero is achieved for bicubic polynomials. This means that for the regular 4‐valent case, we reproduce the bicubic B‐splines. In other cases, the resulting surfaces are aesthetically well behaved. We extend our constrained minimization framework to handle the case of input mesh with boundary.     

Motorcycle Graphs: Canonical Quad Mesh Partitioning

We describe algorithms for canonically partitioning semi‐regular quadrilateral meshes into structured submeshes, using an adaptation of the geometric motorcycle graph of Eppstein and Erickson to quad meshes. Our partitions may be used to efficiently find isomorphisms between quad meshes. In addition, they may be used as a highly compressed representation of the original mesh. These partitions can be constructed in sublinear time from a list of the extraordinary vertices in a mesh. We also study the problem of further reducing the number of submeshes in our partitions—we prove that optimizing this number is NP‐hard, but it can be efficiently approximated.