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Highlights ► Combinatorial maps are an extension of planar graphs in any dimension. ► We formally define map and submap isomorphism for nD open combinatorial maps. ► We give polynomial time algorithms for solving both problems. ► We illustrate the interest of these tools by searching 2D...
Highlights ► Extends vector quantazation to the quantization of graphs. ► Proves the Lloyd-Max conditions for optimality of graph quantization. ► Provides consistency statements for optimal graph quantizer design. ► Presents an accelerated version of competitive learning graph quantization.
Highlights ► Approximate median graph computation. ► Graph embedding into vector spaces. ► Recursive algorithms. ► Graph matching. ► Structural pattern recognition.
Highlights ► The computation of graph prototypes reduces the complexity of graph classification. ► Discriminative prototypes have a better classification power than median graphs. ► Generalized prototypes provide better classification results than set prototypes. ► Dedicated genetic...
Highlights ► We tackle the problem of embedding a set of relational structures into a metric. ► The embedding is defined as a mixture of class-specific submersions from a Riemannian perspective. ► Submersions are recovered using iterative trust-region method. ► The method is general in...
Highlights ► One of the most important points on computing a graph prototype is to compute the common labelling among all graphs in the set. Most of the approaches up to date perform pair-wise graph matching operations in order to compute the common labelling. We present a set of methods to...
Highlights ► A novel shape parsing approach based on the medial axis is presented. ► A shape is decomposed into a set of salient skeletal parts and their relations. ►The parts and relations are captured in a hierarchical abstraction - the bone graph. ► The bone graph avoids the...
Highlights ► We prove structure as a class identity for visual classification. ► We use spectral graph theory as a way to characterise invariant image structures. ► We propose graph energy as a efficient way for image structure extraction.
Highlights ► We compute representative cocycles invariant to scanning and rotation of the object. ► A graph pyramid provides a reduced object-representation (ROR), preserving topology. ► Cocycles in the ROR are down-projected to the original object, in the pyramid. ► Rotation invariance...
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