  A novel 3D shape classification scheme, based on collaborative representation
learning, is investigated in this work. A data-driven feature-extraction
procedure, taking the form of a simple projection operator, is in the core of
our methodology. Provided a shape database, a graph encapsulating the
structural relationships among all the available shapes, is first constructed
and then employed in defining low-dimensional sparse projections. The recently
introduced method of CRPs (collaborative representation based projections),
which is based on L2-Graph, is the first variant that is included towards this
end. A second algorithm, that particularizes the CRPs to shape descriptors that
are inherently nonnegative, is also introduced as potential alternative. In
both cases, the weights in the graph reflecting the database structure are
calculated so as to approximate each shape as a sparse linear combination of
the remaining dataset objects. By way of solving a generalized eigenanalysis
problem, a linear matrix operator is designed that will act as the feature
extractor. Two popular, inherently high dimensional descriptors, namely
ShapeDNA and Global Point Signature (GPS), are employed in our experimentations
with SHREC10, SHREC11 and SCHREC 15 datasets, where shape recognition is cast
as a multi-class classification problem that is tackled by means of an SVM
(support vector machine) acting within the reduced dimensional space of the
crafted projections. The results are very promising and outperform state of the
art methods, providing evidence about the highly discriminative nature of the
introduced 3D shape representations.
