Recognition of Geometrical Shapes by Dictionary Learning

TL;DR

The paper investigates applying dictionary learning to geometric shape recognition from 2D point clouds. It formulates the SDL objective as $Y \approx D X$ with sparsity constraints $\| X \|_0 \le T$ and compares Orthogonal Matching Pursuit and Least Angle Regression as the sparse-coding solvers. A distance-based preprocessing converts variable-length point clouds into fixed-length vectors via a $D_1$-type distance to the barycenter, followed by sorting and pruning to length $N$. Experiments on a Korchi-derived dataset show that LARS-based dictionaries achieve near-perfect shape-class recognition, highlighting the importance of solver choice and data preprocessing for SDL in shape recognition.

Abstract

Dictionary learning is a versatile method to produce an overcomplete set of vectors, called atoms, to represent a given input with only a few atoms. In the literature, it has been used primarily for tasks that explore its powerful representation capabilities, such as for image reconstruction. In this work, we present a first approach to make dictionary learning work for shape recognition, considering specifically geometrical shapes. As we demonstrate, the choice of the underlying optimization method has a significant impact on recognition quality. Experimental results confirm that dictionary learning may be an interesting method for shape recognition tasks.

Figures (4)

• Figure 1: On the left, is the visualization of the distance computation, exampled on a triangle point cloud. On the right, an enlargement of the points within the point cloud is shown.
• Figure 2: Comparison of the different stages of preprocessing, by the example of a specific triangle shape. With the circle marks, we denote the elements of the distance vector $\bm{d}$. The triangle marks represent the modified distance vector $\bm{d}^{\mathrm{s}}$. And $\bm{d}^{\mathrm{p}}$ is representing the pruned distance vector, indicated with the star marks. Additionally, we indicated the shift between the original and sorted distance vector.
• Figure 3: The hit-rate-matrix when using the OMP algorithm as solver for \ref{['eq:dict_learning_subproblem_2']}. Each row stands for the origin shape class, and the columns indicate the recognition results shape class. A strong diagonal line would indicate a perfect recognition, since the shape classes would be matched against them self. This figure indicates a poor recognition.
• Figure 4: The hit-rate-matrix when using the LARS algorithm as solver for \ref{['eq:dict_learning_subproblem_2']}. Each row stands for the origin shape class, and the columns indicate the recognition results shape class. A strong diagonal line would indicate a perfect recognition, since the shape classes would be matched against them self. This figure indicates a very good recognition.