A rotation-invariant approach to 2d shape representation using the hilbert curve

Abstract

A novel approach to 2D shape representation which is invariant to the rotation is introduced. The proposed system determines how any given shape should be rotated depending on the principal axis of the image. After rotation, a space-filling curve is applied to obtain a 1D vector representation of the image. This vector is later compressed in order to obtain a very small 1D vector that adequately represents an image - this is called the Shape Feature Vector (SFV). The system can import these SFVs into a database and perform retrieval queries for the best possible match to a query image. The SFV of a query image is obtained and the euclidean distance measure is used to determine a best match. Three different space-filling curves, Hilbert, Moore, and Z-order, are compared through the recognition rate results. Results from testing have shown significant improvement over previous shape representation methods using the Hilbert curve in the case of similar shapes with different initial orientations while not sacrificing precision in cases where the orientation is similar. Additionally, it was found that all three space-filling curves performed similarly. © 2009 Springer Berlin Heidelberg.