Abstract
Two new two dimensional (2-D) complex operators for estimating the energy and orientation of 2-D oriented patterns are proposed. The starting point for our work is a new 2-D extension of the Teager-Kaiser energy operator incorporating orientation estimation. The first new energy operator is based on partial derivatives and can be considered a local (point-based) estimator. Using a nonlocal (pseudo-differential) operator we derive a second and more general energy operator. A scale invariant nonlocal operator is derived from the recently proposed spiral phase quadrature (or Riesz) transform. The Teager-Kaiser energy operator and the phase congruency local energy are unified in a single equation for both 1-D and 2- D. Robust orientation estimation, important for isotropic demodulation of fringe patterns is demonstrated. Theoretical error analysis of the local operator is greatly simplified by a logarithmic formulation. Experimental results using the operators on noisy images are shown. In the presence of Gaussian additive noise both the local and nonlocal operators give improved performance when compared with a simple gradient based estimator.
Highlights
The estimation of image feature orientation is important in many areas of image and pattern analysis, especially for orientation adaptive algorithms
We restrict our coverage to fringe pattern analysis much of the work applies to more general signals and images
In fringe pattern analysis the local fringe orientation can be utilized in directional filtering to improve fringe quality: spin filtering in optical interferometry [5,6,7] and fingerprint ridge enhancement by oriented filtering [1, 8, 9] being two pertinent examples
Summary
The estimation of image feature orientation is important in many areas of image and pattern analysis, especially for orientation adaptive algorithms. In fringe pattern analysis the local fringe orientation can be utilized in directional filtering to improve fringe quality: spin filtering in optical interferometry [5,6,7] and fingerprint ridge enhancement by oriented filtering [1, 8, 9] being two pertinent examples. The author proposed an isotropic 2-D demodulation algorithm [10] which relies upon good orientation estimates for its applicability to intricate fringe patterns. We propose to show that by redefining 2-D orientation estimation as a quadratic (Volterra) mix of first and second partial derivatives we obtain an operator that gives energy and orientation estimates that are uniform and isotropic, yet requires just one complex filtering operation (in its extreme formulation). The paper is structured as follows: Section 2 Reviews the previous approaches and problems of orientation estimation. We apologise in advance for any significant papers that may have been overlooked or misinterpreted; regrettably “The truth is rarely pure and never simple” [20]
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