Invariance Properties of Gabor Filter-based Features –Overview and Applications

The most important properties of Gabor filtering are related to invariance to illumination, rotation, scale, and translation.

Introduction

 By invariance, not only are features meant which are invariant to a set of geomeric transforms, but also methods to perform object detection regardless of pose and imaging conditions using features which are not invariant.

Confusing terminologies: Gabor filter, Gabor expansion, Gabor transform, Gabor jet, Gabor frame, or Gabor wavelet?

As Daugman pointed out, the 2-D Gabor filters are good models of the simple cells in the mammalian visual cortex system.

Survey and overview

The uncertainty can be measured by root mean square (rms) bandwidth: dt, df

The signal which occupies the minimum area dt*df=1/4π is the modulation product of a harmonic oscillation of any frequency with pulse of the form of a probability function.

Gabor expansion

It should be noted that the expansion functions do not have to constitute an orthogonal basis as typically assumed in wavelet or FT, but an unconditional basis, a frame, may succeed as well.

 

Invariant recognition

The Gabor filters are optimally joint localized in time and frequency, and thus, distortions and noise present in distinct locations, time or frequency, do not significantly interfere with the filter responses.

 

Examples

Symbol recognition

This first example utilizes a globally computed sum of Gabor responses, corresponding to edge histograms over different orientation, and thus, provides no elegance or novelty as a feature extraction method.

Simplified Gabor wavelets for human face recognition

Date:2008

Introduction

The Gabor wavelet (GW) is similar to the response of the 2-D receptive field of the mammalian simple cortical cell.

As the dimension of the feature vectors using GWs is very large, PCA/FLD are used to reduce the dimension. To further improve the performance, kernel methods are also used with the Gabor features. The improvement of both the linear and the kernel methods is due to the fact that GW features are robust to illumination, rotation, and scale.

Simplified GW (SGW)