http://magic.aladdin.cs.cmu.edu/2007/03/06/switching-from-yap-to-dviout/

http://www.tex.ac.uk/tex-archive/dviware/dviout/

An ideal bandpass filter would have a completely flat passband (e.g. with no gain/attenuation throughout) and would completely attenuate all frequencies outside the passband. Additionally, the transition out of the passband would be instantaneous in frequency. In practice, no bandpass filter is ideal. The filter does not attenuate all frequencies outside the desired frequency range completely; in particular, there is a region just outside the intended passband where frequencies are attenuated, but not rejected. This is known as the filter roll-off, and it is usually expressed in dB of attenuation per octave or decade of frequency. Generally, the design of a filter seeks to make the roll-off as narrow as possible, thus allowing the filter to perform as close as possible to its intended design. Often, this is achieved at the expense of pass-band or stop-band ripple.

The bandwidth of the filter is simply the difference between the upper and lower cutoff frequencies.

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.

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)

Materials and methods

The problem consists of finding the Gabor function hp(t) among the set of normalized Gabor functions that are most similar to sp(t). In each step p, one Gabor function hp(t) is found and the next residual sp+1(t) is computed.

For each EEG raw data, 10 (p=10) AGR (adpative Gabor transform) coefficients are obtained.

Results and discussion

The advantage of this method is the increased spectral and temporal resolution of the signal. Several experiments have shown that the time-frequency analysis method provides narrow frequency peaks, permitting more precise frequency identification and enhanced ability in the determination of frequency changes at any EEG signal point.

Date: May 2006

IEEE PAMI,

Abstract:

A novel pattern recognition framework which integrates Gabor image representation, a novel multiclass Kernel Fisher Analysis (KFA) method, and fractional power polynomial models for improving pattern performance is presented.

Background

Feature extraction in pattern recognition needs to consider the effectiveness on both data representation and class separability.

Kernel Fisher Analysis