# Evaluation of Image Edges using Gabor Filter

November 27, 2017

In the field of image processing, filters play an extremely important role. All image processing operations can be viewed as applying a series of filters to an image and transforming it in some way. Gabor filter is a particular type of filter, and it happens to be an important one.

Gabor filter responses are widely and successfully used as general purpose features in many computer vision tasks, such as in texture segmentation, face detection and recognition, and iris recognition. In a typical feature construction the Gabor filters are utilized via multi-resolution structure, consisting of filters tuned to several different frequencies and orientations. The multi-resolution structure relates the Gabor features to wavelets, but the main difference, non-orthogonality, also is connected to the main weakness of the Gabor features: computational heaviness. The computational complexity prevents their use in many real-time or near real-time tasks, such as in object tracking.

### Gabor Filter Significance

Gabor filters are orientation-sensitive filters, used for edge and texture analysis. It is named after Dennis Gabor. Certain specific bands of frequency components can be extracted by adjusting the orientation and center frequencies of the Gabor filter. They have enjoyed much attention in the field of 2D face recognition and associated fields as researchers attempt to emulate and surpass the face recognition capabilities of human being. A Gabor filter is a complex sinusoid modulated by a Gaussian function. This filter will therefore respond to some frequency, but only in a localized part of the signal.

Gabor features constructed from post-processed Gabor filter responses have been successfully used in various important computer vision tasks, such as in texture segmentation, face detection, and iris pattern description. However, only very rarely the main weakness of Gabor filter based features, the computational heaviness, has received any attention even though it may prevent the use of proposed methods in real applications. It is evident that Gabor filters have many advantageous or even superior properties for feature extraction, but if the computational complexity cannot be improved their application areas will remain limited.

When a Gabor filter is applied to an image, it gives the highest response at edges and at points where texture changes. The following images show a test image and its transformation after the filter is applied.

Figure 1: Gabor Effect

A Gabor filter responds to edges and texture changes. When we say that a filter responds to a particular feature, we mean that the filter has a distinguishing value at the spatial location of that feature (when we’re dealing with applying convolution kernels in spatial domain, that is. The same holds for other domains, such as frequency domains, as well).

### Real Time Applications

Gabor filters have been used in many applications, such as:

• Texture Segmentation: Gabor filters are used to separate multiple textures in an image. This analysis is critical in a lot of fields, including space missions where they have to traverse unknown terrains.
• Optical Character Recognition: To automatically recognize handwritten letters, number plates, billboards, etc.
• Object Recognition: Gabor filters and their modified versions are used extensively in computer vision. Since they can closely mimic the human visual system, they are used in designing object recognition systems.
• Fractal Dimension Management: Fractals are basically self-similar patterns. They are actually quite fascinating.
• Edge Detection: Detecting the edges in an image is preprocessing step in many image processing systems.
• Retina Identification: Identifying the retina of humans reliably. Very important in security.
• Image coding: The encoding of images is used almost everywhere for transmission.

### References

[1] J. Ilonen, J. K. Kamarainen and H. Kalviainen, “Efficient computation of Gabor features”, Research Report, 2005

[2] Barbu, Tudor, “Gabor filter-based face recognition technique”, Proceedings of the Romanian Academy 11, no. 3 (2010): pp. 277-283.

[3] “Understanding Gabor Filters”, Perpetual Enigma, April 26, 2014, available online at: https://prateekvjoshi.com/2014/04/26/understanding-gabor-filters/

## One Comment

Insert math as
$${}$$