A Multi-Class Fisher Linear Discriminant Approach for the Improvement in the Accuracy of Complex Texture Discrimination

Author Name(s): Sanjaykumar Kinge, B. Sheela Rani, Mukul Sutaone
Author Email: sanjaykinge100@gmail.com

Abstract

Texture segmentation has a wide spectrum of applications in diverse fields. This paper presents an elaborated Fisher Linear Discriminant (FLD) based semi-supervised approach for improving the accuracy of segmentation of multi-class complex fine textures. Gabor filter and local statistics (local variance) are used for feature extraction of texture images. Texture segments in the image are separated using K-means clustering. The results obtained using K-means clustering are refined by multi-class Fisher Linear Discriminant (MFLD). The algorithm is tested on wide varieties of several hundred homogenous and complex textures from five texture databases viz. Outex texture database, vision texture database (Vistex), Brodatz textures, Prague textures and Pertex texture database. Fisher distance (FD) is a measure of texture separability. Segmentation of complex textures is relatively a difficult task. The improvement in the segmentation accuracy of complex textures is achieved simply by the termination of MFLD based algorithm when Fisher distance (FD) ceases to increase with the increasing iterations of MFLD. After a quantitative analysis of the experimentation, it is concluded that the segmentation accuracy of complex textures and the combination of complex and homogeneous fine textures (with small texture primitives) increases as high as 29.83% with the increasing iterations of MFLD resulting in a significant improvement at the boundaries. Detailed results are provided in the experimentation and results section of the paper. The results achieve the second rank for 21 benchmark images among the ten state-of-the-art algorithms.

Introduction

Image segmentation is a very important step in image analysis and is used in diverse fields such as computer vision, pattern recognition, medical imaging, machine learning and many other fields. The widely used image segmentation methods are thresholding methods, region and edge-based techniques, clustering and watershed segmentation techniques, level set methods and parametric methods, etc [12]. Texture segmentation is one of the problem domains. This paper describes an elaborated Fisher Linear Discriminant (FLD) based semi-supervised approach for improving the accuracy of segmentation of multi-class complex textures (wherein only a number of classes is required to be known). Texture segmentation problem is difficult due to the fact that researchers have not been able to provide a universal definition of texture till date due to very wide varieties of textures existing in the nature. The popular thesaurus specifies a literal meaning of the word texture as a characteristic of a surface. Clausi DA [5] defines texture as spatial distribution of intensities in image regions observed to be homogeneous throughout the region by a normal human eye.

Conclusion

The textures with straight boundaries and varying sinusoidal boundaries in the terms of different amplitude and different cycles over the edges of the boundaries are used for testing the performance of the proposed algorithm and boundaries of the textures are nicely detected as detailed in experimentation and results section. The proposed algorithm achieves the second rank in ten state-of-the-art algorithms on 21 images in Prague texture segmentation benchmark set. It is observed that texture segmentation accuracy significantly improves for complex fine textures and combination of homogeneous and complex fine textures when the number of iterations of multiclass Fisher linear discriminant (MFLD) is increased. The increased iterations of MFLD result into improved covariance matrices and hence optimum projection vectors which lead to a better segmentation solution. It can thus be inferred that the increasing number of iterations of MFLD results into an improvement in the localization of boundaries and segmentation accuracy of highly complex textures with small texture primitives with respect to the size of an image. The optimum texture segmentation results are obtained with both Gabor Filter and Gaussian smoothing of Gabor filter outputs implemented in frequency domain. Highly complex textures are segmented using spatial co-ordinates of pixels as texture features. Hence, the proposed algorithm is useful for texture images in which the same texture segments do not repeat and appear at different places in the input image. Further improvement in accuracy can be achieved by performing adaptive smoothing of Gabor filter outputs. K-means clustering algorithm sometimes produces erroneous results and can be replaced by Equitz algorithm to avoid such fallacies.

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