3.1.

Nonhomogenous Rock Images

In the field of rock science, the development of digital imaging has made it possible to store and manage the images of the rock material in digital form. Rock represents typical example of nonhomogenous natural image type. This is because there are often strong differences in directionality, granularity, or color of the rock texture, even if the images represented the same rock type.⁸ In bedrock investigation, rock properties are analyzed by inspecting the images that are collected from the bedrock. Different rock layers can be recognized from the borehole images based on the color and texture properties of rock. Therefore, there is a need for an automatic classifier that is capable of classifying the rock images into visually similar classes.

As a testing database, we use a set of rock images that consists of 336 images, which are obtained by dividing large borehole images into parts. These images are manually divided into four classes by an expert. The division is based on their color and texture properties. Figure 2 presents three example images from each of the four classes. The images show that there is directionality in some of the classes, but the orientations vary within the same classes. Therefore, directionality is not used in the classification. In classes 1–4, there are 46, 76, 100, and 114 images in each class, respectively.

Fig. 2

Three examples from each class of the rock images in the testing database.

3.2.

Classification

The database of rock images is classified using feature vectors of Eq. ² in different color channels. The number of scales varyies between two and five. In all cases, the filter centers have been located uniformly to the frequency band such that the frequency channels of the filters cover the whole frequency area. The corresponding filters are presented in Fig. 1. In classification, we have used $k$ -nearest neighbor ( $k$ -NN) classification principle. The selection of the $k$ -NN classifier is due to its robustness with nonhomogenous feature distributions of the rock images. With this type of database, the selected classification algorithm is also fast. The selection of value 5 for $k$ was based on preliminary experiments. In the experiments, a leave-one-out validation method was employed. The distance measure in the classification was Euclidean distance. In preliminary experiments, Euclidean distance outperformed slightly $L_1$ -norm that is other common distance metrics for texture features.

The average classification results are presented as percentages in Table 1 . The results are presented for RGB and HSI color spaces, respectively. In Table 1, the average classification rates are presented for each of the four classes separately and as average value. The dimensionality of each descriptor type is also mentioned in the table. To compare our results to other commonly used visual descriptors, we have calculated the classification results for the testing database using some MPEG-7 texture and color descriptors.⁹ This comparison is presented in Table 2 . We selected the homogenous texture descriptor to represent texture description, because it is based on Gabor filtering in gray-level texture images.⁹ This descriptor is based on the method presented in Ref. 4, and it uses Gabor filters in five scales and six orientations. Because this paper considers also color information of the rock images, we have included also MPEG-7 color descriptors for comparison. Color structure descriptor and color layout descriptor employ HMMD color space⁹ whereas scalable color descriptor uses HSI color space.

Table 1

The average classification rates (%) in each class in RGB and HSI color spaces.

Table 2

The average classification rates (%) in each class using MPEG-7 color and texture descriptors.

3.3.

Results

The classification rates presented in Table 1 show that the rock texture filtering in RGB color space produces slightly better classification results than that in HSI color space. There are remarkable differencies in the classification performance between the classes. Class 1 is especially difficult to classify for all the features. This is due to the nonhomogenous nature of the class 1 images. These images are very varying in terms of their color distributions and texture properties. In class 2, RGB color space gives clearly better results than HSI space. On the other hand, in classes 3 and 4, RGB space is only slightly better. When the comparison with MPEG-7 visual descriptors is considered (Table 2), one can see that these descriptors are outperformed by the proposed methods. Homogenous texture descriptor uses directional Gabor filtering, which yields poorer classification results than the proposed methods. This is due to the fact that especially in classes 1 and 3 the textures are randomly oriented and therefore directionality cannot be regarded as a classifying feature. In addition, color information of texture has not been utilized in this descriptor. The performance of color descriptors is also lower than in the case of the proposed methods. This is natural, because they consider only color distribution of the images and not their texture content.

Computational complexity is always a central matter with practical image classification tasks. Compared to conventional Gabor filtering,^{4, 9} the proposed method is somewhat lighter because it does not calculate the filter responses for different orientation. On the other hand, the filtering is repeated for three color channels instead of one. Therefore the computational cost is dependent on the number of scales and color channels. In fact, the computational complexity can be estimated by comparing the dimensionality of the descriptors. In Tables 1, 2, the dimensionality of each method is presented. For example, by using two scales the dimensionality of the proposed method is 12, which yields to a classification rate of 80.1% in RGB space. This can be regarded as a good result with such a low dimensional descriptor.