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22PHYSICS AND MATHEMATICS | ФИЗИКО-МАТЕМАТИЧЕСКИЕ НАУКИ
FRACTAL-BASED IMAGE SEGMENTATION
Stankevych M.P.
National Technical University of Ukraine "Kyiv Polytechnic In&itute"
ABSTRACT
This paper proposes an advanced algorithm of fractal texture segmentation. Fractal dimension based segmentation is supplemented by image pre-processing and improved using Luv-approach. Image fractal dimension eflimation is done using box-counting method. Pre-processing noise removal and image edging are done. The noise removal is performed by median filtering, which allows to reduce the noise level of the original image without reducing the sharpness of image and avoiding high level of image blurring. Image edging is performed by Roberts method, which reduces the level of false recognition and too high detailization. For making segmentation boundaries more accurate Luv-approach is used, which allows to work with images that have low contrafl. Experiments with images of roads of various sizes, noise degree and contrafl are presented. Based on these experiments, proposed algorithm has made segmentation contours more accurate and the boundaries of algorithm's application wider.
Keywords: digital image, texture segmentation, local fractal dimension, fractal segmentation, box-counting dimension, median filter, edge detection, Roberts cross operator.
Introduction
Image segmentation is the image dividing process into homogeneous areas with respect to one or more characteriflics. One of the mofl important characteriflics of images is texture. Texture segmentation is an urgent task of computer vision [1].
Many natural objects such as soil pores, river networks, mountain ranges, craters, coafllines, ocean waves, cryflals, etc. can be modelled using fractal geometry [2]. Such property of fractals makes calculating fractal image dimensions an effective method of texture image analysis. For the segmentation in this case the characteriflics that calculates the dimension fractal are used.
However, there are many modifications and supplementations of fractal segmentation basic algorithms [3]. There is also the need to adapt the methods for a specific field of application. An important role is played by the methods of image pre-processing. The presence of noise in the image, or too high detailization can lead to erroneous results of segmentation. Therefore, image preparation to the fractal analysis is needed.
1 Methodology
1.1 Noise reduction
The firfl flep of image pre-processing is noise reduction. The chosen method of noise reduction mufl meet the following conditions:
- not to blur an image;
- not to reduce sharpness;
- to work with «salt and pepper» noise.
The firfl two requirements are related to the fact that in the future it is necessary to allocate the image areas' borders, and blur and sharpness reduction can complicate this process significantly. The third requirement is the fact that the noise «salt and pepper» is typical for digital images due to imperfection of these electronic devices.
Median filtration method meets all those conditions.
Median filtering is a nonlinear method used to remove noise from digital images. This method is widely used to preserve image edges from blurring. It is particularly effective in removing noise such as «salt and pepper» [4].
Median filter is very useful for keeping image details.
The median is the befl filter to remove noise without reducing the sharpness and therefore is often used in computer vision applications [5].
1.2 Image edge detection
Image edge detection is the basis of the fundamental image low level processing. Well built edges are needed to handle a higher level processing [6].
The chosen method of image edge detection mufl meet the following conditions:
- not to allocate secondary internal contours;
- not to depend on additional parameters;
- to work unified for images with different characteriflics;
- to have low computational complexity.
The firfl requirement is the fact that it is necessary to diflinguish main segmentation contours and neglect all the surrounding adverse contours. The second and third requirements are related to the fact that the method should work equally well for different image qualities and sizes and should not require manual configuration by the user. The fourth requirement is related to the fact that the main computing power is given to texture filtering.
The Roberts cross operator is a discrete differential operator used in image processing and computer vision to highlight the image edges. It approximates gradient.
The resulting image highlights the intensity changes in the diagonal direction. The main advantage of this method - its simplicity: kernels are small and contain only integers. Although the method is suffering from a large amount of noise in the image. That however is not a problem as the noise filtering is performed preliminary [7].
1.3 Fractal texture segmentation
There are many methods for calculating the local fractal dimension. In this paper a box-counting method is used. The algorithm is shown in Figure 1.
Figure 1. Box-counting based image fractal segmentation
However classical box-counting algorithm is inefficient and leads to messy results for images with low contrafl or blur. In such cases, it makes sense to use the Luv-approach.
CIE Luv colour space allows to determine the diflinction for a person with «average» vision. For this segmentation box-counting is used separately for each channel of Luv representation
of the image. Previous experiments have shown that the colour components u and v contain similar information, that's why they are mixed with maximum function. Then calculated the arithmetic mean of the diflribution of mixed colour matrix and local fractal dimension matrix of brightness (L) [8]. The algorithm is shown in Figure 2.
Figure 2. Luv-approach box-counting segmentation [8]
2. Results and discussion 2.1. Different methods
It was implemented a comparative analysis of fractal segmentation method with flandard methods of texture segmentation implemented by mathematical package Matlab.
A comparative analysis was conducted on two groups of images:
- images with contrafl textured element (Figure 3);
- images containing elements with similar texture (Figure
Figure 3. The series' «The wood» segmentation.
Figure 4 The series' «The beach» segmentation
As seen in Figure 3, mofl of the flandard texture filters don't give the desired segmentation for the series «The wood». For different algorithms applied the result is either not a complete object contour or excessive contours inside the object. This is because the Satirical algorithms are taking into account the very small picture elements. In this case - wood texture contains fine lines, misleading texture filters that try to interpret them as the boundaries of individual objects. So more or less correct result gives a rough mask method, which simplifies image, but in this case there is a drawback - it treats object's shadow as an intimation it's part. At the same time for the series «The wood" fractal algorithm provides much better, and sometimes almofl ideal results are. Images' contours of objects almofl exactly coincide with the image fractal function contour line shown in
blue. Thus, for the analysis of textures with a complex flructure it's better to use fractal algorithm.
As a result of tefls for a series of images «Beach» (Figure 4) was observed that the flandard texture filters can only work properly in some rare cases. These are images that have clear borders between textures and textures themselves are not highly detailed. But for different visually similar images, better segmentation method may be a variety of Satirical methods and identification of some regularity, at leafl based on the data reference examples is too difficult. Fractal algorithm worked on this image series equally well, especially in those areas where the textures have complex flructure.
Thus, we can conclude that it is appropriate to use the fractal segmentation. It works adequately with complex textures,
as well as its work is not affected by the level of sharpness of textures' borders.
2.2 Different subject areas
To tefl the adequacy of the algorithm segmentation and its future application possibility application in different subject areas were tefled using images series «Architecture» (Figures 5 - 7). Segmentation built clear the contours of buildings and
their internal elements, but also the contours around objects images. It can be concluded that the method works adequately. Fractal segmentation can be used in different problem areas, but the method would require additional adjuflments to the specific subject area, the selection of specific methods of images preprocessing and results pofl processing.
Figure 5. Image "Building 1" fractal segmentation results
Figure 6. Image "Building 2" fractal segmentation results
Figure 7. Image "Building 3" fractal segmentation results
2.3 Filtration filtering algorithm shown in Figure 8. We see a significant
The filtration's work adequacy and necessity was tefl with the improvement in image sharpness. image with noise level of 5% (Figure 8). The result of separate
Figure 8. Image median filtration
Figure 9. Segmentation with and without noise filtering
For subflantiation of need of filtration procedure fractal segmentation was performed with and without filtering the input image. The results of segmentation are shown in Figure 9. Segmentation results with previous filtering have more accurate contours and the level of false identification is lower. 2.4 Edge detection
Several edge detection methods were tefled: - method of tracking zero;
- method using the operator Kenny;
- logarithmic method;
- method using Prewitt operator;
- method using Sobel operator;
- Roberts method.
Methods were tefled using two road images. The results of different algorithms' work are shown in Figure 10 for the firfl image and Figure 11 for the second image.
Figure 10. Image edging for image "Road 1"
canny robe rts zerocross
Figure 11. Image edging for image "Road 2"
Both images' edge detection gives the befl result by using Roberts edge detection method. The resulting images contain all the main roads and the fewefl number of excessive lines. If the firfl image has better quality the diflinction between several methods is almofl invisible, for the second image the advantage Roberts method is seen subflantial.
Input image:
Segmentation results:
using log edging uSing Roberts ^¡„3
For subflantiation of the choice of edge detection method essentiality present the results of fractal segmentation using a flandard method of log edge detection and using Roberts method are presented (Figures 12-13).
Figure 12. Image "Road 1" segmentation using different edge detection methods
Figure 13. Image "Road 2" segmentation using different edge detection methods
2.5 Luv - box-counting fractal segmentation made during sunset and rain, so their colors are very similar,
Basic box-counting fractal segmentation algorithm and its and segmentation becomes a very difficult task. Results fractal
Luv-version were compared using three road images (Figures function contour lines of images built using classic and Luv-
14-16). Note that the photos of the Figures 15 and 16 were modified box-counting algorithms are shown in Figures 14-16.
Figure 14. Simple box-counting and luv-box-counting segmentation of image "Road 2
Figure 15. Simple box-counting and luv-box-counting segmentation of image "Road 3
Figure 16. Simple box-counting and luv-box-counting segmentation of image "Road 4"
Luv-modified box-counting algorithm enables more precise contours segmentation, that id especially evidently in Figures 15 and 16 that contain very similar in tone colors. However, the results for image segmentation in Figure 14 show that this approach may neglect some important line elements of the roads, so that segmentation is not complete. Therefore, it was decided that the mofl appropriate solution is to use a combination of these methods.
2.6 Image size dependence
Algorithm was tefled for input images of different sizes. Original image, which has a size of 2100x1400 pixels and at its compressed copies, which conflitute 50%, 25%, 10% of the original image. The results of segmentation are shown in Figure 17.
Figure 17. Segmentation of images with different size
Tefls have shownthatwith image size decreasing segmentation marked. The ratio of segmentation error was calculated by
results become rougher, but the algorithm is working properly the leafl square method. Graphs of segmentation error for two
even with images of small size (210x140 pixels). different road pictures are shown in Figures 18 - 19. The total
2.7 Evaluation of the accuracy errors of segmentation for images 1 and 2 are 0.07% and 2.84%
For the eflimation of segmentation accuracy reference respectively. points on the input image and the segmentation results were
Figure 18. Segmentation of image "Road 1" accuracy
ÎJiir of MJjntflftliOn ter riJrfîjPÏ 1JC0|-I-.-.-.-.Input image
Figure 19. Segmentation of image "Road 2" accuracy
Conclusions
It was considered the problem of segmentation of digital images using fractal segmentation.
To solve this problem the following methods were chosen. Median filtering method was chosen for preprocessing image noise reduction because it can effectively remove «salt and pepper» noise without image blurring. For preprocessing edge detection Roberts method was chosen because it is cofl effective in terms of computational cofls without requiring additional options, and it can be used unified for all images.
Box-counting based image fractal segmentation was implemented. It was also implemented Luv-modificated fractal algorithm to refine the segmentation boundaries for low contrafl images.
Fractal segmentation algorithm was tefled on images of different subject areas: objects on the contrafling background, landscapes, buildings.
Developed algorithm's work was analyzed using images with different size, contrafl, noise level.
The accuracy of segmentation was determined by contracting anchor points on the source and segmented images and computed by the leafl squares method. It is 0.07 - 2.84%.
Subsequently, the algorithm can be used in the field of contraction of augmented reality for design and architecture, analysis of satellite imagery for forefl fires detection, and so on.
The algorithm can be improved by contracting a neural network and adaptation of preprocessing methods to specific input data.
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