Boundary Detection of Textured Regions

1. llfTRODVCTION

Texture is an important property for segmentation of input pictures into regions in scene analysis. Many methods have been proposed to extract meaningful textural properties of local regions such as coarseness or orientation [ l ]; however, few attempts have been made for detection of exact textural boundaries. Usual methods apply local operators sensitive to some statistical properties of local regions, and then the textural boundary is obtained as the boundary of regions having homogeneous textural properties.

However, such a simple method cannot find correct location of textural boundaries. The reason is that statistical properties do not change abruptly on the boundary, but gradually change from one region to another region. Therefore, there are relatively broad regions having mixed properties of two neighboring regions around the boundary. Thus, existing methods find a boundary somewhere in this broad region around the true boundary. In this paper, we propose a good measure of textural boundary and a method to find a globally good boundary with respect to the defined measure of boundary.

~. MEASURE OF TEXTURAL BOUNDARY

For the sake of simplicity, let us first consider the problem of finding the boundaries of two textural regions R1 and R2 that are known to have homogeneous properties P1 and P2 respectively. As shown in Fig. I, the boundary exists in the region S between two homogeneous regions R1 and R2 and the local properties of the region S are not homogeneous and have some mixed properties of two regions. Let us define a local operator that has two regions r 1 and r2 on both sides of a center line L as shown in Fig. 2, and denote the local properties of r1 and r2 as p1 and boundary M as:

The value of the measure M is large when the operator is on the boundary and is very small in other places. Fig. 3 shows the values of Dtt. Dtl, !ht. D11 and M when the operator is on the rig.nt of the boundary.

Then, the boundary can be found by searching the region S for points having large value of M. However, local decisions such as finding points having local maximum of M cannot produce a good boundary since noise causes many false boundary points and gaps on the true boundary. We utilize the optimization method to find a globally good boundary with respect to the measure M in the regionS.

S. GLOBAL DETECTION OF IJOUNDARY

Let us represent a line by any sequence of oonnected linear segments Lt . k .. ... LN of length t, and define a merit function ~ of the line ( Lt. k ..... LN ) as

Where M( L1 ) is the measure of the boundary of the linear segment Lt computed by the local operator parallel to the linear segment L1 · as shown in Fig. 4.

Then, the sequence of linear segments Lt ... .. LN having the maximum value in the region S can be considered as the globally good boundary. Therefore, the problem of finding the globally good boundary becomes the problem of finding the sequence of linear segments Lt .. .. . LN which maximizes the merit function ~ given in (2) . This problem can be solved by the multistage optimization procedure. An efficient method for solving this problem is described by the authors[2]. We may embed shape information such as smoothness into the merit function ~ as

Where e ( L1 ) is the slope of the line L, and k is a constant. This merit function find a boundary having large value of M and low-curvatures.

4. INITIAL SEGMENTATION OF PICTURES

We have described a global method to find exact location of boundaries in the region S. In this section, we will briefly describe a method of the initial segmentation of a picture into regions having homogeneous textural properties. Fig. 5 shows a flowchart of the initial segmentation procedure. First, the input picture is averaged to obtain the reduced version of the image. The initial segmentation is performed on this reduced image and the segmentation results are used as a plan for detecting exact locations of textural boundaries in the full size image. We use not only a single textural property but also multiple textural properties such as gray-level distribution, edges per unit area or edge direction for segmentation. After obtaining these textural properties in the image, a non- linear averaging operator proposed by Tomita and Tsuji[3] is applied to smooth textural properties of each point in the image. Then, the recursive thresholding method proposed by Tomita et al[ 4] is applied to segment the image using multiple textural properties.

First, the histograms of the entire image are computed for all textural properties. Then, by analyzing these histograms, the most promising property for partitioning the image is selected. That is, the property whosP. histogram has deep valleys between two prominent peaks is selected as the promising property for partitioning and the threshold is determined as the value of the bottom of the valley. Then, the image is segmented by the selected threshold of the selected property. For each of the segmented regions, we apply the same procedure as described above until each region has only one prominent peak in the histograms.

These segmented regions of the reduced image are utilized as the plan for detecting exact locations of the boundaries of textural regions in the full size image by the textural boundary detector described before. The plan gives the textural boundary detector the following two things: l) search region of the boundary, and 2) textural properties of two neighboring regions to be utilized in finding the boundary.

5. £XP£RIM£NT.4L RESULTS

To show the ability of detecting exact locations of textural boundaries, we tested the proposed method on the image shown in Fig. 6. Fig. 7 shows the initial segmentation procedure obtained for this image. Fig. 8 shows the boundaries detected by the textural boundary detector.

REFERENCE

1. R. M. Harallck. : Statistical and Structural Approac.'1es to Texture, 4th IJCPR, pp. 45-69, 1978.
2. M. Yachida, M. Ikeda and S. Tsuji : A Knowledge Directed Line Finder for Analysis of Complex Scenes, 6th IJCAI.
3. F. Tomita and S. Tsuji : Extraction of Multiple Regions by Smoothing in Selected Neighborhoods, IEEE Trans. SMC-7, pp. 107-109, 1977.
4. F. Tomita, M. Yachida and S. Tsuji :Detection of Homogeneous Regions by Structural Analysis, Jrd IJCAI, pp. 564-571, 1973.

Fig. 8. Boundaries obtained by the textural boundary detector.