|
The paper presents the application of image analysis and mathematical morphology for the investigation of fibrous structures. The directional analysis of fibers is widely applied in biology, geology, metallurgy etc. With respect to the purpose of the analysis the investigations were divided into two groups. Each fiber was distinguished and recognized individually or the surface areas containing fibers of the same orientation were segmented. Based on the methods of mathematical morphology, the algorithms of directional detection of fibrous structures were developed. The investigations were conducted utilizing the binary source images. These images were subjected to preliminary filtering and thinning. The directional erosion by a pair of points oriented in 6 or 9 directions was performed. The corresponding grey level was assigned to the result of each erosion. A grey image was obtained, encoded in such a way, that each grey level corresponded to a different structure orientation. The properties of the computer image and the structure of fibers did not allow to obtain fibers coded uniformly along their entire length. The coding of the particular fibers was unified to enable the description of each of them through one variable (a single grey level). Each fiber was a collection of pixels of various grey levels. The adjoining pixels of identical grey levels formed segments of various length. Distance functions for these segments were calculated. The global maximum of the distance function contained in the particular fibers corresponded to the central point of the longest segment. An algorithm assigned the grey level consistent with the grey level of this segment to the entire object. In order to connect again the fibers which might have been broken earlier the propagation method was used. The main advantage of the presented algorithm is the possibility of a simultaneous analysis of all fibers within the boundaries of the analyzed image. THe method has been used for analysis of various fibrous structures. The other group of applications of fiber analysis is connected with the detection of area in which the fibers are of the same orientation. The above algorithm also helped to solve this problem. The obtained results was used to calculate the mosaic image included areas of different grey levels. Each of these levels was analyzed separately. In the next step of the algorithm the watershed was used to separate objects connected by narrow strips, and next the opening by reconstruction in order to eliminate the negligible objects. The algorithm enable the segmentation of areas of the same direction of fibers. The minimal surface area was determined by the size of the opening by reconstruction. The algorithm is illustrated with some examples of metallurgical structures.
|
