This dissertation work is concerned with the one dimensional and the multidimensional threshold selection methods for segmentation and their applications to the color image segmentation.
Firstly, a new valley detection procedure is proposed for the one-dimensional threshold selection. The critical peaks and the critical valleys are defined as the peaks and valleys to be detected, and some relations between the critical peaks and valleys are derived. The conditions for the uniqueness of the maximal critical peak and valley set are found with several theorems. The procedure which can extract all the possible critical peaks and valleys are presented and verified. By applying this procedure to the histogram of real images, some desirable results are obtained and experiments show that the concept of the critical valleys are useful for the selection of threshold values.
Secondly, for the threshold selection in multi-dimensional spaces, two methods of growing approach and splitting approach are studied, both of which change a multi-dimensional problem to repetitions of one-dimensional problems. In the growing approach, an iterative algorithm is proposed which uses one-dimensional threshold section techniques and a new concept of the conditional one-dimensional histogram depending on the current threshold values. In the splitting approach, by using the projection techniques and 1-D threshold selection techniques, two algorithms are proposed. These are modified algorithms from the Ohlander's recursive splitting algorithm. By applying these two approaches to the extraction of a specified color region, it is shown that desirable results are obtainable, although the splitting approach is found to be not applicable to the some images.
Finally, the new threshold selection algorithms are applied for extraction of some color region and segmentation of color image. It is shown that in the feature space the cluster corresponding to a color region is narrow and elongated in the direction from the origin to the center of the cluster. Color axis transformation methods are studied for efficient representation of feature cluster as a rectangular parallelepiped. It is shown that all of the clusters can be extracted by sequentially applying the new threshold techniques.
