Abstract
From early 20th, the homology have been studied as a branch of mathematics. It has been one of a major topic in mathematics and applied in many scientific fields. The homology can be regarded as a mathematical concept of quantifying the contact degree. Because it belongs to modern mathematics, advanced knowledge of mathematics are required to understand this concept. Fortunately, since the definition of the homology is very simple in two-dimensional case, we can easily apply this to image analyzing methods. Fracture surface is composed of a process that cracks grow. If these cracks contact one another, rupture occurs. Progress of the fracture would vary due to the effect of external force. We identify the rapid and the fatigue fracture surface by a homology method. By analyzing the state of fracture via a homology method, it is believed that the cause of fracture can be estimated.
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