Abstract
A previous paper presented a method of transforming observed images from figure to 2nd-order differential figure. In this paper, the invariance of the figure source equation for observational transformation is discussed, when the theory is formed with the figure source equation as its core. The redefined observational transformation is constructed using three types of mapping: intensive transformation, blur transformation, and isomorphic transformation. The sets of these transformations form groups, and by making use of algebraic properties, it is possible to categorize the images. Furthermore, it is shown that the commutative law for transformational groups can be derived by analyzing their structure.
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