Some Basic Invariant Properties of the Multidimensional Hough Transform

The paper discusses the presentation in the multidimensional Hough space of a contour set and also the presentation of the two sets.. external and internal, to which this contour divides the convex hypersurface, which is determined in the object space. Each point of these sets is represented by an indirect transform in the Hough space, i.e. by means of the supporting hyperplane (maybe not unique), related to the convex hypersurface in this point. The results of the theoretical research indicate, that in this representation, the basic properties of the sets are preserved. In the given case this means that in the object space the connected sets, which are the contour and the generated by it external and internal sets, correspond to the connected sets in the Hough space. These sets are parts of the convex hypersurface with the same mutual disposition, i.e. the contour set in the object space corresponds to a contour set in the Hough space. Analogously, the external and internal sets in the first space correspond to an external set and an internal one in the second space.