In this paper we take first steps in addressing the 3D Digital Subplane Recognition Problem. Let us consider a digital plane (w.l.o.g. ) and a finite subplane S of P defined as the points (x, y, z) of P such that . The Digital Subplane Recognition Problem consists in determining the characteristics of the subplane S in less than linear (in the number of voxels) complexity. We discuss approaches based on remainder values of the subplane. This corresponds to a bilinear congruence sequence. We show that one can determine if the sequence contains a value in logarithmic time. An algorithm to determine the minimum and maximum of such a bilinear congruence sequence is also proposed. This is linked to leaning points of the subplane with remainder order conservation properties.

discrete subplane, image recognition, discrete geometry