On the recognition of digital planes in three-dimensional space
Pattern Recognition Letters
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Digital Planarity of Rectangular Surface Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Simplified Recognition Algorithm of Digital Planes Pieces
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Recognizing arithmetic straight lines and planes
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Discrete Applied Mathematics
A generalized preimage for the digital analytical hyperplane recognition
Discrete Applied Mathematics
Gift-wrapping based preimage computation algorithm
Pattern Recognition
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A naive digital plane is a subset of points (x, y, z) ∈ Z3 verifying h ≤ ax + by + cz + max{|a|, |b|, |c|}, where (a, b, c, h) ∈ Z4. Given a finite unstructured subset of Z3, the problem of the digital plane recognition is to determine whether there exists a naive digital plane containing it. This question is rather classical in the field of digital geometry (also called discrete geometry). We suggest in this paper a new algorithm to solve it. Its asymptotic complexity is bounded by O(n7) but its behavior seems to be linear in practice. It uses an original strategy of optimization in a set of triangular facets (triangles). The code is short and elementary (less than 300 lines) and available on http://www.loria.fr/~debled/plane.