Motivation
1. Digital image processing and pattern recognition
MPP and consequently MNBIC belong to the means where the digitized figures are represented by the external characteristics – its border. This can be useful for computer processing and image recognition. The advantage consists in the fixed length of the MNBIC regardless of the starting point and rotation for the fixed inner and outer contour border of the closed input curves. The ambition here is to proclaim the unique value of the length as the shortest length among the vertices of the grid inscribed into the cellular contours.
2. Approximation of the digitised curves on the plane
Finding the MNBIC on the rectangular grid can be useful as the alternative method for an approximation of explicit and implicit functions where their discrete values are at disposal. In such cases the rectangular grid basis at first should be taken into the consideration. Where the discrete values of functions are at disposal, the horisontal ( Dx ) grid side is recommended to be equal to the equidistant step for arguments.
3. Data compression techniques
MNBIC technique can be stright forwardly used for data compression and storing the big volumes of data for digitised figures , particularly their countours. The advantage is the inclusion of fault tollerance norm ( see below Dx and Dy role)
4. Relation to the Linear optimization calculation
Without going to the theory or details of the linear optimization methods let me consider this example ( not necessarily simple ):
The task is to design the MNBIC inside the rectangular cellular contours of the digitized figure( contours represented by the inner and outer border ). Besides the minimal length for the output polygonal line we require that MNBIC passes through any contour cell or at least one point of contour cell.
Furthermore we have two rolls of tapes in stock , in blue and red color . Blue tape will be used for the MNBIC edges where at least one vertex belongs to the inner grid border , red tape will be used for the MNBIC edges where both vertices belong to the outer grid border and only to outer grid border. The sequence of the adjacent edges in the MNBIC will not be cut but unrolled en block if the same color is assigned to the edges.
Some questions like below can arise:
a: What is the shortest length of the sum of tapes inscribed into the cellular contour of the figure ?
b : What are the longest tapes for each color ?
c: If overlapped edges in the MNBIC exist – how much length we can spare by excluding double counting for overlapped parts ?