Here are four fields of interest where the solution could be exploited.
 

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 an invariant on rotation. Besides the unique value of the length as the shortest length inscribed into the cellular contours I suppose that the number of vertices linked to this length for MPP or MNBIC having the origin in the inner and outer countours is also minimal.
However, it is worth of mentioning, that there can be more than one representation of the MPP or MNBIC for a given figure but each of them must have the same length and number of vertices. Otherwise some of the variants should not be entitled for MPP or MNBIC qualification when we estimate the final result of the calculation. Further we will operate with the MNBIC term and everything for MNBIC will be valid also for MPP.

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2. Approximation of the digitised curves on the plane

Finding the MNBIC on 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 equidistant step for arguments.
In fact, the MNBIC technique can be applied to wide spectrum of figures regardless of they are or not are expressed in an analytical form.

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3. Data compression techniques
MNBIC technique can be strightforwardly 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).

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4. Relation to 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 boundary of the digitized figure (contours).
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 edges in MNBIC can be shared (not to confuse with the input contours where it is not possible). In such cases no double tapes of the overlapped part are needed.

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Some questions like below can arise:
a: What is the shortest length of the sum of tapes inscribed into the cellular countour 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?