A strong chord property for 4-connected convex digital sets
Computer Vision, Graphics, and Image Processing
On the Number of Digital Straight Line Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
The Number of N-Point Digital Discs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Straight Line Segments
IEEE Transactions on Computers
Convex functions on discrete sets
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
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We determine the number of Khalimsky-continuous functions defined on an interval, having two fixed endpoints, and with values in Z, in N, or in a bounded interval. The number of Khalimsky-continuous functions with two points in their codomain gives an example of the Fibonacci sequence. A recurrence formula shall be presented to determine the number of Khalimsky-continuous functions with the values in a bounded interval. Using a generating function leads us to determine the number of increasing Khalimsky-continuous functions. Considering N as a codomain of these functions yields a new example of the classical Fibonacci sequence.