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• W2093933910 abstract "A finite image I is a function assigning colors to a finite, rectangular array of discrete pixels. Thus, the information directly encoded by I is purely locational. Such locational information is of little visual use in itself: perception of visual structure requires extraction of relational image information. A very elementary form of relational information about I is provided by its dipole histogram DI. A dipole is a triple, ((dx, dy), α, β), with dx and dy horizontal and vertical, integer-valued displacements, and α and β colors. For any such dipole, DI((dx, dy), α, β) gives the number of pixel pairs ((x1, y1), (x2, y2)) of I such that I[x1, y1]=α, I[x2, y2]=β, and, (x2, y2)−(x1, y1)=(dx, dy). Note that DI explicitly encodes no locational information. Although DI is uniquely determined by (and easily constructed from) I, it is not obvious that I is uniquely determined by DI. Here we prove that any finite image I is uniquely determined by its dipole histogram, DI. Two proofs are given; both are constructive, i.e. provide algorithms for reconstructing I from DI. In addition, a proof is given that any finite, two-dimensional image I can be constructed using only the shorter dipoles of I: those dipoles ((dx, dy), α, β) that have ∣dx∣≤ceil((#columns in I)/2) and ∣dy∣≤ceil((#rows in I)/2), where ceil(x) denotes the greatest integer ≤x." @default.
• W2093933910 created "2016-06-24" @default.
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• W2093933910 date "2000-03-01" @default.
• W2093933910 modified "2023-09-27" @default.
• W2093933910 title "Every discrete, finite image is uniquely determined by its dipole histogram" @default.
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• W2093933910 doi "https://doi.org/10.1016/s0042-6989(99)00191-1" @default.
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