Steven B. Damelin, David L. Ragozin, Michael Werman
We study a realization of motion and similarity group equivalence classes of $n\geq 1$ labeled points in $\mathbb R^k,\, k\geq 1$ as a metric space with a computable metric. Our study is motivated by applications in computer vision.
Steven B. Damelin, David L. Ragozin, Michael Werman
We study Min-Max affine approximants of a continuous convex or concave function $f:Δ\subset \mathbb R^k\xrightarrow{} \mathbb R$ where $Δ$ is a convex compact subset of $\mathbb R^k$. In the case when $Δ$ is a simplex we prove that there is a vertical translate of the supporting hyperplane in $\mathbb R^{k+1}$ of the graph of $f$ at the vertices which is the unique best affine approximant to $f$ on $Δ$. For $k=1$, this result provides an extension of the Chebyshev equioscillation theorem for linear approximants. Our result has interesting connections to the computer graphics problem of rapid rendering of projective transformations.