Endoscopy and Computer Vision
EnCoV is a research group located at the Faculty of Medicine in Clermont-Ferrand.
It is part of the Image-Guided Therapies research axis of Institut Pascal, a joint venture between CNRS, Université Clermont Auvergne and SIGMA.
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We do research in computer vision, endoscopy and computer-aided endoscopy.
Below is a list of subjects and open problems.
Find the point pairs aligned with some direction where the tangent slopes of two conics match
Imagine that we have two conics \(A\) and \(B\) represented by their \(3\times3\) homogeneous symmetric matrices and a direction \(d\) represented by a \(2\times1\) homogeneous vector.
The question we ask here is for which point pairs \(q,p\), each represented by a \(3\times1\) homogeneous vectors, on \(A,B\) respectively and forming a line with direction \(d\), do the slope of the tangents to \(A\) and \(B\) at \(p\) and \(q\) respectively match?
An easier question to start is to determine how many such point pairs exist in the complex Euclidean plane and then in the real Euclidean plane.
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