# 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.

### Geometry

#### 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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