# Research

From a general point of view, I'm interested in everything that is
"visually appealing". But in facts, I'm especially doing stuff related
to Digital Geometry.
I've spent my PhD working on noisy digital objects. I've first
developed recognition algorithms for blurred pieces of digital planes
(BPDP). A digital plane is actually the set of integer solutions
(x,y,z) of a double inequality μ ≤ a.x + b.y + c.z < μ + ω,
where a, b, c, μ and ω are five integers,
(a,b,c) ≠ (0,0,0) and ω > 0.
(a,b,c) denotes the normal vector of the plane and ω its
arithmetical thickness. Blurred pieces of such a plane admit that some
points are missing in order to adapt to noisy discrete data.

I've then used this new digital primitive to extract geometric
features, such as normal vectors or a shape information (flat, hole,
bump), from the border of digital objects, and to decompose this border
into pieces of BPDP – a first step toward a polyhedrization
process for digital objects.

More recently, I've focused my attention on Digital Level Layers, an
approach investigated with Yan Gerard in order to define
non-linear digital primitives and explore their properties. We've
proposed recognition algorithms for such primitives as well as a way
to use them to estimate the k^{th} derivative of the
digitization of a continuous function.