  This paper proposes a segmentation-free, automatic and efficient procedure to
detect general geometric quadric forms in point clouds, where clutter and
occlusions are inevitable. Our everyday world is dominated by man-made objects
which are designed using 3D primitives (such as planes, cones, spheres,
cylinders, etc.). These objects are also omnipresent in industrial
environments. This gives rise to the possibility of abstracting 3D scenes
through primitives, thereby positions these geometric forms as an integral part
of perception and high level 3D scene understanding.
  As opposed to state-of-the-art, where a tailored algorithm treats each
primitive type separately, we propose to encapsulate all types in a single
robust detection procedure. At the center of our approach lies a closed form 3D
quadric fit, operating in both primal & dual spaces and requiring as low as 4
oriented-points. Around this fit, we design a novel, local null-space voting
strategy to reduce the 4-point case to 3. Voting is coupled with the famous
RANSAC and makes our algorithm orders of magnitude faster than its conventional
counterparts. This is the first method capable of performing a generic
cross-type multi-object primitive detection in difficult scenes. Results on
synthetic and real datasets support the validity of our method.
