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# 3D-2D projective registration of free-form curves and surfaces

1 EPIDAURE - Medical imaging and robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Some medical interventions require knowing the correspondence between an MRI/CT image and the actual position of the patient. Examples occur in neurosurgery and radiotherapy, but also in video surgery (laparoscopy). We present in this paper three new techniques for performing this task without artificial markers. To do this, we find the \bf 3D-2D projective transformation (composition of a rigid displacement and a perspective projection) which maps a 3D object onto a 2D image of this object. Depending on the object model (curve or surface), and on the 2D image acquisition system (X-Ray, video), the techniques are different but \bf the framework is common: \beginitemize \item We first find an estimate of the transformation using bitangent lines or bitangent planes. These are first order semi-differential invariants \citeMundy. \item Then, introducing the normal or tangent, we define a distance between the 3D object and the 2D image, and we minimize it using extensions of the Iterative Closest Point algorithm (\citeBesl,Zhang). \item We deal with the critical problem of outliers by computing Mahalanobis distances and performing generalized $\chi^2$ tests. \enditemize Results are presented on a variety of real medical data to demonstrate the validity of our approach.
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https://hal.inria.fr/inria-00074241
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Submitted on : Wednesday, May 24, 2006 - 2:50:44 PM
Last modification on : Friday, February 4, 2022 - 3:15:43 AM
Long-term archiving on: : Tuesday, April 12, 2011 - 4:16:38 PM

### Identifiers

• HAL Id : inria-00074241, version 1

### Citation

Jacques Feldmar, Nicholas Ayache, Fabienne Betting. 3D-2D projective registration of free-form curves and surfaces. RR-2434, INRIA. 1994. ⟨inria-00074241⟩

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