We present a geometric model and a computational method for
segmentation of images with missing boundaries.
In many situations, the human
visual system fills in missing gaps in edges and boundaries,
building and completing information that is not present.
These situations have been widely studied by Gestalt psycologists both
in the case of modal and amodal completion.
Boundary completion presents a considerable challenge in computer
vision, since most algorithms attempt to exploit existing
A large body of work concerns completion models, which postulate how to
construct missing data; these models are often trained and specific to
particular images. In this paper, we take the following,
alternative perspective: we consider
a reference point within an image as given, and then develop an
algorithm which tries to build missing information on the basis of the
given point of view and the available information as
boundary data to the algorithm. Starting from the point of view,
a surface is constructed. Then it is
evolved with the mean curvature flow
in the metric induced by the image until a piecewise constant
We test the computational model to modal completion,
amodal completion, texture, photo and medical images.
We extend the geometric model and the algorithm to 3D in order to
extract shapes from low signal/noise ratio medical volumes. Results
in 3D echocardiograpghy and 3D fetal echography are presented.