Many computer vision papers tend to apply signal processing techniques
rather than discrete geometry, to be very heuristic,
or to simply describe coordinate systems or other geometric modelling tools.
However there has been some work in the computational geometry
community on exact solution of geometric pattern matching problems
associated with vision, for instance by Dan Huttenlocher's group at Cornell.
Several vision projects use Voronoi diagrams
to represent the structure of the image under study.
- 3d shape and surface matching. Elias Kalaitzis of Edinburgh
uses 3d Voronoi diagrams in an iterated parallel procedure for
approximating a geometric transformation aligning a pair of shapes.
- Computational Topology.
Survey paper by Dey, Edelsbrunner, and Guha, presented at the conference
"Computational Geometry -- Ten Years After". Includes descriptions of
applications in image processing, cartography, graphics, solid modeling,
mesh generation, and molecular modeling.
- Computer Vision home page (CMU).
- Detecting actin fibers in cell images.
A. E. Johnson and
R. E. Valdes-Perez use minimum spanning trees for biomedical image analysis.
- Extracting features from remotely sensed images. Mark Dobie and co-workers use minimum spanning trees to find road networks in satellite and aerial imagery.
- Geometry references for computer vision.
From Fleck and Stevenson's
Computer Vision Handbook.
- Hausdorff Distance Image Comparison,
Dan Huttenlocher, Cornell.
Processing and Pattern Recognition in Soil Structure. D. Luo of
Glasgow uses convex hulls and other geometric techniques to analyze
images of soil particles.
- Image tilings.
The PRISME group at INRIA proposes stitching together multiple images of
a scene (e.g. multiple aerial or satellite views of a piece of land)
using a form of Voronoi diagram to choose which image has the best quality
for each piece of scenery.
salient features for real-time face verification, K. Jonsson, J. Matas,
and J. Kittler. Includes a minimum-spanning-tree based algorithm
for registering the images in a database of faces.
axis pruning. Robert Ogniewicz of Harvard uses medial axes for
octree generation from rotating objects
R. Szeliski of DEC uses octrees in computer vision.
- SPIE Signal and Image Processing publication list
contains abstracts from several vision conferences with geometric
content, notably Vision Geometry
Geometric Methods in Computer Vision
Tuceryan's computational geometry research page describes an
Voronoi diagrams to finding neighbor relationships between image
tokens, and includes bibliographic references to related papers by
Tuceryan, Ahuja, and
Patent 4704694 uses convex hulls to recognize objects from video images.
Patent 5054098 describes a method of detecting whether a scanned
image has been turned at an angle from the original, using an algorithm
for finding minimum enclosing rectangles along with other techniques.
Patent 5483606 describes a method of registering (lining up) copied
pages with each other in a copying machine, using the convex hulls of
images of the pages.
- Using the
Voronoi Tessellation for Grouping Words and Multi-part Symbols in
Documents, M. Burge and G. Monagan.
- Yahoo directory of Computer Vision resources.
Geometry in Action,
a collection of applications of computational geometry.
from a common source file.