Snakes: Active Contour Models
Active Contour Models
Speak by
Lingfeng Mo
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
Introduction
Snakes( energy-minimizing systems):
1. is an energy-minimizing spline guided by external
constraint forces and influenced by image forces that
pull it toward features such as lines and edges.
2. Snakes are active contour models: they lock onto
nearby edges, localizing them accurately.
3. The way the contours slither while minimizing their
energy, hence the name.
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
What can snakes do?
1. Former: detection of edges, lines, and subjective
contours; motion tracking; and stereo matching.
2. Now: interactive interpretation, in which user-imposed
constraint forces guide the snake near features of interest.
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
Energy minimizing model
Former: have a rich history but regarded as autonomous
Now: developed interactive techniques for guidding them
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
Main Work: finding salient image contours-edges,
lines, and subjective contours-as well as tracking those
contours during motion and matching them in stereopsis.
Traditional way: detect edges and linking them
Now: use high level computation, and high-level
mechanisms can interact with the contour model by
pushing it toward an appropriate local minimum.
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
Fig.1 Lower-left: original wood pgotograph from Brodatz.
Others: Three different local minima for the active contour
model.
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
How good can snakes do?
1. Can not finding entire salient image contours but rely
on other mechanisms to place them near the desired
contour.
2. Once snakes were placed close to an intended contour,
its energy minimization will take care of the rest of the
way.
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
Some terms:
1. Internal spline forces: impose a piecewise
smoothness constraint.
2. Image forces: push the snake toward salient image
features, such as lines, edges, and subjective
contours.
3. External constraint forces: putting the snake near
the desired local minimum. Can be user interface,
automatic attentional mechanisms or high-level
interpretations.
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
Representing the position of a snake parametrically
by v(s) = (x(s), y(s)), we can write its energy
functional as
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
2.1 Internal Energy
The internal spline energy can be written
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
Snake Pit: Specify the particular image
feature in a certain picture.
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
1. Line Functioan
Image Forces
2. Edge Function
3. Termination Funciont
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
Line Function
PS: Used in Fig. 2
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
Edge Function
snake is attracted to contours with large
image gradients.
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
Scale Space Continuation
How to deal with a picture with very blurry energy functional
and reduce the blurring?
Add his energy term to snake means that it is attracted to
zero-crossings but still constrained by its own smoothness.
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
Termination Function
Use the curvature of level lines in a slightly smoothed mage
to find terminations of line segments and corners.
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
Combining E-edge and E-term, can creat a snake
that is attracted to edges or terminations.
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
snakes are constantly minimizing their energy, they
can exhibit hysteresis when shown moving
stimuli. Figure 6 shows a snake tracking a
moving
subjective contour.
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
Stereo
Snakes can also be applied to the problem of stereo
matching. In stereo, if two contours correspond,
then the disparity should vary slowly along the contour
unless the contour rapidly recedes in depth.
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
Psychophysical evidence [4] of a disparity gradient limit in
human stereopsis.
human visual system do not change too rapidly with space.
This disparities constraint can be expressed in an
additional energy functional for a stereo snake:
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
Motion
Shows the “Lock on” function of the snakes
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
Pros:
1. Prove that snakes is useful for interactive specitication
of image contours.
2. Scale-space continuation greatly enlarge the capture region
around features of interest.
3. The snake model provides a unified treatment
to a collection of visual problems that have been
treated differently in the past.
4. The snake provides a number of widely separated local minima
to further levels of processing. Instead of committing
irrevocably to a single interpretation, snakes can change their
interpretation based on additional evidence from higher
levels of processing.
1.
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands
Snakes: Active Contour Models
Cons:
1. Lack of some background about the research in the past
in detail
2. Omit the important function step for introducing the
function.
3. Many grammar mistakes are not hard to find. Such as the
adjective and noun. Sometimes made me confused.
International Journal of Computer Vision, 321-331 (1988)
o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands