Snakes : Active Contour modelsMichael Kass, Andrew Witkin and

Demetri Terzopoulos

Presentation : Bhargava Kamarapu

Agenda• Abstract• Introduction• Areas Incorporated• Basic Snake Behavior• Snake Energy• Snake Pit• Image Forces• Subjective Contour• Scale Space• Applications• Stereo and Motion• Conclusion• Bibliography

Abstract

• An energy minimizing spline guided by external constraint forces and pulled by image forces toward features:• Edge detection• Line detection• Subjective contours• Motion tracking• Stereo matching

• They lock onto nearby edges to localize them accurately.• Scale-space continuation used to enlarge the capture

region.

Introduction

• The goal of this work is to find salient image contours, edges, lines and subjective contours as well as tracking those contours during motion and matching them in case of stereopsis.

• In this paper the use of energy minimization is investigated as framework in order to realize this goal.

• The variational approach that is used in this paper differs the traditional approach of detecting edges and then linking them.

• In this model, issues such as connectivity of the contours and the presence of corners affect the energy functional and the detailed structure of the locally optimum contour.

• The way the contours slither while minimizing their energy, we call them snakes.

Areas Incorporated• It deals with physics, geometry and approximation theory

are the three different areas and finally gives the exact place, position and size of objects.

Lower-left: Original wood photograph and three different local minima for the Active Contour Model

Basic Snake Behavior• A snake falls into the desired closest local energy

minimum.• The local energy of the snake energy comprises the set of

alternative solutions.• A higher level knowledge is needed to choose the correct one from

these solutions• High-level reasoning• User Interaction

• These high-level methods can interact with the contour model by pushing it toward an appropriate local minimum.

Snake Behavior

• They rely on other mechanisms to place them near the desired contour.• The existence of such an initializer is application independent.• Even in the case of manual initialization, snakes are quite powerful

in refining user’s input.

• Basically, snakes are trying to match a deformable model to an image by means of energy minimization.

Snake Energy

• Parametric representation: v(s) = (x(s), y(s))

• E-internal = internal energy due to bending. Serves to impose smoothness constraint.

• E-image = image forces pushing the snake toward image features (lines, edges, etc)

• E-con = external constraints are responsible for putting the snake near the desired local minimum. It may come from:

• Higher level interpretation• User interaction

Internal Energy

• The snake is a controlled continuity spline.• Regularizes the problem.

• The first order derivative makes the spline act like a membrane i.e. elasticity.

• The second order derivative makes the spline act like a thin plate i.e. rigidity.

• and ) controls the relative importance of membrane and thin-plate terms.

• Setting ) = 0 for a point allows the snake to become second order discontinuous and develop a corner.

Snake Pit• A graphical user interface which allows a user to select

starting points (springs) and exert forces on snakes interactively to minimize their energy.

• Energy minimization is gained by pushing a snake near to particular image feature.

• Volcano is very useful for pushing a snake out of one local minimum and into another.

The Snake Pit user-interface. Snakes are shown in black, springs and the volcano are in white.

Image Forces

• Attracts the snake to features such as

• Lines: the simplest functional is the image intensity.• Depending on the sign of , the snake will be attracted either to

the light or dark nearby contour.

• Edges: one can simply set.• attracts the snake to large intensity gradients.

• Terminations: Attracts the snake toward termination of line segments and corners.

.

Subjective Contour• Combining E-edge and E-term, we can create a snake

attracted to edges and terminations.• The shape of the snake between the edges and lines in the

illusion is completely determined by the spline smoothness term.

• The same snake can find traditional edges in natural images.

Scale Convergence

• If part of a snake finds a low-energy image feature, the spline term will pull neighboring parts of the snake toward a possible continuation of the feature.

• This effectively places a large energy well around a good local minimum.

Scale Space• Minimization by scale continuation is achieved by-

• Spatial smoothing the edge or line functional.• Snake comes to equilibrium on a blurry energy.• Slowly reduce the blurring

Subjective Contour: hystheresis• Snake tracking a moving subjective contour.• The snake bends until the internal spline forces overcome

image forces.• Then the snake falls off the line and returns to a smoother

shape.

Applications of Snakes

• 2D Image Segmentation : Medical Imaging Segmentation• 3D Image Segmentation : Volume Image Segmentation.

Either segment 2D images and then using active contour models and then connect them. Or 3D snakes are used for extracting 3D objects.

• Matching : consists of two different tasks labeling and registration. Labeling is the matching process between regions in the image and a priori models. Registration is the matching process between two volumes in different 3D images.

• Stereo• Motion, Tracking : 3D deformable models have been used

for measuring the dynamic behavior of the heart.

Stereo

• Psychological Evidence : During the process of localizing a contour on one eye, information about the corresponding contour in the other eye is used.

• Where is left snake contour and is right snake contour.

Motion Tracking• Once a snake finds a feature it “locks on”.• If the feature begins to move, the snake will track the same

local minimum.• Fast motion could cause the snake to flip into a different

minimum.Selected frames from a 2-second video sequence showing snakes used for motion tracking. After being initialized to the speaker’s lips in the first frame, the snakes automatically track the lip movements with high accuracy.

Conclusion

• The minimization of the energy function is too sensitive to the initial seed of the snake. This means that if the initial radius of the snake is small then boundary of object will not be effectively captured.

• The important weights of the internal and external forces, in the energy objective function affect snake performance. There is a fine tuning process that is required such that the results to be acceptable.

• The number of pixels that snake contains plays a critical role in the minimization process. If the number of pixels is small the snake will not be able to capture the boundaries of the regions of our interest.

Bibliography• http://www-static.cc.gatech.edu/classes/cs7322_97_spring/participants/ir

fan/lectures/lecture.06/snakes.html• http://www.cogs.susx.ac.uk/users/davidy/teachvision/vision7.html• http://72.14.203.104/search?q=cache:spJTNrEiyooJ:www.soe.ucsc.edu/

classes/ee264/Winter02/amyn.ppt+Snakes+active+contour+models+internal+energy&hl=en&gl=us&ct=clnk&cd=7

• http://www• static.cc.gatech.edu/classes/cs7322_97_spring/participants/Sumner/

discussions/snakes.html• http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/

MARBLE/medium/snakes/snakes.htm• http://www.icaen.uiowa.edu/~dip/LECTURE/Understanding2.html• http://www.vision.caltech.edu/mweber/research/CNS248/node17.html• http://72.14.203.104/search?q=cache:3H_qo4zmr0kJ:www-

users.itlabs.umn.edu/classes/Spring-2005/csci8980-2/presentations/vaggelis.ppt+Snakes+active+contour+models+matrix&hl=en&gl=us&ct=clnk&cd=6&lr=lang_en