International Journal of Computer Vision, 321-331 (1988) o 1987 KIuwer Academic Publishers, Boston,...

International Journal of Computer Vision, 321-331 (1988)o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands

Snakes: Active Contour Models

Active Contour Models

Speak by

Lingfeng Mo



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.

Introduction



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.



Energy minimizing model

Former: have a rich history but regarded as autonomous

Now: developed interactive techniques for guidding them



Main Work: finding salient image contours-edges, lines, and subjective contours-as well as tracking thosecontours 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.



Fig.1 Lower-left: original wood pgotograph from Brodatz.Others: Three different local minima for the active contour model.



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.



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.



Representing the position of a snake parametricallyby v(s) = (x(s), y(s)), we can write its energyfunctional as



2.1 Internal Energy

The internal spline energy can be written



Snake Pit: Specify the particular image feature in a certain picture.



Image Forces

1. Line Functioan

2. Edge Function

3. Termination Funciont



Line Function

PS: Used in Fig. 2



Edge Function

snake is attracted to contours with large image gradients.



Add his energy term to snake means that it is attracted to zero-crossings but still constrained by its own smoothness.

Scale Space Continuation

How to deal with a picture with very blurry energy functional and reduce the blurring?



Termination Function

Use the curvature of level lines in a slightly smoothed mage to find terminations of line segments and corners.



Combining E-edge and E-term, can creat a snake that is attracted to edges or terminations.



snakes are constantly minimizing their energy, they can exhibit hysteresis when shown moving stimuli. Figure 6 shows a snake tracking a movingsubjective contour.



StereoSnakes 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.



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:



Motion

Shows the “Lock on” function of the snakes



Pros:1. Prove that snakes is useful for interactive speciticationof image contours. 2. Scale-space continuation greatly enlarge the capture region

around features of interest.3. The snake model provides a unified treatmentto a collection of visual problems that have beentreated 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.



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,...

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