International Journal of Computer Vision, (1988) o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands Snakes: Active Contour Models Active Contour Models Speak by Lingfeng Mo

International Journal of Computer Vision, (1988) o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands Snakes: Active Contour Models 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

International Journal of Computer Vision, (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, (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, (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, (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, (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, (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, (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, (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, (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, (1988) o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands Snakes: Active Contour Models Image Forces 1.Line Functioan 2.Edge Function 3.Termination Funciont

International Journal of Computer Vision, (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, (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, (1988) o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands Snakes: Active Contour Models

International Journal of Computer Vision, (1988) o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands Snakes: Active Contour Models 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?

International Journal of Computer Vision, (1988) o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands Snakes: Active Contour Models

International Journal of Computer Vision, (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, (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, (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, (1988) o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands Snakes: Active Contour Models

International Journal of Computer Vision, (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, (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, (1988) o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands Snakes: Active Contour Models

International Journal of Computer Vision, (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, (1988) o 1987 KIuwer Academic Publishers, Boston, Manufactured in The Netherlands Snakes: Active Contour Models

International Journal of Computer Vision, (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, (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.