Deformation contours are divided into active contours and dynamic contours.
1. Active Contours: Snake is a morphing 2D de-counter that produces morphing motions under the influence of image forces.
·The image force is divided into internal force and external force. The internal force plays the role of smooth restriction, and the external force guides it to move toward the image feature.
Application areas: 1) Still image processing, which can be used for edge detection, region segmentation, and contour extraction
(2) Sequence image processing, tracking human lip movements, and tracking closed contour lines of 3D objects. Snake is suitable for tracking deformation motion of non-rigid objects.
(3) Medical image processing,
(4) 3D target reconstruction
Disadvantages: Sensitive to the initialization position, it should be placed near the target of interest; the model is sensitive to the parameter settings in its own energy function; it is easy to fall into the local minimization process and converge to the wrong position.
2. Dynamic contour line: It is a special deformation contour line. Two expressions: discrete points and B-splines.
3.B-spline dynamic contour:
1. Due to the shortcomings of the Bezier curve, in order to overcome the shortcomings, the Bezier polynomial is replaced with a B-spline curve.
2. Disadvantages of Beizer: (1) The number of feature polygon vertices determines the order of the curve, which is inflexible.
(2) There is no possibility of local modification
3.B-spline function:
(1). The spline function x(s) is expressed as the weighted sum of the B-spline basis functions Bn(s) (n=0,...,q-1). In the simplest case, each B-spline basis function consists of a polynomial of order d defined over a span on the S axis, and the curve has continuous derivatives of order d-2. Analytical formula: 
In general, the construction of B-spline basis functions satisfies the following conditions: 
Under the simplest B-spline premise with uniform distribution of nodes, the first B-spline basis function is 
(2). Normal form and inner product of B-spline functions
(3) B-style parameter curve
(4) The area and centroid of the closed B-spline curve: obtained by the method of matrix: set the control point vector of the closed B-spline curve as Q = (q1, q2,...qN), qi = (xi ,yi)T,N is the number of control points. The formula for calculating the hungry area of a closed quadratic uniform B-spline curve is as follows: (Because the blogger was too lazy to type, a screenshot was taken)
The corresponding centroid calculation formula: 
4. The advantages of B-spline curve: (1) It has local support. When a certain control point changes, it only affects the shape of the relevant part of the curve. (2) It has convex hull, the B-spline curve completely falls within the convex hull composed of the control point sequence, (3) the B-spline basis function with multiple nodes can control the continuity to the present node, (it can be expressed as corner information)
5. Dynamic contour line convergence: In order to make the dynamic contour line converge from the initial position to the target contour edge. Three steps are required:
(1) Apply the feature search in the normal direction and the LOG operator to obtain the corresponding feature points and feature curves (the feature curves are formed after the discrete feature points are connected)
(2) Apply B-spline curve fitting* (reverse B-spline curve control point vector) to get P
(3) Use an iterative algorithm to make the dynamic contour line converge towards P. Two kinds of iterative distributions based on Newmark method and Wilson 