Addendum circle extraction algorithm for tooth-shaped structure assembly
A technology of addendum circle and tooth shape, applied in the field of addendum circle extraction algorithm, to achieve the effect of improving accuracy and robustness, eliminating statistical deviation, and improving measurement accuracy
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Embodiment 1
[0094] S1 Tooth structure tooth top angle point extraction:
[0095] Parameterize the curve with arc length u as:
[0096] Γ(u)=(x(u),y(u))
[0097] With different scales, the curve can change to
[0098] Γ(u)=(X(u,ν),Y(u,ν))
[0099] In the formula: The Gaussian convolution kernel Gaussian(u, ν) with a scale factor ν is used to filter the noise in the curve and smooth the curve at the same time; x, y are the horizontal and vertical coordinates of the points on the curve in the pixel coordinate system. Then the curvature can be expressed as
[0100]
[0101] The curvature of each curve is calculated by the above formula, and the point where the local maximum of the absolute value of the curvature is located is the candidate corner point. The steps of the improved algorithm based on CSS addendum corner detection are as follows:
[0102] a1: Carry out Canny edge detection with an adaptive threshold on the input image Image_input to obtain the edge image Canny_edge;
...
Embodiment 2
[0110] Sub-pixel positioning of S2 addendum corners:
[0111] The basic unit of an image is a pixel, and the accuracy of extracting the corner point of the tooth tip using the improved CSS corner detection algorithm is 1 pixel. However, the real coordinates of the corner point of the tooth tip are not integers, and the coordinates in Corner_Point deviate from the real coordinates, which is To ensure the fitting accuracy of the addendum circle, the sub-pixel technology is used to accurately locate the addendum corner points.
[0112] Use the quadratic polynomial to approximate the corner response function R(x,y) to obtain the sub-pixel corner coordinates. The quadratic polynomial is
[0113] R(x,y)=a+bx+cy+dx 2 +exy+fy 2 ;
[0114] Traverse the corner points in Corner_Point (x i ,y i ) neighborhood of 9 pixels, establish an overdetermined equation system containing a total of 6 coefficients a ~ f, use the least square method to solve the unknown, and derive the above formu...
Embodiment 3
[0120] S3 super least square method to fit the addendum ellipse:
[0121] When the tooth tip surface is not parallel to the image plane, the addendum circle is imaged as an ellipse, and the addendum corner point in Corner_Point is used to fit the addendum ellipse to obtain the addendum circle parameters.
[0122] The parametric equation of the ellipse is:
[0123] Ax 2 +2Bxy+Cy 2 +2f 0 (Dx+Ey)+f 0 2 F=0
[0124] Where: f 0 is a constant of proportionality. The least square method makes the ellipse and Corner_Point (x i ,y i ), the algebraic distance J of i=1~N is the smallest and A=...=F≠0.
[0125] definition
[0126] Will (x i ,y i ) into ξ to get the vector ξ i , then the elliptic parametric equation and algebraic distance can be expressed as (ξ,θ)=0 and
[0127]
[0128] In order to avoid θ = 0, scale normalize θ (θ, Zθ) = c, where Z is a symmetric matrix, and c is a non-zero constant. This problem evolves into the solution Mθ = λZθ of generalized eigenva...
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