Statistical model

• US 20050027492A1
• Filed: 12/06/2001
• Published: 02/03/2005
• Est. Priority Date: 06/12/2001
• Status: Active Grant

• Current Assignee: MAKO Surgical Corporation (Stryker Corporation)
• Original Assignee: Imorphics Limited (Stryker Corporation)
• Inventors: Davies, Rhodi, Taylor, Christopher J., Twining, Carole, Cootes, Timothy F.
• Granted Patent: US 7,584,080 B2
• Time in Patent Office: Days
• US Class Current: 703/2
• CPC Class Codes: G06F 18/28 Determining representative reference patterns, e.g. by averaging or distorting; Generating dictionaries
• CPC Class Codes: G06V 10/46 Descriptors for shape, contour or point-related descriptors, e.g. scale invariant feature transform [SIFT] or bags of words [BoW]; Salient regional features colour feature extraction G06V10/56
• CPC Class Codes: G06V 10/471 using approximation functions
• CPC Class Codes: G06V 10/76 based on eigen-space representations, e.g. from pose or different illumination conditions; Shape manifolds
• CPC Class Codes: G06V 10/772 Determining representative reference patterns, e.g. averaging or distorting patterns; Generating dictionaries

Abstract

A method of building a statistical shape model by automatically establishing correspondence between a set of two dimensional shapes or three dimensional shapes, the method comprising: a) determining a parameterisation of each shape, building a statistical shape model using the parameterisation, using an objective function to provide an output which indicates the quality of the statistical shape model; performing step a) repeatedly for different parameterisations and comparing the quality of the resulting statistical shape models using output of the objective function to determine which parameterisation provides the statistical shape model having the best quality, wherein the output of the objective function is a measure of the quantity of information required to code the set of shapes using the statistical shape model.

Claims

1. A method of building a statistical shape model by automatically establishing correspondence between a set of two dimensional shapes or three dimensional shapes, the method comprising:

a. determining a parameterisation of each shape, building a statistical shape model using the parameterisation, using an objective function to provide an output which indicates the quality of the statistical shape model,

b. performing step a repeatedly for different parameterisations and comparing the quality of the resulting statistical shape models using output of the objective function to determine which parameterisation provides the statistical shape model having the best quality, wherein the output of the objective function is a measure of the quantity of information required to code the set of shapes using the statistical shape model.

2. A method according to claim 1, wherein the parameterisation used to perform step a are selected using an optimization method based upon previous parameterisations and the quality of the statistical shape models generated using those parameterisations as indicated by the output of the objective function.

3. A method according to claim 2, wherein the output of the objective function comprises a value indicative of the amount of information required to code parameters of the model, and a value indicative of the information required to code residuals for the set of shapes.

4. A method according to claim 3, wherein the output of the objective function further comprises a value indicative of the amount of information required to code mapping between parameters and the shapes.

5. A method according to claim 4 wherein for a given parameterisation the objective function provides a single scalar output.

6. A method according to claim 5 wherein the single scalar output comprises a combination of the value indicative of the amount of information required to code parameters of the model, the value indicative of the information required to code residuals for the set of shapes, and the value indicative of the amount of information required to code mapping between parameters and the shapes.

7. A method according to claim 4, wherein the mapping comprises a mean vector and a covariance matrix.

8. A method according to claim 3 wherein the parameters of the model are parameter vectors, and the average amount of information per parameter vector is determined and multiplied by the number of shapes in the training set, to provide the value indicative of the amount of information required to code parameters of the model.

9. A method according to claim 3 wherein the residuals are residual vectors, and the average amount of information per residual vector is determined and multiplied by the number of shapes in the training set, to provide the value indicative of the information required to code residuals for the complete set of training shapes.

10. A method according to claim 9, wherein the number of residuals in each residual vector is twice the number of parameterisations used to generate the model.

11. A method according to claim 1, wherein the number of modes of variation of the model is selected to represent the training set to a given accuracy.

12. A method according to claim 1, wherein the boundary of each two-dimensional shape of the training set is recursively subdivided by inserting landmarks the parameterisation of the boundary being represented by the position of each landmark as a fraction of boundary path length between preceding and following landmarks.

13. A method according to claim 12, wherein the parameterisation which provides the best optimisation value is determined using a stochastic optimisation method.

14. A method according to claim 1 wherein a set of curves is used to determine a parameterisation function for the training set.

15. A method according to claim 14, wherein the set of curves is a cumulative density function.

16. A method according to claim 15, wherein the cumulative density function comprises a sum of kernel curves.

17. A method according to claim 16, wherein the cumulative density function is determined by combining increasing numbers of kernel curves to provide increasing resolution levels, and the parameterisation function which provides the statistical shape model of the best quality is determined using the output of the objective function for each resolution level.

18. A method according to claim 16, wherein the kernel curves are Gaussian functions.

19. A method according to claim 16 wherein the kernel curves are Cauchy functions.

20. A method according to claim 16 wherein the kernel curves are two dimensional curves.

21. A method according to claim 16 wherein the kernel curves are three dimensional curves.

22. A method according to claim 1 wherein the boundary of each shape of the training set is parameterised by specifying a set of control landmarks used to determine a parameterisation function.

23. A method according to claim 22, wherein the parameterisation function is determined for increasing numbers of control landmarks to provide increasing resolution levels, and the parameterisation function which provides the statistical shape model of the best quality is determined using the output of the objective function for each resolution level.

24. A method according to claim 22 wherein equally spaced landmarks are provided between the control landmarks.

25. A method according to claim 1, wherein the shape and grey-level appearance are both included in model.

26. A method of parameterising a set of three dimensional shapes, the method comprising:

a. mapping each three dimensional shape to a simple canonical form of an appropriate topology,

b. applying a set of landmarks to the simple form for a given level of resolution, each landmark being constrained to lie inside a spherical triangle formed by a triple of landmark points of a lower resolution level,

c. upon the completion of the application of the set of landmarks for the resolution level, projecting the set of landmarks onto the three dimensional shapes,

d. building a statistical shape model using the set of landmarks of the resolution level,

e. using an objective function to provide an output which indicates the quality of the statistical shape model determined using the set of landmarks of the resolution level,

f. comparing the output with output determined using a different set of landmarks having the same level of resolution, and

g. repeating steps a to f to determine which set of landmarks which provides the best quality of statistical shape model,

h. repeating steps a to g at a higher level of resolution.

27. A method of parameterising a set of three dimensional shapes, the method comprising:

a. mapping each three dimensional shape to simple canonical form of an appropriate topology,

b. applying a set of landmarks to the simple form,

c. modifying the locations of the landmarks by applying a transformation,

d. projecting the set of landmarks onto the three dimensional shapes,

e. building a statistical shape model using the set of landmarks,

f. using an objective function to provide an output which indicates the quality of the statistical shape model determined using the set of landmarks,

g. comparing the output with output determined using landmarks having different locations, and

h. repeating steps c to g to determine which set of landmarks which provides the best quality of statistical shape model.

28. A method according to claim 27, wherein the transformation comprises for a selected landmark pushing other landmarks away from the selected landmark along the surface of the simple form, or pulling other landmarks towards the selected landmark along the surface of the simple form.

29. A method according to claim 28, wherein the transformation is defined by a wrapped kernel.

30. A method according to claim 29, wherein the wrapped kernel is a warpped Cauchy distribution.

31. A method according to claim 29, wherein the wrapped kernel is a wrapped Gaussian distribution.

32. A method according to claim 28 wherein the simple form is a sphere or a torus.