Pre-morbid characterization of anatomical object using statistical shape modeling (SSM)
Techniques are described for determining a pre-morbid shape of an anatomical object. Processing circuitry may determine an aligned shape based on image data with under- or over-segmentation. The processing circuitry may utilize the aligned shape and a shape model such as a mean shape model of the anatomical object to register the aligned shape to the shape model and generate information indicative of the pre-morbid shape of the anatomical object.
1. A method for determining a pre-morbid shape of an anatomical object of an orthopedic joint of a patient, the method comprising:
determining respective medialization values for each of a plurality of estimated shape models, wherein the plurality of estimated shape models is generated from a first shape model, and wherein each of the medialization values is indicative of an amount by which each respective one of the estimated shape models is medialized relative to a current position of the anatomical object;
determining respective cost values for each of the plurality of estimated shape models based at least in part on the respective determined medialization values for each of the plurality of estimated shape models;
selecting an estimated shape model from the plurality of estimated shape models having a cost value of the respective cost values that satisfies a function for the cost value; and
generating information indicative of the pre-morbid shape of the anatomical object based on the selected estimated shape model.
2. The method of claim 1 , further comprising:
determining a shape based on the first shape model and an aligned shape generated from image data of the anatomical object; and
determining respective distance and orientation difference values for each of the plurality of estimated shape models, wherein each of the respective distance and orientation difference values is indicative of a difference in distance and orientation between respective estimated shape models and the determined shape,
wherein determining the respective cost values for each of the plurality of estimated shape models comprises determining the respective cost values for each of the plurality of estimated shape models based at least in part on the respective determined medialization values for each of the plurality of estimated shape models and the respective determined distance and orientation difference values.
3. The method of claim 2 , wherein determining the respective distance and orientation difference values for each of the plurality of estimated shape models comprises:
determining respective distances between corresponding points on respective estimated shape models and the determined shape;
determining respective angular differences between normal vectors for the corresponding points on respective estimated shape models and the determined shape; and
determining the respective distance and orientation difference values based on the determined respective distances and the determined respective angular differences.
4. The method of claim 1 , further comprising:
determining respective weighting values based on a likelihood of each of the respective estimated shape models being representative of the pre-morbid shape of the anatomical object,
wherein determining the respective cost values for each of the plurality of estimated shape models comprises determining the respective cost values for each of the plurality of estimated shape models based at least in part on the respective determined medialization values for each of the plurality of estimated shape models and the respective weighting values.
5. The method of claim 4 , wherein determining the respective weighting values comprises performing
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l
N
∑
j
i
λ
j
∑
j
N
λ
j
×
b
i
2
,
wherein N equals a number of modes used to build respective plurality of estimated shape models, wherein equals eigenvalues of the first shape model, and b equals a scaling factor used to determine respective plurality of estimated shape models.
6. The method of claim 1 , wherein determining respective medialization values for each of the plurality of estimated shape models comprises:
dividing image data of the anatomical object into a plurality of portions;
projecting points from each of the plurality of portions to a transverse axis;
determining a threshold point from one of the projected points;
determining a most lateral portion from the plurality of portion;
determining a portion in each of the plurality of estimated shape models that corresponds to the determined most lateral position;
projecting points from the determined portion in each of the plurality of estimated shape models to the transverse axis;
determining distances from the projected points to the threshold point; and
determining the respective medialization values for each of the plurality of estimated shape models based on the determined distances.
7. The method of claim 1 , wherein determining the respective medialization values for each of the plurality of estimated shape models comprises:
projecting points from the anatomical object to a transverse axis;
projecting respective points from each of the plurality of estimated shape models to the transverse axis; and
determining the respective medialization values for each of the plurality of estimated shape models based on the projected points from the anatomical object to the transverse axis and the respective projected points from each of the plurality of estimated shape models to the transverse axis.
8. A device for determining a pre-morbid shape of an anatomical object of an orthopedic joint of a patient, the device comprising:
a memory configured to store one or more of a first shape model and a plurality of estimated shape models; and
processing circuitry configured to:
determine respective medialization values for each of the plurality of estimated shape models, wherein the plurality of estimated shape models is generated from the first shape model, and wherein each of the medialization values is indicative of an amount by which each respective one of the estimated shape models is medialized relative to a current position of the anatomical object;
determine respective cost values for each of the plurality of estimated shape models based at least in part on the respective determined medialization values for each of the plurality of estimated shape models;
select an estimated shape model from the plurality of estimated shape models having a cost value of the respective cost values that satisfies a function for the cost value; and
generate information indicative of the pre-morbid shape of the anatomical object based on the selected estimated shape model.
9. The device of claim 8 , wherein the processing circuitry is further configured to:
determine a shape based on the first shape model and an aligned shape generated from image data of the anatomical object; and
determine respective distance and orientation difference values for each of the plurality of estimated shape models, wherein each of the respective distance and orientation difference values is indicative of a difference in distance and orientation between respective estimated shape models and the determined shape,
wherein to determine the respective cost values for each of the plurality of estimated shape models, the processing circuitry is configured to determine the respective cost values for each of the plurality of estimated shape models based at least in part on the respective determined medialization values for each of the plurality of estimated shape models and the respective determined distance and orientation difference values.
10. The device of claim 9 , wherein to determine the respective distance and orientation difference values for each of the plurality of estimated shape models, the processing circuitry is configured to:
determine respective distances between corresponding points on respective estimated shape models and the determined shape;
determine respective angular differences between normal vectors for the corresponding points on respective estimated shape models and the determined shape; and
determine the respective distance and orientation difference values based on the determined respective distances and the determined respective angular differences.
11. The device of claim 8 , wherein the processing circuitry is configured to:
determine respective weighting values based on a likelihood of each of the respective estimated shape models being representative of the pre-morbid shape of the anatomical object,
wherein to determine the respective cost values for each of the plurality of estimated shape models, the processing circuitry is configured to determine the respective cost values for each of the plurality of estimated shape models based at least in part on the respective determined medialization values for each of the plurality of estimated shape models and the respective weighting values.
12. The device of claim 11 , where to determine the respective weighting values, the processing circuitry is configured to perform
∑
l
N
∑
j
i
λ
j
∑
j
N
λ
j
×
b
i
2
,
wherein N equals a number of modes used to build respective plurality of estimated shape models, wherein λ equals eigenvalues of the first shape model, and b equals a scaling factor used to determine respective plurality of estimated shape models.
13. The device of claim 8 , wherein to determine respective medialization values for each of the plurality of estimated shape models, the processing circuitry is configured to:
divide image data of the anatomical object into a plurality of portions;
project points from each of the plurality of portions to a transverse axis;
determine a threshold point from one of the projected points;
determine a most lateral portion from the plurality of portion;
determine a portion in each of the plurality of estimated shape models that corresponds to the determined most lateral position;
project points from the determined portion in each of the plurality of estimated shape models to the transverse axis;
determine distances from the projected points to the threshold point; and
determine the respective medialization values for each of the plurality of estimated shape models based on the determined distances.
14. The device of claim 8 , wherein to determine the respective medialization values for each of the plurality of estimated shape models, the processing circuitry is configured to:
project points from the anatomical object to a transverse axis;
project respective points from each of the plurality of estimated shape models to the transverse axis; and
determine the respective medialization values for each of the plurality of estimated shape models based on the projected points from the anatomical object to the transverse axis and the respective projected points from each of the plurality of estimated shape models to the transverse axis.
15. A non-transitory computer-readable storage medium storing instructions thereon that when executed cause one or more processors to:
determine respective medialization values for each of a plurality of estimated shape models, wherein the plurality of estimated shape models is generated from a first shape model, and wherein each of the medialization values is indicative of an amount by which each respective one of the estimated shape models is medialized relative to a current position of an anatomical object;
determine respective cost values for each of the plurality of estimated shape models based at least in part on the respective determined medialization values for each of the plurality of estimated shape models;
select an estimated shape model from the plurality of estimated shape models having a cost value of the respective cost values that satisfies a function for the cost value; and
generate information indicative of a pre-morbid shape of the anatomical object based on the selected estimated shape model.
16. The computer-readable storage medium of claim 15 , further comprising instructions that cause the one or more processors to:
determine a shape based on the first shape model and an aligned shape generated from image data of the anatomical object; and
determine respective distance and orientation difference values for each of the plurality of estimated shape models, wherein each of the respective distance and orientation difference values is indicative of a difference in distance and orientation between respective estimated shape models and the determined shape,
wherein the instructions that cause the one or more processors to determine the respective cost values for each of the plurality of estimated shape models comprise instructions that cause the one or more processors to determine the respective cost values for each of the plurality of estimated shape models based at least in part on the respective determined medialization values for each of the plurality of estimated shape models and the respective determined distance and orientation difference values.
17. The computer-readable storage medium of claim 16 , wherein the instructions that cause the one or more processors to determine the respective distance and orientation difference values for each of the plurality of estimated shape models comprise instructions that cause the one or more processors to:
determine respective distances between corresponding points on respective estimated shape models and the determined shape;
determine respective angular differences between normal vectors for the corresponding points on respective estimated shape models and the determined shape; and
determine the respective distance and orientation difference values based on the determined respective distances and the determined respective angular differences.
18. The computer-readable storage medium of claim 15 , further comprising instructions that cause the one or more processors to:
determine respective weighting values based on a likelihood of each of the respective estimated shape models being representative of the pre-morbid shape of the anatomical object,
wherein the instructions that cause the one or more processors to determine the respective cost values for each of the plurality of estimated shape models comprise instructions that cause the one or more processors to determine the respective cost values for each of the plurality of estimated shape models based at least in part on the respective determined medialization values for each of the plurality of estimated shape models and the respective weighting values.
19. The computer-readable storage medium of claim 18 , wherein the instructions that cause the one or more processors to determine the respective weighting values comprise instructions that cause the one or more processors to perform
∑
l
N
∑
j
i
λ
j
∑
j
N
λ
j
×
b
i
2
,
wherein N equals a number of modes used to build respective plurality of estimated shape models, wherein λ equals eigenvalues of the first shape model, and b equals a scaling factor used to determine respective plurality of estimated shape models.
20. The computer-readable storage medium of claim 15 , wherein the instructions that cause the one or more processors to determine respective medialization values for each of the plurality of estimated shape models comprise instructions that cause the one or more processors to:
divide image data of the anatomical object into a plurality of portions;
project points from each of the plurality of portions to a transverse axis;
determine a threshold point from one of the projected points;
determine a most lateral portion from the plurality of portion;
determine a portion in each of the plurality of estimated shape models that corresponds to the determined most lateral position;
project points from the determined portion in each of the plurality of estimated shape models to the transverse axis;
determine distances from the projected points to the threshold point; and
determine the respective medialization values for each of the plurality of estimated shape models based on the determined distances.
21. A system for determining a pre-morbid shape of an anatomical object of an orthopedic joint of a patient, the system comprising:
means for determining respective medialization values for each of a plurality of estimated shape models, wherein the plurality of estimated shape models is generated from a first shape model, and wherein each of the medialization values is indicative of an amount by which each respective one of the estimated shape models is medialized relative to a current position of the anatomical object;
means for determining respective cost values for each of the plurality of estimated shape models based at least in part on the respective determined medialization values for each of the plurality of estimated shape models;
means for selecting an estimated shape model from the plurality of estimated shape models having a cost value of the respective cost values that satisfies a function for the cost value; and
means for generating information indicative of the pre-morbid shape of the anatomical object based on the selected estimated shape model.
22. The system of claim 21 , further comprising:
means for determining a shape based on one of the first shape model and an aligned shape generated from image data of the anatomical object; and
means for determining respective distance and orientation difference values for each of the plurality of estimated shape models, wherein each of the respective distance and orientation difference values is indicative of a difference in distance and orientation between respective estimated shape models and the determined shape,
wherein the means for determining the respective cost values for each of the plurality of estimated shape models comprises means for determining the respective cost values for each of the plurality of estimated shape models based at least in part on the respective determined medialization values for each of the plurality of estimated shape models and the respective determined distance and orientation difference values.
23. The system of claim 22 , wherein the means for determining the respective distance and orientation difference values for each of the plurality of estimated shape models comprises:
means for determining respective distances between corresponding points on respective estimated shape models and the determined shape;
means for determining respective angular differences between normal vectors for the corresponding points on respective estimated shape models and the determined shape; and
means for determining the respective distance and orientation difference values based on the determined respective distances and the determined respective angular differences.
24. The system of claim 21 , further comprising:
means for determining respective weighting values based on a likelihood of each of the respective estimated shape models being representative of the pre-morbid shape of the anatomical object,
wherein the means for determining the respective cost values for each of the plurality of estimated shape models comprises means for determining the respective cost values for each of the plurality of estimated shape models based at least in part on the respective determined medialization values for each of the plurality of estimated shape models and the respective weighting values.
25. The system of claim 24 , wherein the means for determining the respective weighting values comprises means for performing
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l
N
∑
j
i
λ
j
∑
j
N
λ
j
×
b
i
2
,
wherein N equals a number of modes used to build respective plurality of estimated shape models, wherein λ equals eigenvalues of the first shape model, and b equals a scaling factor used to determine respective plurality of estimated shape models.
26. The system of claim 21 , wherein the means for determining respective medialization values for each of the plurality of estimated shape models comprises:
means for dividing image data of the anatomical object into a plurality of portions;
means for projecting points from each of the plurality of portions to a transverse axis;
means for determining a threshold point from one of the projected points;
means for determining a most lateral portion from the plurality of portion;
means for determining a portion in each of the plurality of estimated shape models that corresponds to the determined most lateral position;
means for projecting points from the determined portion in each of the plurality of estimated shape models to the transverse axis;
means for determining distances from the projected points to the threshold point; and
means for determining the respective medialization values for each of the plurality of estimated shape models based on the determined distances.