Method and apparatus for the rigid and non-rigid registration of 3D shapes
View Patent ↗A method for registering two three-dimensional shapes is disclosed whereby the two shapes are represented as zero level set of signed distance functions and the energy between these two functions is minimized. In a first embodiment, two undetailed ear impression models are rigidly registered with each other. In another embodiment, a detailed ear impression is initially aligned with an undetailed ear impression model and, then, the detailed ear impression model is rigidly registered with the undetailed ear impression model as a function of the signed distance functions. In accordance with another embodiment, an undetailed ear impression model is non-rigidly registered with a template ear impression model as a function of the signed distance functions.
1. A method for registering a first ear impression model in a plurality of ear impression models with a second ear impression model in said plurality of ear impression models, said method comprising:
identifying a first signed distance function wherein a surface of a first ear impression model is defined as a zero level of said first signed distance function;
identifying a second signed distance function wherein a surface of a second ear impression model is defined as a zero level of said second signed distance function; and
registering the first ear impression model with the second ear impression model by minimizing an energy function representing an energy between said first signed distance function and said second signed distance function.
2. The method of claim 1 wherein said step of registering comprises:
receiving a template ear impression model as said second ear impression model;
registering via rigid registration said first ear impression model with said template ear impression model;
computing a mean ear impression model as a function of said template ear impression model and said first ear impression model; and
registering via rigid registration said first ear impression model with said mean ear impression model.
3. The method of claim 1 wherein said energy function is defined by the equation:
E ( g )=∫ Ω χ α (Φ T ( X ),Φ( g ( X )))[Φ T ( X ))−Φ( g ( X ))] 2 dX
where E is the energy function; χ α is a characteristic function used to reduce computational complexity such that only a limited number of points around the surfaces to be registered are considered in the registration computations; g is a rigid registration function g(X)=RSX+T where R is the rotation, T is the translation and S is the nonuniform scaling required to map a first ear impression onto a second ear impression;
and φ T and φ represent signed distance functions of two ear impressions to be registered, the zero level of which correspond to the surface of each respective ear impression.
4. The method of claim 1 wherein said step of registering comprises:
aligning a feature of said first ear impression model with a corresponding feature of said second ear impression model, said first ear impression model comprising a detailed ear impression model and said second ear impression model comprising an undetailed ear impression model;
identifying a portion of said second ear impression to be used in registering said first and second ear impression models; and
registering via rigid registration said first ear impression model with said second ear impression model.
5. The method of claim 4 wherein said step of identifying said portion of said second ear impression to be used in registering comprises:
restricting the portion of said second ear impression to be registered by using asymmetric rigid registration.
6. The method of claim 5 wherein said asymmetric rigid registration is defined by the equation:
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where g is rigid registration function g(X)=RSX+T where R is the rotation, T is the translation and S is the nonuniform scaling required to map a first ear impression onto a second ear impression; and φ T and φ represent signed distance functions of two ear impressions to be registered, the zero level of which correspond to the surface of each respective ear impression; and χ β is defined as 0 for max(|φ u |, |φ d |)>β and where χ β is defined as 1 for max(|φ u , |φ d |)<β, where φ u represents the undetailed ear impression model shape and φ d represents the detailed ear impression model shape.
7. The method of claim 1 wherein said step of registering comprises:
receiving a template ear impression model as said second ear impression model;
defining a non-rigid evolution stopping criteria;
determining a mask field for preventing an evolution of at least a portion of said second ear impression model; and
registering via non-rigid registration deformation said second ear impression model with said first ear impression model as a function of said non-rigid evolution stopping criteria and said mask field.
8. The method of claim 7 wherein said non-rigid evolution stopping criteria comprises a function for determining when at least a portion of said second ear impression model substantially conforms to said first ear impression model.
9. An apparatus for registering a first ear impression model in a plurality of ear impression models with a second ear impression model in said plurality of ear impression models, said apparatus comprising:
means for identifying a first signed distance function wherein a surface of a first ear impression model is defined as a zero level of said first signed distance function;
means for identifying a second signed distance function wherein a surface of a second ear impression model is defined as a zero level of said second signed distance function; and
means for registering the first ear impression model with the second ear impression model by minimizing an energy function representing an energy between said first signed distance function and said second signed distance function.
10. The apparatus of claim 9 wherein said means for registering comprises:
means for receiving a template ear impression model as said second ear impression model;
means for registering via rigid registration said first ear impression model with said template ear impression model;
means for computing a mean ear impression model as a function of said template ear impression model and said first ear impression model; and
means for registering via rigid registration said first ear impression model with said mean ear impression model.
11. The apparatus of claim 9 wherein said energy function is defined by the equation:
E ( g )=∫ Ω χ α (Φ T ( X ),Φ( g ( X )))[Φ T ( X ))−Φ( g ( X ))] 2 dX
where E is the energy function; χ α is a characteristic function used to reduce computational complexity such that only a limited number of points around the surfaces to be registered are considered in the registration computations; g is rigid registration function g(X)=RSX+T where R is the rotation, T is the translation and S is the nonuniform scaling required to map a first ear impression onto a second ear impression; and φ T and φ represent signed distance functions of two ear impressions to be registered, the zero level of which correspond to the surface of each respective ear impression.
12. The apparatus of claim 9 wherein said means for registering comprises:
means for aligning a feature of said first ear impression model with a corresponding feature of said second ear impression model, said first ear impression model comprising a detailed ear impression model and said second ear impression model comprising an undetailed ear impression model;
means for identifying a portion of said second ear impression to be used in registering said first and second ear impression models; and
means for registering via rigid registration said first ear impression model with said second ear impression model.
13. The apparatus of claim 12 wherein means for identifying said portion of said second ear impression to be used in registering comprises:
means for restricting the portion of said second ear impression to be registered by using asymmetric rigid registration.
14. The apparatus of claim 13 wherein said asymmetric rigid registration is defined by the equation:
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where g is rigid registration function g(X)=RSX+T where R is the rotation, T is the translation and S is the nonuniform scaling required to map a first ear impression onto a second ear impression; and φ T and φ represent signed distance functions of two ear impressions to be registered, the zero level of which correspond to the surface of each respective ear impression; and χ β is defined as 0 for max(|φ u , |φ d |)>β and where χ β is defined as 1 for max(|φ u , |φ d |)<β, where φ u represents the undetailed ear impression model shape and φ d represents the detailed ear impression model shape.
15. The apparatus of claim 9 wherein said means for registering comprises:
means for receiving a template ear impression model as said second ear impression model;
means for defining a non-rigid evolution stopping criteria;
means for determining a mask field for preventing an evolution of at least a portion of said second ear impression model; and
means for registering via non-rigid registration deformation said second ear impression model with said first ear impression model as a function of said non-rigid evolution stopping criteria and said mask field.
16. The step of claim 15 wherein said non-rigid evolution stopping criteria comprises a function for determining when at least a portion of said second ear impression model substantially conforms to said first ear impression model.
17. A computer readable medium comprising computer program instructions which, when executed by a processor, define steps for registering a first ear impression model in a plurality of ear impression models with a second ear impression model in said plurality of ear impression models, said steps comprising:
identifying a first signed distance function wherein a surface of a first ear impression model is defined as a zero level of said first signed distance function;
identifying a second signed distance function wherein a surface of a second ear impression model is defined as a zero level of said second signed distance function; and
registering the first ear impression model with the second ear impression model by minimizing an energy function representing an energy between said first signed distance function and said second signed distance function.
18. The computer readable medium of claim 17 wherein the computer program instructions defining the step of registering comprise computer program instructions defining the steps of:
receiving a template ear impression model as said second ear impression model;
registering via rigid registration said first ear impression model with said template ear impression model;
computing a mean ear impression model as a function of said template ear impression model and said first ear impression model; and
registering via rigid registration said first ear impression model with said mean ear impression model.
19. The computer readable medium of claim 17 wherein said energy function is defined by the equation:
E ( g )=∫ Ω χ α (Φ T ( X ),Φ( g ( X )))[Φ T ( X ))−Φ( g ( X ))] 2 dX
where E is the energy function; χ α is a characteristic function used to reduce computational complexity such that only a limited number of points around the surfaces to be registered are considered in the registration computations; g is rigid registration function g(X)=RSX+T where R is the rotation, T is the translation and S is the nonuniform scaling required to map a first ear impression onto a second ear impression;
and φ T and φ represent signed distance functions of two ear impressions to be registered, the zero level of which correspond to the surface of each respective ear impression.
20. The computer readable medium of claim 17 wherein the computer program instructions defining the step of registering comprise computer program instructions defining the steps of:
aligning a feature of said first ear impression model with a corresponding feature of said second ear impression model, said first ear impression model comprising a detailed ear impression model and said second ear impression model comprising an undetailed ear impression model;
identifying a portion of said second ear impression to be used in registering said first and second ear impression models; and
registering via rigid registration said first ear impression model with said second ear impression model.
21. The computer readable medium of claim 20 wherein the computer program instructions defining step of identifying said portion of said second ear impression to be used in registering comprise computer program instructions defining the step of:
restricting the portion of said second ear impression to be registered by using asymmetric rigid registration.
22. The computer readable medium of claim 21 wherein said asymmetric rigid registration is defined by the equation:
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where g is rigid registration function g(X)=RSX+T where R is the rotation, T is the translation and S is the nonuniform scaling required to map a first ear impression onto a second ear impression; and φ T and φ represent signed distance functions of two ear impressions to be registered, the zero level of which correspond to the surface of each respective ear impression; and χ β is defined as 0 for max(|φ u |, |φ d |)>β and where χ β is defined as 1 for max(|φ u |, |φ d |)<β, where φ u represents the undetailed ear impression model shape and φ d represents the detailed ear impression model shape.
23. The computer readable medium of claim 17 wherein the computer program instructions defining the step of registering comprise computer program instructions defining the steps of:
receiving a template ear impression model as said second ear impression model;
defining a non-rigid evolution stopping criteria;
determining a mask field for preventing an evolution of at least a portion of said second ear impression model; and
registering via non-rigid registration deformation said second ear impression model with said first ear impression model as a function of said non-rigid evolution stopping criteria and said mask field.
24. The computer readable medium of claim 23 wherein said non-rigid evolution stopping criteria comprises a function for determining when at least a portion of said second ear impression model substantially conforms to said first ear impression model.