Determination of registration accuracy

Abstract

A medical data processing method, performed by a computer (2), for determining error analysis data describing the registration accuracy of a first elastic registration between first and second image data (A, B) describing images of an anatomical structure of a patient, comprising the steps of: —acquiring the first image data (A) describing a first image of the anatomical structure, —acquiring the second image data (B) describing a second image of the anatomical structure, —determining first registration data describing a first elastic registration of the first image data (A) to the second image data (B) by mapping the first image data (A) to the second image data (B) using a registration algorithm, —determining second registration data describing a second elastic registration of the second image data (B) to the first image data (A) by mapping the second image data (B) to the first image data (A) using the registration algorithm, —determining error analysis data describing the registration accuracy of the first elastic registration based on the first registration data and the second registration data.

Claims

1. A system, comprising at least one computer having at least one processor configured to execute a method for determining error analysis data describing registration accuracy of a first elastic registration between first and second image data describing images of an anatomical structure of a patient, the method comprising executing, by the at least one processor of the at least one computer, the steps of: acquiring, at the at least one processor, the first image data describing a first image of the anatomical structure; acquiring, at the at least one processor, the second image data describing a second image of the anatomical structure; determining, by the at least one processor, first registration data describing the first elastic registration of the first image data to the second image data by mapping the first image data to the second image data using a registration algorithm; determining, by the at least one processor, second registration data describing a second elastic registration of the second image data to the first image data by mapping the second image data to the first image data using the registration algorithm; determining, by the at least one processor, error analysis data describing the registration accuracy of the first elastic registration based on the first registration data and the second registration data; wherein determining, by the at least one processor, the error analysis data comprises: transforming an original position of a data point within the first image data using the first registration data; transforming the transformed position using the second registration data to obtain a new position of the data point; calculating a distance between the original position and the new position of the data point to obtain an observed error specific to the anatomical structure; wherein determining error analysis data comprises determining observed errors for a plurality of data points within the first image data; wherein determining error analysis data comprises determining at least one statistical parameter from the plurality of observed errors; wherein determining error analysis data comprises defining at least one data area with respect to the anatomical structure within the first image data and determining at least one local statistical parameter for the observed errors obtained for data points within the at least one data area, wherein the at least one local statistical parameter is a maximum observed error, a median observed error, a mean observed error or a standard deviation of the observed error; wherein the method further includes the step of acquiring, at the at least one processor, critical structure data describing a position of at least one critical structure corresponding to a region of interest within the anatomical structure in the first image data and calculating the distance between the position of the at least one critical structure and a position of at least one data area within the first image data, the critical structure data representing an area within the first image data which is distinct from the at least one data area; wherein by calculating the distance between the position of the at least one critical structure and the position of the at least one data area within the first image data, the at least one local statistical parameter for the observed errors within the at least one data area is related to the at least one critical structure.

2. A method for determining error analysis data describing registration accuracy of a first elastic registration between first and second image data describing images of an anatomical structure of a patient, the method comprising executing, by at least one processor of at least one computer, the steps of: acquiring, at the at least one processor, the first image data describing a first image of the anatomical structure; acquiring, at the at least one processor, the second image data describing a second image of the anatomical structure; determining, by the at least one processor, first registration data describing the first elastic registration of the first image data to the second image data by mapping the first image data to the second image data using a registration algorithm; determining, by the at least one processor, second registration data describing a second elastic registration of the second image data to the first image data by mapping the second image data to the first image data using the registration algorithm; determining, by the at least one processor, error analysis data describing the registration accuracy of the first elastic registration based on the first registration data and the second registration data; wherein determining, by the at least one processor, the error analysis data comprises: transforming an original position of a data point within the first image data using the first registration data; transforming the transformed position using the second registration data to obtain a new position of the data point; calculating a distance between the original position and the new position of the data point to obtain an observed error specific to the anatomical structure; wherein determining error analysis data comprises determining observed errors for a plurality of data points within the first image data; wherein determining error analysis data comprises determining at least one statistical parameter from the plurality of observed errors; wherein determining error analysis data comprises defining at least one data area with respect to the anatomical structure within the first image data and determining at least one local statistical parameter for the observed errors obtained for data points within the at least one data area, wherein the at least one local statistical parameter is a maximum observed error, a median observed error, a mean observed error or a standard deviation of the observed error; wherein the method further includes the step of acquiring, at the at least one processor, critical structure data describing a position of at least one critical structure corresponding to a region of interest within the anatomical structure in the first image data and calculating the distance between the position of the at least one critical structure and a position of at least one data area within the first image data, the critical structure data representing an area within the first image data which is distinct from the at least one data area; wherein by calculating the distance between the position of the at least one critical structure and the position of the at least one data area within the first image data, the at least one local statistical parameter for the observed errors within the at least one data area is related to the at least one critical structure.

3. The method according to claim 2, wherein determining, by the at least one processor, the first registration data involves determining a first transformation vector field for transforming the first image data to the second image data and determining, by the at least one processor, the second registration data involves determining a second transformation vector field for transforming the second image data to the first image data, wherein determining the first transformation vector field is independent from determining the second transformation vector field.

4. The method according to claim 2, further comprising the step of determining, by the at least one processor, an associating function which describes a relation of the observed errors to real mapping errors or target registration errors.

5. The method according to claim 4, further comprising the step of determining, by the at least one processor, for each of a plurality of sample data points within the first image data a set comprising an observed error and a real mapping error or a target registration error and determining the associating function from associating the sets of observed errors and real mapping errors or target registration errors.

6. The method according to claim 4, wherein determining, by the at least one processor, a real mapping error comprises: defining a sample data point within the first image data; transforming the original position of the sample data point within the first image data using the first registration data; identifying the transformed position of the sample data point; calculating the distance between the transformed position of the sample data point and a real position of the sample data point within the second image data corresponding to the sample data point within the first image data to obtain the real mapping error.

7. The method according to claim 4, wherein determining, by the at least one processor, a real mapping error comprises: calculating virtual image data by transforming the first image data using the first registration data; determining auxiliary registration data describing an ideal elastic registration without errors of the first image data to the virtual image data by mapping the first image data to the virtual image data using the registration algorithm; defining a sample data point within the first image data; transforming the original position of the sample data point within the first image data using the first registration data to obtain a first transformed position of the sample data point; transforming the original position of the sample data point within the first image data using the auxiliary registration data to obtain a second transformed position of the sample data point; calculating the distance between the first transformed position and the second transformed position to obtain the real mapping error.

8. The method according to claim 2, wherein acquiring, at the at least one processor, the critical structure data comprises acquiring atlas data describing a model of the anatomical structure.

9. A non-transitory computer-readable program storage medium storing a computer program which, when executed by at least one processor of at least one computer, causes the at least one computer to perform a medical data processing method for determining error analysis data describing registration accuracy of a first elastic registration between first and second image data describing images of an anatomical structure of a patient, the method comprising the steps of: acquiring, at the at least one processor, the first image data describing a first image of the anatomical structure; acquiring, at the at least one processor, the second image data describing a second image of the anatomical structure; determining, by the at least one processor, first registration data describing the first elastic registration of the first image data to the second image data by mapping the first image data to the second image data using a registration algorithm; determining, by the at least one processor, second registration data describing a second elastic registration of the second image data to the first image data by mapping the second image data to the first image data using the registration algorithm; determining, by the at least one processor, error analysis data describing the registration accuracy of the first elastic registration based on the first registration data and the second registration data; wherein determining, by the at least one processor, the error analysis data comprises: transforming an original position of a data point within the first image data using the first registration data; transforming the transformed position using the second registration data to obtain a new position of the data point; calculating a distance between the original position and the new position of the data point to obtain an observed error specific to the anatomical structure; wherein determining error analysis data comprises determining observed errors for a plurality of data points within the first image data; wherein determining error analysis data comprises determining at least one statistical parameter from the plurality of observed errors; wherein determining error analysis data comprises defining at least one data area with respect to the anatomical structure within the first image data and determining at least one local statistical parameter for the observed errors obtained for data points within the at least one data area, wherein the at least one local statistical parameter is a maximum observed error, a median observed error, a mean observed error or a standard deviation of the observed error; wherein the method further includes the step of acquiring, at the at least one processor, critical structure data describing a position of at least one critical structure corresponding to a region of interest within the anatomical structure in the first image data and calculating the distance between the position of the at least one critical structure and a position of at least one data area within the first image data, the critical structure data representing an area within the first image data which is distinct from the at least one data area; wherein by calculating the distance between the position of the at least one critical structure and the position of the at least one data area within the first image data, the at least one local statistical parameter for the observed errors within the at least one data area is related to the at least one critical structure.

10. A computer, comprising a non-transitory computer-readable program storage medium storing a computer program which, when executed by at least one processor of the computer, causes the computer to perform a medical data processing method for determining error analysis data describing registration accuracy of a first elastic registration between first and second image data describing images of an anatomical structure of a patient, the method comprising the steps of: acquiring, at the at least one processor, the first image data describing a first image of the anatomical structure; acquiring, at the at least one processor, the second image data describing a second image of the anatomical structure; determining, by the at least one processor, first registration data describing the first elastic registration of the first image data to the second image data by mapping the first image data to the second image data using a registration algorithm; determining, by the at least one processor, second registration data describing a second elastic registration of the second image data to the first image data by mapping the second image data to the first image data using the registration algorithm; determining, by the at least one processor, error analysis data describing the registration accuracy of the first elastic registration based on the first registration data and the second registration data; wherein determining error analysis data comprises determining observed errors for a plurality of data points within the first image data; wherein determining error analysis data comprises determining at least one statistical parameter from the plurality of observed errors specific to the anatomical structure; wherein determining error analysis data comprises defining at least one data area with respect to the anatomical structure within the first image data and determining at least one local statistical parameter for the observed errors obtained for data points within the at least one data area, wherein the at least one local statistical parameter is a maximum observed error, a median observed error, a mean observed error or a standard deviation of the observed error; wherein determining, by the at least one processor, error analysis data comprises: transforming an original position of a data point within the first image data using the first registration data; transforming an transformed position using the second registration data to obtain a new position of the data point; calculating a distance between the original position and the new position of the data point to obtain an observed error; wherein the method further includes the step of acquiring, at the at least one processor, critical structure data describing a position of at least one critical structure corresponding to a region of interest within the anatomical structure in the first image data and calculating the distance between the position of the at least one critical structure and a position of the at least one data area within the first image data, the critical structure data representing an area within the first image data which is distinct from the at least one data area; wherein by calculating the distance between the position of the at least one critical structure and the position of the at least one data area within the first image data, the at least one local statistical parameter for the observed errors within the at least one data area is related to the at least one critical structure.

11. A method for determining error analysis data describing a registration accuracy of a first elastic registration between first and second image data describing images of an anatomical structure of a patient, the method comprising executing, by at least one processor of at least one computer, the steps of: acquiring, at the at least one processor, the first image data describing a first image of the anatomical structure; acquiring, at the at least one processor, the second image data describing a second image of the anatomical structure; determining, by the at least one processor, first registration data describing the first elastic registration of the first image data to the second image data by mapping the first image data to the second image data using a registration algorithm; determining, by the at least one processor, second registration data describing a second elastic registration of the second image data to the first image data by mapping the second image data to the first image data using the registration algorithm; determining, by the at least one processor, error analysis data describing the registration accuracy of the first elastic registration based on the first registration data and the second registration data; wherein determining error analysis data comprises determining observed errors for a plurality of data points within the first image data; the determining a plurality of observed errors for the plurality of data points within the first image includes: transforming the original positions of a data points within the first image data using the first registration data; transforming the transformed positions using the second registration data to obtain a new positions of the data points; calculating distances between the original positions and the new positions of the data points to obtain an observed error; determining at least one statistical parameter from the plurality of observed errors; defining at least one data area with respect to the anatomical structure within the first image data and determining at least one local statistical parameter for the observed errors obtained for the data points within the at least one data area; acquiring critical structure data describing a position of at least one critical structure corresponding to a region of interest within the anatomical structure in the first image data and calculating a distance between the position of the at least one critical structure and a position of at least one data area within the first image data; the at least one local statistical parameter for the plurality of observed errors within the at least one data area is related to the at least one critical structure.

Description

(1) In the following, the invention is described with reference to the enclosed figures which represent preferred embodiments of the invention. The scope of the invention is not however limited to the specific features disclosed in the figures, which show:

(2) FIG. 1 a flow chart of a method for determining error analysis data,

(3) FIG. 2 a schematic diagram of the formation of errors during elastic registration and the application of the method,

(4) FIG. 3 a diagram of target registration error (TRE) versus observed error (E.sub.M),

(5) FIG. 4 a diagram of mean observed error (E.sub.M) versus mean real error,

(6) FIG. 5 a diagram of standard deviation of observed error (E.sub.M) versus standard deviation of real error, and

(7) FIG. 6 a computer performing the method.

(8) FIG. 1 shows a flowchart of a method for determining error analysis data describing the registration accuracy of a first elastic registration between first and second image data describing images of an anatomical structure of a patient. The terms “elastic registration”, “elastic fusion” and “deformable registration” are used synonymously.

(9) Step S01 involves acquiring first image data (Volume A) describing a first image of the anatomical structure. Step S02 involves acquiring second image data (Volume B) describing a second image of the anatomical structure. The image data may be provided by means of any one of the above-mentioned imaging methods.

(10) Step S03 involves determining first registration data describing a first elastic registration of the first image data to the second image data by mapping the first image data to the second image data using a registration algorithm. Step S04 involves determining second registration data describing a second elastic registration of the second image data to the first image data by mapping the second image data to the first image data using the registration algorithm.

(11) Step S05 involves determining error analysis data describing the registration accuracy of the first elastic registration based on the first registration data and the second registration data. In an optional step S06 the determined error analysis data may be further processed by a post-processing method.

(12) FIG. 2 is a schematic diagram showing the formation of errors during the disclosed method. A data point P.sub.A in the first image data A is transformed by a first transformation vector T.sub.AB to a data point P.sub.B′ in the second image data B. The first transformation vector T.sub.AB is included in the first registration data. Transforming a data point in the first image data A to a data point in the second image data B means transforming the original position of the data point in the first image data to the transformed position in the second image data B.

(13) Furthermore, FIG. 2 shows that transforming the data point P.sub.A in the first image data A to the data point P.sub.B′ in the second image data B is not correct. The corresponding data point for P.sub.A in image data B is P.sub.B. A hypothetical vector T.sub.R describes the real transformation from P.sub.A to P.sub.B. The data point P.sub.B′ and P.sub.B are separated by a distance which represents a real mapping error E.sub.AB of the transformation by the first transformation vector T.sub.AB. One aspect of the disclosed method is to estimate the real mapping error E.sub.AB.

(14) As shown by FIG. 2, the data point P.sub.B′ in the second image data is transformed by a second transformation vector T.sub.BA into the data point P.sub.N in the first image data. The second transformation vector T.sub.BA is included in the second registration data. Furthermore, the data point P.sub.B′ is transformed by the inverse of the real transformation vector T.sub.R.sup.−1 into data point P.sub.A″ in the first image data. The distance between the data point P.sub.A′ and the data point P.sub.A″ represents an error E.sub.BA in the second transformation vector T.sub.BA.

(15) The real mapping error E.sub.AB of the first transformation vector T.sub.AB and the error E.sub.BA of the second transformation vector T.sub.BA cannot be measured directly.

(16) The distance between the data point P.sub.A and the data point P.sub.A′ represents an observed error E.sub.M which can be measured. The observed error E.sub.M is expressed by the following formula:
E.sub.M=|T.sub.BA(T.sub.AB(P.sub.A))−P.sub.A|=E.sub.AB+E.sub.BA

(17) Registration accuracy indicators (RAI) may be determined by a plurality of observed errors E.sub.m according to the following formulae, where f is an associating function:

(18) ${\mathrm{RAI}}_{\mathrm{mean}}=f\left(\frac{1}{n}\underset{i=1}{\overset{n}{.Math.}}{E}_M^i\right)$${\mathrm{RAI}}_{\sigma }=f\left(\sqrt{\frac{1}{n}\underset{i}{\overset{}{.Math.}}{\left(x_i-{\mathrm{RAI}}_{\mathrm{mean}}\right)}^2}\right)\mathrm{let}$$E_M^i\in \left\{E_M^1,\mathrm{.Math.},E_M^n\right\}=M\mathrm{with}{E}_M^i\le E_M^{i+1}\mathrm{and}n=.Math.M.Math.,\mathrm{then}$${\mathrm{RAI}}_{\mathrm{median}}=f\left(E_M^{\frac{.Math.M.Math.}{2}}\right)$${\mathrm{RAI}}_{\min }=f\left(E_M^1\right)$${\mathrm{RAI}}_{\max }=f\left(E_M^n\right)$

(19) In one embodiment the observed errors E.sub.M may be related to real mapping errors E.sub.AB or target registration errors (TRE). Nevertheless, the following assumptions are made: the registration algorithm is not symmetric the registration is not biased, i.e. there is no systematic errors (under- or overestimation) of the registration normally distributed scattering of the observed errors E.sub.M around the real error E.sub.AB+E.sub.BA the transformation vector fields do not have a large gradient the real mapping errors E.sub.AB do not have a large gradient

(20) FIG. 3 depicts a diagram of target registration error (TRE) versus observed error E.sub.M for five data sets, i.e. patient1 to patient5. FIG. 3 shows that for a particular registration algorithm fulfilling above assumptions, E.sub.M and TRE are essentially the same (on average) except for a scaling factor. Therefore, the observed error E.sub.M actually provides a valuable indication for the registration accuracy of the elastic registration.

(21) The least squares fitting function shown in FIG. 3 is an example for an associating function which describes a relation of observed errors E.sub.M to target registration errors (TRE). Using such an associating function, one can predict a measurable target registration error (TRE) from the observed errors E.sub.M. Analogously, one can derive such an associating function for the standard deviation of errors. All such fitting may be part of the optional post-processing step.

(22) Making above assumptions the observed errors E.sub.M may be related to real mapping errors E.sub.AB. As long as the error from mapping data point P.sub.A to data point P.sub.E is small, mapping data point P.sub.B′ to data point P.sub.A′ is similar to mapping data point P.sub.B′ to data point P.sub.A″. When this is true, the distribution of the observed errors E.sub.M resembles a mixed Gaussian distribution. With this knowledge a real error distribution may be deducted analytically. Under the assumptions above the standard deviation of the real errors E.sub.AB is smaller than the standard deviation of observed errors E.sub.M.

(23) As mentioned above, TRE has a limited usability. A way of determining the real mapping error E.sub.AB comprises calculating virtual image data by transforming the first image data A using the first registration data, determining auxiliary registration data describing an elastic registration of the first image data A to the virtual image data by mapping the first data to the virtual image data, defining a sample data point within the first image data, transforming the original position of the sample data point within the first image data using the first registration data to obtain a first transformed position of the sample data point, transforming the original position of the sample data point within the first image data using the auxiliary registration data to obtain a second transformed position of the sample data point and calculating the distance between the first transformed position and the second transformed position to obtain the real mapping error E.sub.AB. In other words, virtual image data is calculated by using a real transformation vector field.

(24) A sample data point is transformed using a transformation vector field comprising the (ideal) first registration data and is also transformed by the auxiliary registration data. Calculating the distance between the two transformed data points provides the real mapping error E.sub.AB for the auxiliary registration data. Similarly a real mapping error E.sub.BA may be calculated by using the inverse of the first registration data and a second auxiliary registration data.

(25) For the tests shown in FIGS. 4 and 5 noise was added to the virtual image data to generate worse registrations. In FIG. 4 mean E.sub.M is plotted against mean real errors E.sub.AB determined as mentioned above. In FIG. 5 the standard deviation of E.sub.M is plotted against the standard deviation of the real errors E.sub.AB. When comparing the values for mean E.sub.M and mean real errors E.sub.AB, one may notice that E.sub.M is not a perfect match for the real error E.sub.AB. In FIGS. 4 and 5 two associating functions which describe a relation of E.sub.M to real mapping errors E.sub.AB are depicted. The associating functions were derived by using least squares fitting with a linear function. Other fitting functions are applicable.

(26) The observed errors E.sub.M may be used in the raw form to rank registrations or to threshold the results within a certain limit. Furthermore, the observed errors E.sub.M may be used to generate a reference model like the (measurable) TRE. Furthermore, as discussed above, the observed and cumulated errors E.sub.M may be related to real mapping errors E.sub.AB.

(27) By defining a data area within the image data and determining a statistical parameter for the observed errors obtained for the data points within the data area a localized error may be determined. In particular, the defined data area may be a sliding region which is moved over the image data. By calculating local statistical parameters for observed errors within a plurality of defined data areas a meaningful localized error may be generated.

(28) Furthermore, the data area may be defined with respect to a specific anatomical structure, for example the lung or the liver of a patient. The observed error for the data points within such a defined data area is then specific to the anatomical structure. Determining localized errors may provide valuable information to the user of the elastic registration. For example, areas with a bad mapping could be highlighted, minimizing the risk of wrong interpretation. Furthermore, localized errors may be determined for a region within the image data comprising a critical structure, such as a tumor. Providing the user with information about localized errors in relation to a critical structure allows a more meaningful evaluation of the registration accuracy. This way confidence intervals for the registrations errors may be provided to the user.

(29) FIG. 6 shows a computer 2 including a processor 3, a memory 4 and an interface 5. The computer 2 is connected to an input unit 6, such as a mouse, a keyboard or a touch-sensitive surface, and an output unit 7 such as a display, a speaker or a tactile sensation generation unit. A program causing the computer 2 to perform the method according to the invention may be loaded into the memory 4 of the computer. In one embodiment the program may be stored on a program storage medium comprised in or connected to the computer 2.