Ana səhifə

Dicom correction Proposal


Yüklə 377 Kb.
tarix25.06.2016
ölçüsü377 Kb.
DICOM Correction Proposal

STATUS

Letter Ballot

Date of Last Update

2012/08/27

Person Assigned

David Clunie dclunie@dclunie.com

Submitter Name

2012/03/08

Submission Date

Michael Jensen mlj@milj.dk



Correction Number CP-1213

Log Summary: Clarify affine transformation matrix constraints

Name of Standard

PS 3.3 2011



Rationale for Correction:

The explanatory text in PS 3.17 Annex P makes it clear that the transformation matrix uses homogeneous coordinates, and the normative text in the description of the attribute uses the word “homogeneous”, but the normative text for the AFFINE type of matrix contradicts this stating that that the element values are “unconstrained”. Correct the normative text.

Also, the question arises as to whether other values may be used in the matrix when the type (which is a defined term not an enumerated value) is not one of the specified types. Make these enumerated values.

Also, the same matrix is historically used in the RT Structure Set but with a different type attribute with a single defined term of HOMOGENEOUS; add a note about this too. It is not clear whether in the RT use case this should be an enumerated value, or whether the matrix should be constrained to be homogeneous too.



Correction Wording:

Amend PS 3.3 A.35:

C.20.2 Spatial Registration Module


...

Table C.20.2-1
SPATIAL REGISTRATION MODULE ATTRIBUTES


Attribute Name

Tag

Type

Attribute Description

>>Matrix Sequence

(0070,030A)

1

Specifies one transformation, that registers the Source RCS/images to the Registered RCS. It is expressible as multiple matrices, each in a separate item of the sequence.

One or more Items shall be included in this sequence.

The item order is significant and corresponds to matrix multiplication order. See C.20.2.1.1.


>>>Frame of Reference Transformation Matrix

(3006,00C6)

1

A 4x4 homogeneous affine transformation matrix that registers a homogeneous coordinate system A to B. Matrix elements shall be listed in row-major order. See C.20.2.1.1.

>>>Frame of Reference Transformation Matrix Type

(0070,030C)

1

Type of Frame of Reference Transformation Matrix (3006,00C6). Defined terms Enumerated Values:

RIGID


RIGID_SCALE

AFFINE


See C.20.2.1.2










C.20.2.1 Registration Module Attribute Descriptions

C.20.2.1.1 Frame of Reference Transformation Matrix

The Frame of Reference Transformation Matrix (3006,00C6) AMB describes how to transform a point (Bx,By,Bz) with respect to RCSB into (Ax,Ay,Az) with respect to RCSA according to the equation below.

The Matrix Registration is expressible as multiple matrices, each in a separate item of the Matrix Sequence (0070,030A). The equation below specifies the order of the matrix multiplication where M1, M2 and M3 are the first, second and third items in the sequence.



where =

Registration often involves two or more RCS, each with a corresponding Frame of Reference Transformation Matrix. For example, another Frame of Reference Transformation Matrix AMC can describe how to transform a point (Cx,Cy,Cz) with respect to RCSC into (Ax,Ay,Az) with respect to RCSA. It is straightforward to find the Frame of Reference Transformation Matrix BMC that describes how to transform the point (Cx,Cy,Cz) with respect to RCSC into the point (Bx,By,Bz) with respect to RCSB. The solution is to invert AMB and multiply by AMC, as shown below:


C.20.2.1.2 Frame of Reference Transformation Matrix Type

There are three types of Registration Matrices:

RIGID: This is a registration involving only translations and rotations. Mathematically, the matrix is constrained to be orthonormal and describes six degrees of freedom: three translations, and three rotations.

RIGID_SCALE: This is a registration involving only translations, rotations and scaling. Mathematically, the matrix is constrained to be orthogonal and describes nine degrees of freedom: three translations, three rotations and three scales. This type of transformation is sometimes used in atlas mapping.

AFFINE: This is a registration involving translations, rotations, scaling and shearing. Mathematically, there are no constraints on the elements of the Frame of Reference Transformation Matrix other than that the last row shall be (0,0,0,1) to preserve the homogeneous coordinates, so it conveys twelve degrees of freedom. This type of transformation is sometimes used in atlas mapping.



Note: The AFFINE value for Frame of Reference Transformation Matrix Type (0070,030C) has the same meaning as the use of the HOMOGENEOUS value for Frame of Reference Transformation Type (3006,00C4) in the Structure Set module. See Section C.8.8.5.

See the PS 3.17 Annex on Transforms and Mappings for more detail.



Add note to PS 3.3 A.35:

C.8.8.5 Structure Set Module


A structure set defines a set of areas of significance. Each area can be associated with a Frame of Reference and zero or more images. Information that can be transferred with each region of interest (ROI) includes geometrical and display parameters, and generation technique.

Table C.8-41—STRUCTURE SET MODULE ATTRIBUTES

Attribute Name

Tag

Type

Attribute Description









>>Frame of Reference Transformation Type

(3006,00C4)

1

Type of Transformation.

Defined Terms:

HOMOGENEOUS


>>Frame of Reference Transformation Matrix

(3006,00C6)

1

Four-by-four transformation Matrix from Related Frame of Reference to current Frame of Reference. Matrix elements shall be listed in row-major order. See C.8.8.5.2.










C.8.8.5.2 Frame of Reference Transformation Matrix

In a rigid body system, two coordinate systems can be related using a single 4 x 4 transformation matrix to describe any rotations and/or translations necessary to transform coordinates from the related coordinate system (frame of reference) to the primary system. The equation performing the transform from a point (X’,Y’,Z’) in the related coordinate system to a point (X,Y,Z) in the current coordinate system can be shown as follows, where for affine homogeneous transforms of homogeneous coordinates M41 = M42 = M43 = 0 and M44 = 1:

X M11 M12 M13 M14 X’

Y = M21 M22 M23 M24 x Y’

Z M31 M32 M33 M34 Z’

1 M41 M42 M43 M44 1

Note: The HOMOGENEOUS value for Frame of Reference Transformation Type (3006,00C4) has the same meaning as the use of the AFFINE value for Frame of Reference Transformation Matrix Type (0070,030C) in the Structure Set module. See Section C.8.8.5.

For reference unchanged, PS 3.17 Annex P Transforms and Mappings (Informative)

The Homogenous Transform Matrix is of the following form.



This matrix requires the bottom row to be [0 0 0 1].

The matrix can be of type: RIGID, RIGID_SCALE and AFFINE. These different types represent different conditions on the allowable values for the matrix elements.

RIGID:


This transform requires the matrix obey orthonormal transformation properties:

    for all combinations of j = 1,2,3 and k = 1,2,3 where delta = 1 for i = j and zero otherwise.

The expansion into non-matrix equations is:

    M11 M11 + M21 M21 + M31 M31 = 1 where j = 1, k = 1

    M11 M12 + M21 M22 + M31 M32 = 0 where j = 1, k = 2

    M11 M13 + M21 M23 + M31 M33 = 0 where j = 1, k = 3

    M12 M11 + M22 M21 + M32 M31 = 0 where j = 2, k = 1

    M12 M12 + M22 M22 + M32 M32 = 1 where j = 2, k = 2

    M12 M13 + M22 M23 + M32 M33 = 0 where j = 2, k = 3

    M13 M11 + M23 M21 + M33 M31 = 0 where j = 3, k = 1

    M13 M12 + M23 M22 + M33 M32 = 0 where j = 3, k = 2

    M13 M13 + M23 M23 + M33 M33 = 1 where j = 3, k = 3


The Frame of Reference Transformation Matrix AMB describes how to transform a point (Bx,By,Bz) with respect to RCSB into (Ax,Ay,Az) with respect to RCSA.

The matrix above consists of two parts: a rotation and translation as shown below;

Rotation: Translation:

The first column [M11,M21,M31] are the direction cosines (projection) of the X-axis of RCSB with respect to RCSA. The second column [M12,M22,M32] are the direction cosines (projection) of the Y-axis of RCSB with respect to RCSA. The third column [M13,M23,M33] are the direction cosines (projection) of the Z-axis of RCSB with respect to RCSA. The fourth column [T1,T2,T3] is the origin of RCSBwith respect to RCSA.

There are three degrees of freedom representing rotation, and three degrees of freedom representing translation, giving a total of six degrees of freedom.

RIGID_SCALE

The following constraint applies:


    for all combinations of j = 1,2,3 and k = 1,2,3 where delta = 1 for i=j and zero otherwise.

The expansion into non-matrix equations is:

M11 M11 + M21 M21 + M31 M31 = S12 where j = 1, k = 1

M11 M12 + M21 M22 + M31 M32 = 0 where j = 1, k = 2

M11 M13 + M21 M23 + M31 M33 = 0 where j = 1, k = 3

M12 M11 + M22 M21 + M32 M31 = 0 where j = 2, k = 1

M12 M12 + M22 M22 + M32 M32 = S22 where j = 2, k = 2

M12 M13 + M22 M23 + M32 M33 = 0 where j = 2, k = 3

M13 M11 + M23 M21 + M33 M31 = 0 where j = 3, k = 1

M13 M12 + M23 M22 + M33 M32 = 0 where j = 3, k = 2

M13 M13 + M23 M23 + M33 M33 = S32 where j = 3, k = 3

The above equations show a simple way of extracting the spatial scaling parameters Sj from a given matrix. The units of Sj2 is the RCS unit dimension of one millimeter.

This type can be considered a simple extension of the type RIGID. The RIGID_SCALE is easily created by pre-multiplying a RIGID matrix by a diagonal scaling matrix as follows:



where MRBWS is a matrix of type RIGID_SCALE and MRB is a matrix of type RIGID.

AFFINE:

No constraints apply to this matrix, so it contains twelve degrees of freedom. This type of Frame of Reference Transformation Matrix allows shearing in addition to rotation, translation and scaling.



For a RIGID type of Frame of Reference Transformation Matrix, the inverse is easily computed using the following formula (inverse of an orthonormal matrix):

annex.

For RIGID_SCALE and AFFINE types of Registration Matrices, the inverse cannot be calculated using the above equation, and must be calculated using a conventional matrix inverse operation.



Page




Verilənlər bazası müəlliflik hüququ ilə müdafiə olunur ©atelim.com 2016
rəhbərliyinə müraciət