Материал: part17

Figure O.4-1. Spatial Registration Encoding​

Figure O.4-2 shows an information model of a Deformable Spatial Registration to illustrate the relationship of the Attributes to the​ objects of the model. The DICOM Attributes that describe each object are adjacent to the object.​

Figure O.4-2. Deformable Spatial Registration Encoding​

Figure O.4-3 shows a Spatial Fiducials information model to illustrate the relationship of the Attributes to the objects of the model.​ The DICOM Attributes that describe each object are adjacent to the object.​

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Figure O.4-3. Spatial Fiducials Encoding​

O.5 Matrix Registration​

A4x4affinetransformationmatrixdescribesspatialrotation,translation,scalechangesandaffinetransformationsthatregisterreferenced​ images to the Registration IE's homogeneous RCS. These steps are expressible in a single matrix, or as a sequence of multiple in-​ dependent rotations, translations, or scaling, each expressed in a separate matrix. Normally, registrations are rigid body, involving​ only rotation and translation. Changes in scale or affine transformations occur in atlas registration or to correct minor mismatches.​

O.6 Spatial Fiducials​

Fiducials are image-derived reference markers of location, orientation, or scale. These may be labeled points or collections of points​ in a data volume that specify a shape. Most commonly, fiducials are individual points.​

Correlated fiducials of separate image sets may serve as inputs to a registration process to estimate the spatial registration between​ similar objects in the images. The correlation may, or may not, be expressed in the fiducial identifiers. A fiducial identifier may be an​ arbitrary number or text string to uniquely identify each fiducial from others in the set. In this case, fiducial correlation relies on oper-​ ator recognition and control.​

Alternatively, coded concepts may identify the acquired fiducials so that systems can automatically correlate them. Examples of such​ coded concepts are points of a stereotactic frame, prosthesis points, or well-resolved anatomical landmarks such as bicuspid tips.​ Such codes could be established and used locally by a department, over a wider area by a society or research study coordinator, or​ from a standardized set.​

The table below shows each case of identifier encoding. A and B represent two independent registrations: one to some image set A,​ and the other to image set B.​

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Fiducials may be a point or some other shape. For example, three or more arbitrarily chosen points might designate the inter-hemi-​ spheric plane for the registration of head images. Many arbitrarily chosen points may identify a surface such as the inside of the skull.​

A fiducial also has a Fiducial UID. This UID identifies the creation of the fiducial and allows other SOP Instances to reference the fi-​ ducial assignment.​

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P Transforms and Mappings (Informative)​

The Affine Transform Matrix is of the following form.​

This matrix requires the bottom row to be [0 0 0 1] to preserve the homogeneous coordinates.​

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 δ = 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:​

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Page 190​ DICOM PS3.17 2020a - Explanatory Information​

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]arethedirectioncosines(projection)oftheY-axisofRCSB withrespecttoRCSA. Thethirdcolumn[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 RCSB​ with 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:​

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:​

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