# Image Registration

## Overview

Image registrations are used medically to align two image sets into a common coordinate system. Image registrations are used throughout the diagnostic and radiation therapy process.

### Components of Image Registration

**Transformation:** The method used to align the secondary image to the primary image. Transformations may be either rigid, affine, or deformed.

**Similarity Metric: **The metric which defines how well the secondary image aligns with the primary image. Similarity metrics may be as simple as a users subjective analysis or a complex scoring method such as mutual information.

### Registration Techniques

Image registration technique is defined by the 9 criteria:

- Dimensionality: either 2D or 3D
- Nature of registration basis: either extrinsic (using molds or markers as registration points) or intrinsic (using anatomical features or voxel properties) features to assess the quality of the registration (i.e. the registration metric)
- Nature of transformation: this describes the algorithm which transforms the moving image to align it with the stationary image.
- Interaction: addresses the extent to which the user is involved in the registration. This may be completely manual, completely automated, or somewhere in between.
- Optimization procedure: describes the methods used in manipulating the registration variables to achieve an optimal result.
- Modalities involved: common registration schemes involve a planning CT to a diagnostic CT, PET, SPECT, CBCT, MVCT, or ultrasound image.
- Subject/patient: image registration may be made between images of the same subject/patient (e.g. planning CT and a daily CBCT) or between different subjects (e.g. planning CT and atlas contour set)
- Object/anatomical region: appropriate image registration techinique may vary between objects being registered.

**Work cited:** Maintz JA, Viergever MA. A survey of medical image registration. *Med Image Anal. *2003;2:1-36.

## Image Transformations

**Rigid Transformation **

A transformation technique which preserves the distance between all points on the image. The only allowed operations in the alignment are *translation* and *rotation* of the entire image as a unit.

**Affine Transformation **

A transformation technique which includes the operations of a rigid registration and adds the additional transformations of *scaling, sheering *and *plane reflection*. Distance between points in the moving image are not maintained however, parallel lines remain parallel after the transformation.

**Deformation
**

A transformation in which the image can be spatially variant with a large number of degrees of freedom (up to three times the number of voxels in the data set). This transformation can completely change the shape of the object.

## Similarity Metrics

Registration metrics quantify the degree to which the pair of registered images are correctly aligned. Several registration metrics are in use and specific implementation of a metric may vary with vendor implementation.

### Geometry-based metrics

The most common geometry-based registration metrics use *point* *matching *or *surface matching*. Geometry-based metrics require image processing to assign corresponding points or contours. These points/contours may represent either physical anatomical features (as in atlas-based or manual contouring) or may be an edge defined by a gradient rate or Chamfer matching. With chamfer matching, the image is converted to a binary map (values of 0 or 1) – the edge of which defines the surface.

##### Point Matching

**Point Matching**, the difference in the distance separating well defined points in each image are summed and normalized to the total number of such points, as in the below equation where * d_{n} *is the distance between corresponding well defined points.

##### Surface Matching

**Surface Matching **operates similarly to *point matching *but does not require a defined point by point relationship along each surface. Rather, the metric assesses the squared distance from each point on the surface in image A to *the closest* on the surface in image B, as in the below equation. * d(p_{n}, S)_{min}* is the minimum distance from point n on surface A to the closest point on surface B.

##### Dice's Coefficient

**Dice’s Coefficient:** A statistical method of comparing the similarity between two samples. It is calculated as the ratio of the overlapping portions of a structure in each image to the total volume of the structure in each image.

### Intensity based metrics

Intensity based metrics, sometimes referred to as *similarity metrics* determine the similarity of corresponding voxel intensities in an image registration.

**Sum of Squared Differences (SSD) **seeks to minimize the average squared intensity difference between registered sets.

**Cross Correlation (C) **seeks to maximize the sum of product of corresponding voxel intensities.

**Mutual Information (MI): **both *Sum of Square Differences* and *Cross Correlation* have difficulties in registering images sets of differing modalities because of the large differences of intensity between the same structure in each image. *Mutual information *overcomes this limitation by seeking to pair voxels of a given intensity in image A with voxels of a corresponding but uniform, but not necessarily similar, intensity in image B. That is, mutual information is able to consider matching all light voxels in image A to all dark voxels in image B provided that the shape and size of the voxel areas is similar.

**Jacobian Determinant**

The Jacobian Determinant can be a useful metric for identifying errors in deformable registrations. The determinant identifies local volume change as a result of registration and outputs a numerical value corresponding to the vector field of deformation.

Jacobian Determinant | Indication |

>1 | volume expansion |

1 | no changes |

between 0 and 1 | volume reduction |

≤0 | non-physical motion (region folded in on itself) |

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