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Since the size and shape of structures vary across modalities, evaluating the alignment quality can be more challenging. Thus, similarity measures such as mutual information may be used; Characterizing a population of subjects. In contrast to intra-subject registration, a one-to-one mapping may not exist between subjects, depending on the structural variability of the organ of interest. Inter-subject registration may be used for atlas construction in computational anatomy. Here, the objective may be to statistically model the anatomy of organs across subjects; Computer-assisted surgery: in computer-assisted surgery pre-operative images such as CT or MRI may be registered to intra-operative images or tracking systems to facilitate image guidance or navigation. There may be several considerations made when performing image registration: The transformation model. Common choices are rigid, affine, and deformable transformation models. B-spline and thin plate spline models are commonly used for parameterized transformation fields. Non-parametric or dense deformation fields carry a displacement vector at every grid location; this may use additional regularization constraints. A specific class of deformation fields are diffeomorphisms, which are invertible transformations with a smooth inverse; The similarity metric. A distance or similarity function is used to quantify the registration quality. This similarity can be calculated either on the original images or on features extracted from the images. Common similarity measures are sum of squared distances (SSD), correlation coefficient, and mutual information. The choice of similarity measure depends on whether the images are from the same modality; the acquisition noise can also play a role in this decision. For example, SSD may be the optimal similarity measure for images of the same modality with Gaussian noise. However, the image statistics in ultrasound may be significantly different from Gaussian noise, leading to the introduction of ultrasound specific similarity measures.

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<w:p w14:paraId="4264CAAD" w14:textId="77777777" w:rsidR="00D326F9" w:rsidRDefault="00CA420D" w:rsidP="00EE75FD"><w:pPr><w:pStyle w:val="NumberedParagraph"/><w:tabs><w:tab w:val="clear" w:pos="360"/><w:tab w:val="num" w:pos="1080"/></w:tabs><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr></w:pPr><w:r w:rsidRPr="00CA420D"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:t xml:space="preserve">Since the size and shape of structures vary across modalities, evaluating the alignment quality can be more challenging. Thus, similarity measures such as mutual information may be used; Characterizing a population of subjects. In contrast to intra-subject registration, a one-to-one mapping may not exist between subjects, depending on the structural variability of the organ of interest. Inter-subject registration may be used for atlas construction in computational anatomy. Here, the objective may be to statistically model the anatomy of organs across subjects; Computer-assisted surgery: in computer-assisted surgery pre-operative images such as CT or MRI may be registered to intra-operative images or tracking systems to facilitate image guidance or navigation. There may be several considerations made when performing image registration: The transformation model. Common choices are rigid, affine, and deformable transformation models. B-spline and thin plate spline models are commonly used for parameterized transformation fields. Non-parametric or dense deformation fields carry a displacement vector at every grid location; this may use additional regularization constraints. A specific class of deformation fields are diffeomorphisms, which are invertible transformations with a smooth inverse; The similarity metric. A distance or similarity function is used to quantify the registration </w:t></w:r><w:r w:rsidRPr="00CA420D"><w:rPr><w:rFonts w:asciiTheme="minorHAnsi" w:hAnsiTheme="minorHAnsi"/></w:rPr><w:lastRenderedPageBreak/><w:t xml:space="preserve">quality. This similarity can be calculated either on the original images or on features extracted from the images. Common similarity measures are sum of squared distances (SSD), correlation coefficient, and mutual information. The choice of similarity measure depends on whether the images are from the same modality; the acquisition noise can also play a role in this decision. For example, SSD may be the optimal similarity measure for images of the same modality with Gaussian noise. However, the image statistics in ultrasound may be significantly different from Gaussian noise, leading to the introduction of ultrasound specific similarity measures. </w:t></w:r></w:p>