# Shape Operations

## Surface Curvature Page

There must be a surface in the main window and this main window surface is used for the curvature measurements. To view the curvature, select shape as one of the surface overlays.

The algorithm used by Caret for computing curvature is based upon Interactive Texture Mapping by J. Maillot, Yahia, and Verroust, 1993, ACM-0-98791-601-8/93/008, http://portal.acm.org/citation.cfm?id=166120.

### Curvatures

• Folding (Mean Curvature) - If selected, mean curvature is calculated for the Main Window surface.
• Gaussian Curvature - If selected, gaussian curvature is calculated for the Main Window surface.
• K1 - Principle Curvature - The greatest value of the two principal curvatures at each node.
• K2 - Principal Curvature - The least value of the two principal curvatures at each node.

Note: Mean Curvature = ((K1 + K2) / 2), Gaussian Curvature = (K1 * K2).

### Options

• Replace Existing Columns If selected, previous curvature measurements in the Surface Shape File are replaced with newly calculated values (providing the Surface Shape Column Names are the same).

## Surface Distortion Page

Compute distortion, differences in triangles areas and edge lengths between two surfaces.

### Surface Distortion Page

The distortion measurements are from taking ratios of the Surface divided by the Reference Surface.

• Reference Surface The reference surface.
• Surface The surface.
• Areal Distortion - Measures differences in triangle areas. The distortion for a triangle is $\frac{\ln(\frac{Area}{RefArea})}{\ln(2)}$. The areal distortion at each node is the average of the triangle distortions that have the node as a vertex.
• Linear Distortion - Measures differences in triangle edge lengths. The distortion for a triangle edge is $\frac{Length}{RefLength}$. The linear distortion at each node is the average of the edges that have the node as a vertex.

### Options

• Replace Existing Columns If selected, previous distortion measurements in the Surface Shape File are replaced with newly calculated values (providing the Surface Shape Column Names are the same).

## Surface Sulcal Depth

Sulcal Depth is the depth (or distance) from the Cerebral Hull Surface to the Anatomical Surface.

### Anatomical Surface File

The anatomical surface.

### Cerebral Hull Surface File

The cerebral hull surface.

### Depth Measurements

• Depth Distance from the Cerebral Hull Surface to each node in the Anatomical Surface.
• Smoothed Depth A smoothed variant of Depth.

### Smoothing

• Hull Smoothing The Cerebral Hull Surface is smoothed this number of interations.
• Depth Smoothing The Smoothed Depth measurement is created by smoothing the Depth measurements this number of iterations.

### Options

• Create Hull Surface Creates a hull surface for the subject with the same number of nodes as the Anatomical Surface.
• Replace Existing Columns If selected, previous depth measurements in the Surface Shape File are replaced with newly calculated values (providing the Surface Shape Column Names are the same).