Shepp–Logan phantom
# Shepp–Logan phantom

The Shepp–Logan phantom is a standard test image created by Larry Shepp and Benjamin F. Logan for their 1974 paper The Fourier Reconstruction of a Head Section. It serves as the model of a human head in the development and testing of image reconstruction algorithms.

## Definition

The function describing the phantom is defined as the sum of 10 ellipses inside a 2×2 square:

| Ellipse | Center | Major Axis | Minor Axis | Theta | Gray Level |
| - | - | - | - | - | - |
| a | (0,0) | 0.69 | 0.92 | 0 | 2 |
| b | (0,−0.0184) | 0.6624 | 0.874 | 0 | −0.98 |
| c | (0.22,0) | 0.11 | 0.31 | −18° | −0.02 |
| d | (−0.22,0) | 0.16 | 0.41 | 18° | −0.02 |
| e | (0,0.35) | 0.21 | 0.25 | 0 | 0.01 |
| f | (0,0.1) | 0.046 | 0.046 | 0 | 0.01 |
| g | (0,−0.1) | 0.046 | 0.046 | 0 | 0.01 |
| h | (−0.08,−0.605) | 0.046 | 0.023 | 0 | 0.01 |
| i | (0,−0.605) | 0.023 | 0.023 | 0 | 0.01 |
| j | (0.06,−0.605) | 0.023 | 0.046 | 0 | 0.01 |
