What does ADHT mean in UNCLASSIFIED

ADHT is a geometric transformation that scales and rotates a shape by varying amounts at different angles. It combines the properties of homothety (scaling) and rotation, resulting in a deformed shape that differs from both the original shape and a simple dilation or rotation.

Homothety scales a shape uniformly in all directions, while rotation preserves the shape's size but alters its orientation. ADHT, however, scales and rotates the shape differently at different angles, creating a more complex deformation.

ADHT is used in various fields, including computer vision, medical imaging, and shape analysis. It can be employed for image registration, feature extraction, and deformation modeling. For example, in medical imaging, ADHT is used to align and compare medical images taken at different angles or time points.

ADHT is represented by a matrix transformation. The matrix contains scaling coefficients and rotation angles that vary depending on the angle of rotation. The transformation equation is typically expressed as follows:

[x' y'] = [s(θ)cos(θ) s(θ)sin(θ)] [x y]

where [x y] is the original point, [x' y'] is the transformed point, s(θ) is the scaling factor at angle θ, and θ is the rotation angle.

ADHT can only be applied to shapes that can be represented by a continuous function. Additionally, it assumes that the scaling and rotation variations are smooth and continuous, which may not always be the case in real-world applications.