Overview
• • Registrationinvolves finding a
transformation to align one dataset with
another.
• • Transformations include rotation,
translation, and scaling.
• • Applications:
• - Aligning MRI images for surgeries
• - Object detection in aerial images
3.
Types of RegistrationProblems
• 1. **Rigid Objects:**
• - Transformations: Rotation, Translation,
Scaling
• - Example: Aligning 3D object scans
• 2. **Projection Registration:**
• - Aligning 3D objects with 2D images
• - Uses camera consistency
• 3. **Deformable Objects:**
• - Complex transformations for flexible
4.
Registering Rigid Objects
•• Given two point sets:
• - Source set: S = {xi}
• - Target set: T = {yj}
• • Goal: Compute rotation (R), translation (t),
and scale (s).
• • Minimization formula:
• Minimize Σ || sR(θ)xi + t - yc(i) ||²
• • Horn's Algorithm:
• - Translation: Derived from centroids
5.
Challenges in RigidRegistration
• • No one-to-one correspondence between S
and T.
• • Outliers and noise in datasets.
• • Sampling errors may prevent accurate
moment estimation.
• • Strategies:
• - Iterative estimation of correspondences and
transformations.
• - Using small groups of features for
transformation estimation.
6.
Key Equation forRegistration
• G(s, θ, t)S = {sR(θ)xi + t | xi S}
∈
• • At the solution:
• - Most points in G(s, θ, t)S lie close to points
in T.
• - Correspondences emerge naturally.
7.
Projection Registration
• •Aligning 3D objects with their 2D
projections.
• • Uses camera consistency:
• - All image features are from the same
camera view.
• • Steps:
• 1. Identify feature correspondences.
• 2. Estimate pose and camera calibration.
• 3. Confirm using other features.
8.
Deformable Object Registration
•• Challenges:
• - Large family of possible transformations.
• - Requires advanced search techniques.
• • Applications in medical imaging:
• - Aligning flexible human organs.
• - Handling multi-modal imaging data.
