Geometric computation for machine vision

A 2D geometric model is a geometric model of an object as a two-dimensional figure, usually on the Euclidean or Cartesian plane.

Geometric feature learning is a technique combining machine learning and computer vision to solve visual tasks.
The main goal of this method is to find a set of representative features of geometric form to represent an object by collecting geometric features from images and learning them using efficient machine learning methods.
Humans solve visual tasks and can give fast response to the environment by extracting perceptual information from what they see.
Researchers simulate humans' ability of recognizing objects to solve computer vision problems.
For example, M.
Mata et al.(2002) applied feature learning techniques to the mobile robot navigation tasks in order to avoid obstacles.
They used genetic algorithms for learning features and recognizing objects (figures).
Geometric feature learning methods can not only solve recognition problems but also predict subsequent actions by analyzing a set of sequential input sensory images, usually some extracting features of images.
Through learning, some hypothesis of the next action are given and according to the probability of each hypothesis give a most probable action.
This technique is widely used in the area of artificial intelligence.

In computer science, geometric hashing is a method for efficiently finding two-dimensional objects represented by discrete points that have undergone an affine transformation, though extensions exist to other object representations and transformations.
In an off-line step, the objects are encoded by treating each pair of points as a geometric basis.
The remaining points can be represented in an invariant fashion with respect to this basis using two parameters.
For each point, its quantized transformed coordinates are stored in the hash table as a key, and indices of the basis points as a value.
Then a new pair of basis points is selected, and the process is repeated.
In the on-line (recognition) step, randomly selected pairs of data points are considered as candidate bases.
For each candidate basis, the remaining data points are encoded according to the basis and possible correspondences from the object are found in the previously constructed table.
The candidate basis is accepted if a sufficiently large number of the data points index a consistent object basis.