This paper presents a detailed error analysis of geometric hashing for 2D object recogition. We analytically derive the probability of false positives and negatives as a function of the number of model and image, features and occlusion, using a 2D Gaussian noise model. The results are presented in the form of ROC (receiver-operating characteristic) curves, which demonstrate that the 2D Gaussian error model always has better performance than that of the bounded uniform model. They also directly indicate the optimal performance that can be achieved for a given clutter and occlusion rate, and how to choose the thresholds to achieve these rates.

The main aim of 3D Object recognition is to recognize objects under translation and rotation. Geometric Hashing is one of the methods which represents a rotation and translation invariant approach and provides indexing of structural features of the objects in an efficient way. In this thesis, Geometric Hashing is used to store the geometric relationship between discriminative surface properties which are based on surface curvature. In this thesis surface is represented by shape index and splash where shape index defines particular shaped surfaces and splash introduces topological information. The method is tested on 3D object databases and compared with other methods in the literature.

3D object recognition is performed by using geometric hashing where transformation and scale invariant 3D surface features are utilized. 3D features are extracted from object surfaces after a scale space search where size of each feature is also estimated. Scale space is constructed based on orientation invariant surface curvature values which classify each surface point&#039 / s shape. Extracted features are grouped into triplets and orientation invariant descriptors are defined for each triplet. Each pose of each object is indexed in a hash table using these triplets. For scale invariance matching, cosine similarity is applied for scale variant triple variables. Tests were performed on Stuttgart database where 66 poses of 42 objects are stored in the hash table during training and 258 poses of 42 objects are used during testing. %90.97 recognition rate is achieved.