**6. Histogram of disparity map (depth)**

118 Advances in Object Recognition Systems

Koenderink separated the shape index in different regions depending on the type of curvature, which is obtained through the eigenvalues of the Hessian matrix, which is represented by K1

The result of the shape index φ has values between [-1, 1] which can be classified, according

Saddle

Figure 5 shows the image from the surface local form depending on the value of the Shape Index, and Figure 6 shows an example of the SFS vector from a rectangular piece used

rotation of the normals involve several iterations represented by the letter k.

and K2 as given by the following equation (Koenderink &. Van Doorn, 1992).

to Koenderink, depending on its local topography, as shown in table 1.

tan�� k� � k� k� � k�

� � 2 π

rut

3 1 , 8 8 

Fig. 5. Representation of local forms in the Shape Index classification.

Cup Rut Saddle

5 3 , 8 8 

Table 1. Classification of the Shape Index

Fig. 6. SFS Vector Descriptor Example

�� are the normals after the smoothness and before

; k� � k� (8)

Ridge Ridge Dome

3 5, 8 8 

5 ,1 8 

��� are the normals after a rotation of θ degrees. The smoothness and

Point Plane Saddle

8 8 


Where n���

the rotation, and n���

**5.4 Shape index** 

5 1, 8 

during experiments.

� are the smoothed normals, n���

With binocular vision, the vision system is able to interact in a three-dimensional world coping with volume and distance within the environment. Due to the separation between both cameras, two images are obtained with small differences between them; such differences are called disparity and form a so-called disparity map. The epipolar geometry describes the geometric relationships of images formed in two or more cameras focused on a point or pole.

The most important elements for this geometric system as illustrated in figure 7 are: the epipolar plane, consisting of the pole (P) and two optical centres (O and O') from two chambers. The epipoles (e and e') are the virtual image of the optical centres (O and O'). The baseline, that join the two optical centres and epipolar lines (l and l'), formed by the intersection of the epipolar plane with both images (ILEFT and IRIGHT) connects the epipoles with the image of the observed points (p, p').

Epipolar line is crucial in stereoscopic vision, because one of the most difficult parts in stereoscopic analysis is to establish the correspondence between two images, mating stereo, deciding which point in the right image corresponds to which on the left.

The epipolar constraint allows you to narrow the search for stereoscopic, correspondence of two-dimensional (whole image) to a search in a dimension on the epipolar line.

Fig. 7. Elements of epipolar geometry.

One way to further simplify the calculations associated with stereoscopic algorithms is the use of rectified images; that is, to replace the images by their equivalent projections on a common plane parallel to the baseline. It projects the image, choosing a suitable system of coordinates, the rectified epipolar lines are parallel to the baseline and they are converted to single-line exploration.

In the case of rectified images, given two points p and p', located on the same line of exploration the left image and right image, with coordinates (u, v) and (u', v'), the disparity

The Use of Contour, Shape and Form in an Integrated Neural Approach for Object Recognition 121

For the specific case of the work presented in this article, the input information is concatenated and presented as a sole input vector A, while the vector B receives the

The experimental results were obtained using two sets of four 3D working pieces of different cross-section: square, triangle, cross and star. One set had its top surface rounded, so that these were referred to as being of rounded type. The other set had a flat top surface

Rounded-Square (RSq) Pyramidal-Square (PSq)

Rounded-Triangle (RT) Pyramidal-Triangle (PT)

correspondence associated to the respective component, during the training process.

and referred to as pyramidal type. The working pieces are showed in figure 9.

Fig. 8. FuzzyARTMAP Architecture

**8. Experimental results** 

is given as the difference d = u'- u. If B is the distance between the optical centres, also known as baseline, it can be shown that the depth of P is z = −B / d.
