**4. Object's contour**

112 Advances in Object Recognition Systems

the FuzzyARTMAP ANN is given in Section 7 followed by Section 8 that describes the results of the proposed integrated approach. Finally, conclusions and future work is

Some authors have contributed with techniques for invariant pattern classification using classical methods such as invariant moments (Hu, 1962); artificial intelligence techniques, as used by Cem Yüceer & Kemal Oflazer (Yüceer and Oflazer, 1993) which describes a hybrid pattern classification system based on pattern pre-processor and an ANN invariant to rotation, scaling and translation. Stavros J. & Paulo Lisboa developed a method to reduce and control the number of weights of a third order network using moment classifiers (Stavros and Lisboa, 1992) and Shingchern D. You & G. Ford proposed a network for invariant object recognition of objects in binary images using four sub-networks (Shingchern and Ford, 1994). Montenegro used the Hough transform to invariantly recognize rectangular objects (chocolates) including simple defects (Montenegro, 2006). This was achieved by using the polar properties of the Hough transform, which uses the Euclidian distance to classify the descriptive vector. This method showed to be robust with geometric figures, however for complex objects it would require more information coming from other techniques such as histogram information or information coming from images with different illumination sources and levels. Gonzalez et al. used a Fourier descriptor, which obtains image features through silhouettes from 3D objects (Gonzalez Garcia, et al., 2004). Their method is based on the extraction of silhouettes from 3D images obtained from laser scan, which increases recognition times. Another interesting method for 2D invariant object representation is the use of the compactness measure of a shape, sometimes called the shape factor, and which is a numerical quantity representing the degree to which a shape is compact. Relevant work in this area within the theory of shape numbers was proposed by

Worthington studied topographical information from image intensity data in grey scale using the Shape from Shading (SFS) algorithm (Worthington and Hancock, 2001). This information is used for object recognition. It is considered that the shape index information can be used for object recognition based on the surface curvature. Two attributes were used, one was based on low-level information using curvature histogram and the other was based on structural arrangement of the shape index maximal patches and its attributes in the associated region.

Lowe defines a descriptor vector named SIFT (Scale Invariant Feature Transform), which is an algorithm that detects distinctive image points and calculates its descriptor based on the histograms of the orientation of key points encountered (Lowe, 2004). The extracted points are invariants to scale, rotation as well as source and illumination level changes. These points are located within a maximum and minimum of a Gaussian difference applied to the space scale. This algorithm is very efficient, but the processing time is relatively high and

Classic algorithms such as moment invariants are popular descriptors for image regions and boundary segments; however, computation of moments of a 2D image involves a significant

described in Section 9.

Bribiesca and Guzman (Bribiesca and Guzman, 1980).

furthermore the working pieces have to have a rich texture.

**3. Original work** 

**2. Related work** 

As mentioned earlier, the Boundary Object Function (BOF) method considers only the object's contour to recognise different objects. It is very important to obtain as accurately as possible, metric properties such as area, perimeter, centroid point, and distance from the centroid to the points of the contour of the object. In this section, a description of the BOF method is presented.
