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I. Introduction
An object recognition system finds an object in the real world from an image of the world, using object models which are known priori [9]. The process of recognition is one of the hardest problems in computer vision. Although human can perform object recognition effortlessly and instantaneously, an algorithmic description of this task for implementation on machine has been very difficult especially in case of 3-D objects. In robotics application such as object grapping or manipulation, efficient 3D object recognition will assist in faster identification and localization process for real-time dynamic arm motion control.

In general most model based object recognition system considers the problem of recognizing objects from the image of a single view [2][5][22]. However, a single view may not contain sufficient features to recognize the object.

In addition, it required complex feature sets and this make the recognition process time consuming [7][22]. To overcome this problem, modeling 3D object recognition using multiple 2D views was proposed by some researchers. It summarised the set of possible 2D appearances of a 3D object. Some of the early studies such as use of aspect graph was proposed by Koenderink and van Doorn [13]. An aspect graph represents all stable 2D views of a 3D object. However, the extraordinarily large in size and complexity of aspect graphs for even simple object has hindered the use of this method. Edelman and Bulthoff [4] found a strong and stable correlation between recognition performance and viewpoint variation and suggest object representations by multiple viewpoint specifically 2D representations. Murase and Nayar [17] and Nene [18] developed a parametric eigenspace method to recognize 3D objects directly from their appearance. This technique however is not robust to occlusion and do not provide indication on how to optimize the size of the database with respect to the types of objects considered for recognition and their respective eigenspace dimensionality.

Recently, some papers have proposed an effective recognition algorithm using neural networks. The advantage of this model is the ability to learn from a training data set and perform a prediction of the other dataset. Lin et. al. [15], Nasrabadi and Li [19] used Hopfield neural networks for their 3D object recognition system.

Compare with conventional 3D object recognition, it provides a more general and parallel implementation paradigm. Lu et al. [16] recognized 3D objects using a back-propagation algorithm, which has been commonly used in pattern recognition applications. Other works using neural networks such as Foresti and Pieroni [6] used neural tree (NT), Ham and Park [7] used hidden Markov modelbasedsystem combined with neural networks and Carpenter and Ross [3] used ART-EMAP networks. However, the use of neuro-fuzzy system; a combination of neural network and fuzzy system, is not widely used in 3D object recognition. In this paper, we used a type of neuro-fuzzy system called Multiple Adaptive Network based Fuzzy Inference System (MANFIS) to perform 3D object recognition.

II. System Overview
In this section, a methodology for image acquisition and data extraction is presented. A 3D object recognition system using multiple views was developed. The system aims to recognize 3D objects which are stand alone, separated and are independent to each other. The possible object and camera set-up for the proposed system is illustrated in Fig. 1. turntable. Three B/W CCD cameras are used to capture the images simultaneously from different viewpoints (different angle).

These cameras are fixed at the same height (y coordinate), at 450 from the center of turntable. The cameras must have same focal length and distance from the center of turntable. The angle that separated camera 1 and camera 2, camera 2 and camera 3 are fixed at 450. We assumed that the location of camera 1 as a reference point (scene at 00).

For the first condition, camera 1 views the scene at 00, camera 2 views the scene at 450 and camera 3 views the scene at 900. Fig. 6 shows an example of images taken from the cameras at the reference points. Next, the object will be rotated 50 clockwise to get the second condition. At this condition, camera 1 views the scene at 50, camera 2 views the scene at 500 and camera 3 views the scene at 950. For image acquisition process, each object will be rotated 3600 and images will be captured for each 50 rotation. Hence, for each object, we will have 72 conditions after a complete 3600 rotation. Captured images are then digitized by the DT3155 frame grabber from Data Translation Inc. and set to the pre-processing and feature extraction stage. In this study, moment invariants are used as a feature as it is invariants with position, orientation and scale changes. The algorithm has been commonly used in pattern recognition because it explains geometrical properties of an object.


Figure 1: Image acquisition set-up

Figure 2: System configuration
Furthermore it takes short processing time as the algorithm is simple. Some works using moment descriptions and its properties can be found in [7, 14, and 21]. All the features extracted from various viewpoints will be presented as an input for the recognition stage. Fig. 2 depicts the overall proposed system. The invariance properties of moments of 2-D and 3-D shapes have received considerable attention in recent years. They are useful as they define a simply calculated set of region properties that can be used for shape classification and part recognition. Hu [8] derived a set of invariants based on combinations of regular moments using algebraic invariants. These invariants are invariant under change of size, translation and rotation. In this work, the first moment invariant is selected to be used as suggested in [23].

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