In any computer vision (CV) application involving the recognition or the detection of ``objects", descriptions of the types of objects to be recognized are required. Object descriptions can be explicitly supplied by a human ``expert". Alternatively, machine learning techniques can be used to derive descriptions from example objects.
There are some advantages to learning object descriptions from examples rather than from direct specification by an expert. Specifically, it may be difficult for a person to provide a CV system with an accurate description of an object that is general enough to cover the possible variations in the visual appearance of different instances of the object. For example, no two tumors in medical images will look exactly the same. Similarly, it would be cumbersome for a human to provide a CV system with the ranges of possible values for all the different physical aspects of chairs (i.e., What are the possible surface areas of the seating surface of a chair? How is the seating surface supported?). Considerable ``tweaking" of the object description parameters may be required by a human expert in order to achieve satisfactory system performance. Machine learning techniques can be used to generate concepts that are consistent with observed examples. Some examples of such learning systems include C4.5 [Quinlan1992], and AQ [Michalski1983]. System performance is affected by the ratio of the number of training examples to the number of features used to describe the examples, and the accuracy with which the examples represent the ``real-world" objects the CV system may encounter.
A function-based object recognition system is an example of a CV system for which machine learning techniques can be useful in the development of object descriptions. A function-based object recognition system recognizes an object by classifying it into one or more generic object categories which describe the function that the object might serve [Bogoni Bajcsy1993,Brand1993,Di Manzo, Trucco, Giunchiglia, Ricci1989,Kise, Hattori, Kitahashi, Fukunaga1993,Rivlin, Rosenfeld, Perlis1993,Stark Bowyer1991,Stark Bowyer1994,Sutton, Stark, Bowyer1993,Vaina Jaulent1991]. Each object category is defined in terms of the functionality required of an object that belongs to the category. For example, an object category might be defined as: straight_back_chair ::= provides_sittable_surface & provides_stability & provides_back_support
indicating that an object can be classified as a straight back chair to the degree that it satisfies the conjunction of the three functional properties.
The functional properties are themselves defined in terms of primitive evaluations of different aspects of an object's shape. For example, candidate surfaces may be checked for provides_sittable_surface by evaluating whether they have appropriate width, depth and height above the support plane. In many cases, there is not a unique ideal value for some given aspect of an object's shape, but instead there is a range of values that can be considered equivalent in terms of ``goodness". For example, anything between 0.45 to 0.55 meters might be an equally acceptable height for a seating surface. However, as a particular shape measurement becomes too small or too large, the evaluation measure should be reduced. Fuzzy set theory provides a mathematical framework for handling this ``goodness of fit" concept. In our case, a fuzzy membership function transforms a physical measurement (i.e., height of an object's surface above the ground) into a membership value in the interval [0,1]. This membership value, or evaluation measure, denotes the degree to which the object (or portion of the object) fits the primitive physical concept (i.e., how well the height of the surface matches the seating surface height of typical chairs). Thus, a separate measure of goodness is produced for each primitive evaluation. These measures are combined to produce a final aggregate measure of goodness for the object.
The GRUFF system [Stark Bowyer1991] is a function-based object recognition system which utilizes fuzzy logic, in the manner just described, to evaluate 3-D shapes. In previous versions of GRUFF, the fuzzy membership functions embedded in the system have been collectively hand-crafted and refined to produce the best results over a large set of example shapes. These membership functions are ideal candidates to be learned from examples using a machine learning approach.
In this paper, we present a method of automatically learning the collection of fuzzy membership functions from a set of labeled example shapes. Due to the system constraints imposed by GRUFF, general-purpose machine learning algorithms, such as neural networks, genetic algorithms, or decision trees, are not readily applicable. Thus, a new special-purpose learning component, called OMLET, has been developed. OMLET is tested with synthetic data for two different object categories (chairs and cups), and with data collected from human evaluations of physical chairs. Results are presented to show that (a) learning the membership functions in this way provides a level of recognition performance equivalent to that obtained from the ``hand-tweaked" GRUFF, and (b) the learning method is compatible with human interpretation of the shapes. The approach should be generally applicable to any system in which a set of primitive evaluation measures is combined to produce an overall measure of goodness for the final result.
This paper is organized as follows. Section 2 discusses some related work, and justifies our need to develop a special-purpose learning component. Section 3 introduces the GRUFF object recognition system. Section 4 presents the new learning component, called OMLET. At this point, we should state that the material in Section 3 has previously been published, and is presented here to facilitate an understanding of the new learning component. Although OMLET has been specifically ``tailored" as an add-on learning component for the GRUFF system, it applies to a data structure that can be used in other systems. In general, OMLET can be described as a system for learning in the context of a fuzzy AND/OR categorization tree. We point the reader with any questions concerning GRUFF'S object recognition paradigm to the references provided. Section 5 describes our experimental design and the data sets that are utilized. Section 6 documents the experimental results and gives our analysis of them. Finally, in Section 7 a summary of the paper is given and conclusions are drawn.