A MULTILAYER HOPFIELD NEURAL NETWORK FOR 3-D 
OBJECT RECOGNITION 
Zhuowen Tu and Ron Li 
Department of Civil and Environmental Engineering and Geodetic Science 
The Ohio State University 
USA 
tu.37@osu.edu 
KEY WORDS: Hopfield neural network, 3-D object recognition, back-projection, 2-D image 
ABSTRACT 
To recognize 3-D objects in aerial images, a two-layer Hopfield neural network that matches extracted edges and regions in images with 
back-projected edges and regions from object models is applied. The interconnection between the line layer and the region layer gives 
strong geometric constraints that force the system to converge to a stable situation if initial values of neuron states are appropriately 
selected. The algorithm is demonstrated by its use in recognition of trucks from aerial images georeferenced by GPS and INS. 
1. INTRODUCTION 
The problem of three dimensional object recognition has been 
studied for many years. Today, we are still challenged by the 
question: "How does the human visual system represent three 
dimensional objects for recognition?" (Bulthoff et al. 1994). 
Different endeavors to answer this question, however, yield 
different achievements of 3-D object recognition systems. For 
example, the viewpoint invariants matching strategy is under 
the assumption that 3-D object is represented in brain by 3-D 
invariants such as relative orientation, collinearity, parallelism 
etc., while viewpoint dependent solution tries to match image 
features with 2-D features stored in database in terms of 
different point of views. In Ullman and Basri (1991), all the 
views of a given rigid object can be represented by linear 
combinations of several views under an orthographic projection 
in which extracted 3-D invariants match with those of a model 
by alignment. In Lin et al. (1991) 3-D geometric invariants, 
specifically, areas and relational distances, are matched with 
those of a model using Hopfield neural network. Properties of 
vanishing points are well used in Shufelt (1996) to recognize 
buildings in airborne images. More published papers are 
dealing with 2-D images of 3-D objects because 3-D invariants 
are quite difficult to obtain in most cases. Clemens (1991) and 
Jacobs (1992) gave a framework of how indexing and grouping 
are applied to recognize 3-D objects in 2-D images while 
keeping searching space small. Interest points in images are 
matched with those of candidate model over affine 
transformations in Lamdan et al. (1990). Pontil and Verri 
(1998) introduced a Support Vector Machine that builds the 
optimal hype-plane dividing linearly separable samples. Cohen 
and Wang (1994) and Wang and Cohen (1994) recognized 
objects from 3-D curves under affine transformation using B- 
splines that conserve some useful properties like view 
invariants. The difficulty of recognition of 3-D objects in 2-D 
images lies in that there are infinite number of 2-D candidates, 
sometimes occluded or deformed, formed by even a single 3-D 
object in different views. Hopfield neural networks (Hopfield 
and Tank 1985) are one of solutions of object recognition as an 
optimization problem when a minimization of Lyapunov 
energy is reached. The global minimum can be obtained when 
initial values are carefully selected. Lin et al. (1991) described 
a hierarchical approach in which a coarse-to-fine strategy is 
addressed to match 3-D object. Suganthan et al.(1995a and 
1995b) introduced a new way of selecting initial states of 
neurons and connection matrix together with annealing method. 
Young et al. (1997) addressed a multilayer Hopfield network 
through pyramid images. In this paper, extracted edges and 
regions are matched with edges and regions back-projected 
from a 3-D model through the known absolute position and 
attitude of the image derived from GPS and INS data. The 
algorithm presented here differs from the above methods in that 
both edges and regions of input features are matched to those 
of the model simultaneously through the constraints in each 
layer and the interconnection between them. More details of 
recognition of 3-D objects from mobile mapping data using 
Hopfield neural networks is addressed in Li et al. (1998a). In 
this paper we first introduce the general concept of Hopfield 
neural networks. A two layer Hopfield neural network 
incorporating edge layer and region layer is then described. 
Finally, an experiment of the application of a two layer 
Hopfield neural network in truck recognition is presented. 
2. SINGLE LAYER HOPFIELD NEURAL NETWORK 
Object recognition by graph matching, also referred to as 
morphism, is a mapping from a scene graph to a model graph. 
The morphism can be categorized on the basis of the 
constraints that are enforced during the mapping as follows: 
when the mapping is one-to-one and onto, it is an isomorphism; 
when it is one-to-one, it is a monomorphism; and when it is 
many-to-one, it is a homomorphism. Figure 1 gives a basic 
framework of the Hopfield neural network. 
k Input features 
Figure 1. Neuron states and candidate model-input features 
correspondence. 
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