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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