approach has several major advantages over other methods on
DSM data. Firstly, segmentation is achieved mainly by local
computation. Secondly, unlike other artificial neural network
approaches, it does not ask for training data. Thirdly, this
neural oscillator network need not always produce periodic
behavior (Wang, 2007). Finally, the neural oscillator network
approach is a dynamic system with parallel and neutrally
implementable computation (Wang and Terman, 1997). Thus,
we use LEGION scheme to address the problem with no
assumption about the underlying structures in DSM data and no
prior knowledge regarding the number of regions to extract
building objects.
LEGION is a network of Terman-Wang oscillators which
comprise a large class of nonlinear dynamic systems, and arise
naturally from neuron-physiological systems(Wang and
Terman, 1995). Based on temporal correlation theory, LEGION
can address the binding problem by using a biologically
plausible representation. Each oscillator in the LEGION
network connects excitatorily with the oscillators in its
neighborhoods as well as inhibitorily with a global inhibitor.
2.1 Original LEGION Algorithm
The basic unit of LEGION is a relaxation oscillator defined as a
feedback loop between an excitatory variable xi and an
inhibitory yi, where x-nullcline is a cubic function and the y-
nullcline is a sigmoid function. It is described as follow.
x -23x-x -2-y -LH(p,-0)*-8,* p (1)
y, =e(y(1+ tanh(x, / B)) — y,)
In this formula, li represents external stimulation to the
oscillator. H(p;-6), a Heaviside function, distinguishes a major
oscillator block to address the fragmentation problem. p; is the
potential of the oscillator i and 8 is a threshold, where 0«0« I. p
denotes the amplitude of Gaussian noise. e defines a typical
relaxation oscillator with two time scales. The parameter y
controls the time which the oscillator spends in these two
phases, B control the gradient of the sigmoid. The coupling
term S; provides the overall input from neighboring oscillators
in the network:
a S, 2S? -W.H(z -0,) Q)
# js the total coupling from the adjacent active neighbors of
oscillator to accomplish the binding problem . The original is
defined summation in Eq.(3).
S* = = W,H(x,) G)
keN(i)
Where JW, defines the dynamic connection weight from
oscillator k to i and N(i) represents a set of oscillators that
comprises the neighborhood of it. H stands for the Heaviside
step function.
zis a threshold, and W. is the weight of inhibition from the
global inhibitor, whose activity is governed by the equation:
2=@(0,-z) (4)
Where °= =1 if 5? 0. for at least one oscillator i, and °> =0
otherwise.
Thus, this segmentation process is the emergent behavior of the
oscillator network. For image segmentation, the LEGION
network generally has two-dimensional (2-D) architecture.
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B3, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
Each oscillator corresponds to a pixel in the given image and is
connected to its eight nearest neighbors except for at the
boundaries where there is no wrap around. The global inhibitor
is connected to all the oscillators on the 2-D grid. It receives
excitation from each oscillator and in turn exerts inhibition to
each oscillator.
2.2 Extended LEGION Segmentation for Building
Extraction from DSM
Due to the large number of pixels in DSM raster data,
numerical integration of hundreds of thousands of differential
equations of original algorithm is prohibitively expensive. Thus,
an extended simplified LEGION framework is proposed.
According to the purpose of building extraction from DSM, the
feature detector associated with each oscillator estimates the
elevation of terrain at its corresponding pixel location. Given
the LEGION dynamics, the main task is to establish lateral
connections based on a similarity measure. Fig.(1) shows the
flow chart of extended LEGION segment for building
extraction from DSM. At the beginning, cells i corresponding
to pixels are initialized into a non-excitated state. Then
coupling weights W;, are calculated between the eight cells k
adjacent to the cells i, which is based on the similarity measure.
Wi, is represented by the following equation:
W, =W,.. | (1+|Dissimlarity(i,k)|),k e Ni) (5)
Where Dissimilarity (7,k) indicate the distance between pixel i
and k and W,,, indicates the maximum value of the pixels’
elevation dissimilarity. Here, we use the maximum value of
dissimilarities for W,,,..
Next step is to distinguish a major oscillator block to address
the fragmentation problem. Usually a lateral potential for each
oscillator is applied. However, this method it is hard for
LEGION to extract a building directly by segmentation,
because high dense trees may contain leaders to participate in
segmentation. Gray Level Co-occurrence Matrix (GLCM)
homogeneity, a feature of DSM height texture, is proposed to
distinguish between buildings and tall trees and locate major
oscillators in building areas. One pixel windows size is used for
GLCM calculation and GLCM homogeneity is represented in
Eq.(6). Homogeneity returns a value that measures the
closeness of the distribution of elements, is chosen to weight
the value decreasing exponentially according to their distance
to the diagonal. Any homogeneity values which are close to 1
are taken as leaders of LEGION segmentation.
1 p(n)
H =
BE [etie
Where p(n) is the DN value of pixel, and i, j is the number of
rows and columns.
According to temporal oscillator correlation, the global
inhibitor acts as a “metronome”, which establishes a single
frequency of oscillation for all objects independently of their
actual input. W, the weight of the global inhibitor plays a
significant role in segmenting pixels into different groups. Yet
the value of JW, usually determines by experience. In this paper,
we find that there exists a relationship between DSM
complexity and W,, which helps to do the determination of W..
(6)
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