Page 112 - Mechanics of Asphalt Microstructure and Micromechanics

104 Ch a p t e r F o u r

4.2.1 Image Analysis
Most imaging systems use what is termed a feature count point (FCP) to identify all
objects in an image. In many systems, the FCP is the last (right most) pixel of the last
(bottom) line of pixels contained in an object. If all measurements are being conducted
on a single image, this is an efficient way for the imaging system to identify objects.
However, if analysis involves several images (e.g., successive images) where particles
may be displaced relative to one another, as is the case in this application, then a given
object’s FCP in one image may not be the same in a subsequent image. For example, of
the 35 objects in the image (Image 10) shown in Figure 4.6a, which was taken from a
specimen prior to loading with the GLWT, 14 have different FCPs in the companion im-
age (Figure 4.6b) taken after loading. Accordingly, an alternative approach to “track”
particles in successive images must be used. A new procedure that uses pattern recogni-
tion based on the morphological characteristics of the particles was identified (Wang,
1999) and implemented in a program, “MATCH,” as described below. After the parti-
cles are tracked, the particle motions, such as translation and rotation, can be computed,
and therefore the strains can be estimated.

4.2.2 The MATCH Program
The MATCH program uses a pattern recognition algorithm to match the particles so
that the displacement can be correctly and automatically computed. As previously in-
dicated, under typical wheel loading, the deformation of aggregate particles is negligi-
ble. Permanent deformation of AC results principally from particle translations and
particle rotations that result from the deformation of the surrounding mastic. In other
words, the particles are only subject to rigid-body motions. Therefore, individual par-
ticle characteristics on a given cut plane such as their cross-section area, perimeter, and
aspect ratio remain relatively constant. For relatively small displacements, their relative
positions do not drastically change either.
The MATCH program requires two images acquired from the same region of a
specimen cross-section before and after testing that contain the same particles. Small
particles considered part of the mastic were removed manually during image process-
ing. For each particle (ith particle) in the un-deformed image, the match procedure was
implemented as follows:
Step 1: The five closest particles to the ith particle in the deformed configuration
were identified. The closest particles are defined by the distances of their centroids from
the centroid of particle i. The particle with the shortest distance to the ith particle was the
closest particle, and so on. The distance was computed using the following formula:

d
u 2
u 2
d
d = ( x − x ) + ( y − y ) (4-1)
j j i j i
Where x and y are the coordinates of the centroids of the particle cross-sections, the
superscripts u and d denote the un-deformed and the deformed configurations respec-
tively, and j is the index corresponding to the number of particles in the deformed im-
age. The particles were then placed in order by this distance and the particle numbers
were indexed in order to keep track of their properties.
Step 2: Particle similarity was evaluated through the similarity index that is de-
fined as |Q − Q u |, j = −15.
d
j i
The quantity Q is the particle characteristic such as area, aspect ratio, etc. being
compared.