6.4 Complex Methodology for Reverse Engineering …
551
stage and determines the size of the frame overlap region. Frame overlap region
is the part of the microcircuit pattern that is present on several fragments at once.
Reverse-engineering specialists have developed a special mathematical apparatus, in
the event of application of which the overlap region includes the regions of search,
bounce, and comparison that are further used to perform the automated alignment
process.
Parts of the signal (search area and comparison area), the characteristics of which
are compared to each other, are selected from the overlap region. After calculating
the most suitable acquisitions, mutual position of the fragments is calculated. Thus,
specific position of each fragment in the two-dimensional space of the panoramic
image is determined.
As of now, there are many methods of aligning two images, which were designed
for various restrictions on source data. It has been established experimentally that,
taking into account the real conditions, the use of the classical function of morphological correlation is most preferable. This function is easy to implement, and has
the clearest minimum at the registration point and is sufficiently resistant to main
types of distortions. However, it should be noted that these methods are inferior to
other methods in terms of operation speed [11].
The essence of the method developed [10] based on the use of the morphological
correlation function is to find the minimum of the morphological correlation function
R m based on the analysis of several samples. In mathematical form, this method is
described by the following simple formula:
R m (T ) = max( f 1 (t) − f 2 (t − r ))(0, N − 1) − min( f 1 (t) − f 2 (t − T ))(0, N − 1),
where f (t) is the size of the reference frame; f 2 (t) is the sample of the connected
frame; N is the size of the compared samples; t is the generalized coordinate.
The function R m reaches its maximum value at the point T 0 , when f (t) = f 2 (t −
T 0 ). Thus, the task of alignment is down to finding the extremum of the function R m .
6.4.3 The Method of Implementing the Process of Stacking
Two Frames of an Image Topology
First of all, let us consider the features of implementation of the process of stacking
along the X-axis. Let us suggest that the 1st frame is already aligned and accept it as
reference and the I + 1st frame as connected.
In the Ist frame, based on the user-set parameters of the overlap region and
software-set parameters, the definition domain is determined. Bounce region d
dimensions are set by software means (Fig. 6.30). The definition domain of f in
the I − 1 frame is determined in the same manner. In the middle of the definition
domain, the first variant of the sample f with a size of N (first reference) is calculated
(see Fig. 6.31). The number of reference values of the morphological correlation
551
stage and determines the size of the frame overlap region. Frame overlap region
is the part of the microcircuit pattern that is present on several fragments at once.
Reverse-engineering specialists have developed a special mathematical apparatus, in
the event of application of which the overlap region includes the regions of search,
bounce, and comparison that are further used to perform the automated alignment
process.
Parts of the signal (search area and comparison area), the characteristics of which
are compared to each other, are selected from the overlap region. After calculating
the most suitable acquisitions, mutual position of the fragments is calculated. Thus,
specific position of each fragment in the two-dimensional space of the panoramic
image is determined.
As of now, there are many methods of aligning two images, which were designed
for various restrictions on source data. It has been established experimentally that,
taking into account the real conditions, the use of the classical function of morphological correlation is most preferable. This function is easy to implement, and has
the clearest minimum at the registration point and is sufficiently resistant to main
types of distortions. However, it should be noted that these methods are inferior to
other methods in terms of operation speed [11].
The essence of the method developed [10] based on the use of the morphological
correlation function is to find the minimum of the morphological correlation function
R m based on the analysis of several samples. In mathematical form, this method is
described by the following simple formula:
R m (T ) = max( f 1 (t) − f 2 (t − r ))(0, N − 1) − min( f 1 (t) − f 2 (t − T ))(0, N − 1),
where f (t) is the size of the reference frame; f 2 (t) is the sample of the connected
frame; N is the size of the compared samples; t is the generalized coordinate.
The function R m reaches its maximum value at the point T 0 , when f (t) = f 2 (t −
T 0 ). Thus, the task of alignment is down to finding the extremum of the function R m .
6.4.3 The Method of Implementing the Process of Stacking
Two Frames of an Image Topology
First of all, let us consider the features of implementation of the process of stacking
along the X-axis. Let us suggest that the 1st frame is already aligned and accept it as
reference and the I + 1st frame as connected.
In the Ist frame, based on the user-set parameters of the overlap region and
software-set parameters, the definition domain is determined. Bounce region d
dimensions are set by software means (Fig. 6.30). The definition domain of f in
the I − 1 frame is determined in the same manner. In the middle of the definition
domain, the first variant of the sample f with a size of N (first reference) is calculated
(see Fig. 6.31). The number of reference values of the morphological correlation