6.4 Complex Methodology for Reverse Engineering …
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center of the domain, and kr − 1 more of values of the function R m are calculated. In
calculations, t is accepted as the value of movement along the X-axis from the center
of the definition domain of f 2 . Maximum offset along the axis X from the center of
the definition domain f 2 is ±kT 2 (Fig. 6.32).
From all the values of R m obtained by kT, the minimum is selected, and the value
of the coordinate at which the minimum was achieved is recorded. Therefore, the
nested cycles (loops) examined in this article help find the sample f in the connected
frame I+.
The morphological correlation function R m with the acquisition f from the reference frame is minimal and determines the pair of offsets PX and PX. These offsets
determined the position of the frame along the X-axis.
Simultaneously with the displacement along the X-axis, the function f shifts up
and down along the axis Y, thus determining the value of T ort displacement from the
initial position. The maximum value of t along the axis Y is +kx/2. Calculated
or t or t
kT ort is the number of values of function R m . During calculations for each T ort , the
cycle by t is performed as an internal loop. The minimum is also selected from the
acquired values of R m , and the coordinate is remembered. Definition of the minimum
in this case will help find the position of the frame along the axis Y. The calculation
results in a pair of coordinates (x, y). Figure 6.32a shows the characteristic view of
the R m (T ) function along the X-axis.
It has been experimentally proven [11] that the function R m reaches its minimum
value at t = 8. For best alignment of two frames, it is necessary to align the overlap
of the /th and I + 1th frame regions and additionally move the I + 1th frame along
the X-axis by t 0 = 8.
However, the I + 1 frame can be shifted relative to the I frame along the Y-axis.
Therefore, for quality alignment, it is necessary to consider the morphological correlation function from two variables R m (T, T ort ), where T ort is the variable orthogonal
to t. In this case, t determines offset along the X-axis, and T ort —offset along the
Y-axis. Figure 6.32b shows the form of the function R m (T, T ort ).
The function R m reaches its peak value in the point t, t ort . Thus, when aligning
two frames, it is first necessary to align their overlap regions and then additionally
shift the I + 1th frame with regard to the Ist frame along the X-axis by PX = t 0 and
along the Y-axis by PX = t 0ort .
In order to improve th quality of alignment of two frames, alignment is calculated
for k acquisitions f from the reference frame. The reference function f is changed,
and all calculations are started anew. Thus, we get k pairs of coordinates x, y, or k
pairs of offsets determining the position of the I + 1st frame relative to the Ist.
From the obtained array of offsets of all k of pairs, average values are calculated
that ultimately determine the position of the frame:
553
center of the domain, and kr − 1 more of values of the function R m are calculated. In
calculations, t is accepted as the value of movement along the X-axis from the center
of the definition domain of f 2 . Maximum offset along the axis X from the center of
the definition domain f 2 is ±kT 2 (Fig. 6.32).
From all the values of R m obtained by kT, the minimum is selected, and the value
of the coordinate at which the minimum was achieved is recorded. Therefore, the
nested cycles (loops) examined in this article help find the sample f in the connected
frame I+.
The morphological correlation function R m with the acquisition f from the reference frame is minimal and determines the pair of offsets PX and PX. These offsets
determined the position of the frame along the X-axis.
Simultaneously with the displacement along the X-axis, the function f shifts up
and down along the axis Y, thus determining the value of T ort displacement from the
initial position. The maximum value of t along the axis Y is +kx/2. Calculated
or t or t
kT ort is the number of values of function R m . During calculations for each T ort , the
cycle by t is performed as an internal loop. The minimum is also selected from the
acquired values of R m , and the coordinate is remembered. Definition of the minimum
in this case will help find the position of the frame along the axis Y. The calculation
results in a pair of coordinates (x, y). Figure 6.32a shows the characteristic view of
the R m (T ) function along the X-axis.
It has been experimentally proven [11] that the function R m reaches its minimum
value at t = 8. For best alignment of two frames, it is necessary to align the overlap
of the /th and I + 1th frame regions and additionally move the I + 1th frame along
the X-axis by t 0 = 8.
However, the I + 1 frame can be shifted relative to the I frame along the Y-axis.
Therefore, for quality alignment, it is necessary to consider the morphological correlation function from two variables R m (T, T ort ), where T ort is the variable orthogonal
to t. In this case, t determines offset along the X-axis, and T ort —offset along the
Y-axis. Figure 6.32b shows the form of the function R m (T, T ort ).
The function R m reaches its peak value in the point t, t ort . Thus, when aligning
two frames, it is first necessary to align their overlap regions and then additionally
shift the I + 1th frame with regard to the Ist frame along the X-axis by PX = t 0 and
along the Y-axis by PX = t 0ort .
In order to improve th quality of alignment of two frames, alignment is calculated
for k acquisitions f from the reference frame. The reference function f is changed,
and all calculations are started anew. Thus, we get k pairs of coordinates x, y, or k
pairs of offsets determining the position of the I + 1st frame relative to the Ist.
From the obtained array of offsets of all k of pairs, average values are calculated
that ultimately determine the position of the frame: