3
becomes possible to accurately trace the displacement of
air particles and debris associated with the air blast over
sequential time intervals. This analytical approach aims
to derive quantitative insights into the air blast’s dynamic
behavior. The research framework, relying on empirical
video data and advanced computer vision methods, offers
a rigorous and data-driven avenue for comprehending the
intricacies of air blast dynamics within the context of pillar
collapse events, potentially contributing to enhanced safety
and risk assessment protocols in underground mining and
related sectors (Dan et al., 2017).
The optical flow algorithm is a computer vision tech-
nique used to track the motion of objects or features within
a sequence of images or frames in a video. It is named “opti-
cal flow” because it simulates the way we perceive the move-
ment of objects when we observe the world around us. The
algorithm identifies specific points or features in one frame
of the video and then tracks how these features move in
subsequent frames. These features can be edges, corners, or
other distinctive points that are easy to follow (Nanonets,
2019).
Optical flow estimates the motion of each feature by
analyzing the changes in pixel intensity between frames. It
assumes that neighboring pixels in the image move together.
The result of the optical flow algorithm is a vector field,
where each vector represents the estimated motion of a fea-
ture from one frame to the next. The direction of the vector
indicates the direction of motion, and the length of the vec-
tor represents the speed or magnitude of motion.
The optical flow methodology is visually explained in
Figure 4. In the context of optical flow analysis, it is pos-
sible to express the variation in image intensity (I) between
successive frames as a function of spatial coordinates (x, y)
and temporal parameters (t). This entails the displacement
of pixels within the initial image, I(x, y, t), by specific spa-
tial increments (dx, dy) over a defined temporal interval
(dt), resulting in the creation of a new image, I(x +dx, y +
dy, t +dt) (Beauchemin and Barron, 1995).
The optical flow methodology applications get more
complicated if the object that we are tracking is not solid,
meaning the shape is not uniform throughout the motion.
This is the case with tracking the dust cloud emanat-
ing from the air blast. While the fundamentals of optical
flow methodology as described above remain the same,
the method is further refined by Lucas and Kanade. Lucas
and Kanade introduced an efficient approach for motion
estimation of distinctive features by analyzing sequential
frames in their publication (Lucas and Kanade, 1981). The
Lucas-Kanade method operates based on two assumptions.
First, the time interval between two consecutive frames is
sufficiently small to ensure minimal object displacement.
Second, the frames capture scenes with naturally textured
objects displaying gradual grayscale variations.
This paper uses the Lucas-Kanade methodology for
optical flow estimation using Python libraries developed by
Chuan-en Lin (Nanonets, 2019). In order to repeat this
methodology for other applications, the readers can use the
Python libraries published by Nanonets. The Python code
used in this paper is shared in Appendix A.
4.0 RESULTS
The air blast velocity was calculated using the above-
described optical flow methodology. Figure 5 below shows
some of the frames from the air blast video captured using
the closed-circuit television cameras at various timeframes.
Overall, the entire air blast dispersed in about 8 seconds,
which makes it very dangerous due to the high air blast
velocities. In Figure 5 below, there are four columns and
three rows. The columns show the frames and data at vari-
ous time stamps from the air blast at the portal. The rows
show different characteristics of the air blast. Row 1shows
the actual frame from the video, row 2 shows the vectors
formed in optical flow, row 3 shows the velocities of differ-
ent number of points in the frame. As noticeable in row 2,
the area marked in green is the area within the video that is
of interest for velocity estimation as this is the area in front
of the portal where the air blast is propagated. As shown in
the column B, the air blast really propagates fast at just 1
second, the dust cloud is expanding, and the peak velocities
at this time were 60–80 mph. In column C, at 2.5 seconds
the peak velocity is 120 mph, which is highly catastrophic
right in from of the portal entries.
5.0 SUMMARY AND FUTURE WORK
In summary, pillar collapses in underground limestone
mines, capable of producing catastrophic air blasts, pose
a severe threat to miners. The room-and-pillar mining
method along with benching increases pillar height, creat-
ing a potential risk of pillar collapse. There have been four
significant pillar collapses since October 2020, leading to Figure 4. Optical Flow Methodology
becomes possible to accurately trace the displacement of
air particles and debris associated with the air blast over
sequential time intervals. This analytical approach aims
to derive quantitative insights into the air blast’s dynamic
behavior. The research framework, relying on empirical
video data and advanced computer vision methods, offers
a rigorous and data-driven avenue for comprehending the
intricacies of air blast dynamics within the context of pillar
collapse events, potentially contributing to enhanced safety
and risk assessment protocols in underground mining and
related sectors (Dan et al., 2017).
The optical flow algorithm is a computer vision tech-
nique used to track the motion of objects or features within
a sequence of images or frames in a video. It is named “opti-
cal flow” because it simulates the way we perceive the move-
ment of objects when we observe the world around us. The
algorithm identifies specific points or features in one frame
of the video and then tracks how these features move in
subsequent frames. These features can be edges, corners, or
other distinctive points that are easy to follow (Nanonets,
2019).
Optical flow estimates the motion of each feature by
analyzing the changes in pixel intensity between frames. It
assumes that neighboring pixels in the image move together.
The result of the optical flow algorithm is a vector field,
where each vector represents the estimated motion of a fea-
ture from one frame to the next. The direction of the vector
indicates the direction of motion, and the length of the vec-
tor represents the speed or magnitude of motion.
The optical flow methodology is visually explained in
Figure 4. In the context of optical flow analysis, it is pos-
sible to express the variation in image intensity (I) between
successive frames as a function of spatial coordinates (x, y)
and temporal parameters (t). This entails the displacement
of pixels within the initial image, I(x, y, t), by specific spa-
tial increments (dx, dy) over a defined temporal interval
(dt), resulting in the creation of a new image, I(x +dx, y +
dy, t +dt) (Beauchemin and Barron, 1995).
The optical flow methodology applications get more
complicated if the object that we are tracking is not solid,
meaning the shape is not uniform throughout the motion.
This is the case with tracking the dust cloud emanat-
ing from the air blast. While the fundamentals of optical
flow methodology as described above remain the same,
the method is further refined by Lucas and Kanade. Lucas
and Kanade introduced an efficient approach for motion
estimation of distinctive features by analyzing sequential
frames in their publication (Lucas and Kanade, 1981). The
Lucas-Kanade method operates based on two assumptions.
First, the time interval between two consecutive frames is
sufficiently small to ensure minimal object displacement.
Second, the frames capture scenes with naturally textured
objects displaying gradual grayscale variations.
This paper uses the Lucas-Kanade methodology for
optical flow estimation using Python libraries developed by
Chuan-en Lin (Nanonets, 2019). In order to repeat this
methodology for other applications, the readers can use the
Python libraries published by Nanonets. The Python code
used in this paper is shared in Appendix A.
4.0 RESULTS
The air blast velocity was calculated using the above-
described optical flow methodology. Figure 5 below shows
some of the frames from the air blast video captured using
the closed-circuit television cameras at various timeframes.
Overall, the entire air blast dispersed in about 8 seconds,
which makes it very dangerous due to the high air blast
velocities. In Figure 5 below, there are four columns and
three rows. The columns show the frames and data at vari-
ous time stamps from the air blast at the portal. The rows
show different characteristics of the air blast. Row 1shows
the actual frame from the video, row 2 shows the vectors
formed in optical flow, row 3 shows the velocities of differ-
ent number of points in the frame. As noticeable in row 2,
the area marked in green is the area within the video that is
of interest for velocity estimation as this is the area in front
of the portal where the air blast is propagated. As shown in
the column B, the air blast really propagates fast at just 1
second, the dust cloud is expanding, and the peak velocities
at this time were 60–80 mph. In column C, at 2.5 seconds
the peak velocity is 120 mph, which is highly catastrophic
right in from of the portal entries.
5.0 SUMMARY AND FUTURE WORK
In summary, pillar collapses in underground limestone
mines, capable of producing catastrophic air blasts, pose
a severe threat to miners. The room-and-pillar mining
method along with benching increases pillar height, creat-
ing a potential risk of pillar collapse. There have been four
significant pillar collapses since October 2020, leading to Figure 4. Optical Flow Methodology