Optimisation of high-speed images of a bullet
penetrating ballistic gelatine for automated
detection and processing of the results
J.F.A. (Sanne) Smeets BSc
aa Student Master Forensic Science (12385239), University of Amsterdam, Netherlands
Supervisor:
Y.S. Khoe MSc
bb TNO, Netherlands
Examiner:
E.J.A.T. Matthijsen MSc
cc University of Amsterdam and Netherlands Forensic Institute (NFI), Netherlands
Project details:
EC 36
Time period 17 Feb. 2020 – 2 Nov. 2020 Research institute TNO
Abstract
Images taken with two high-speed cameras at orthogonal sides of a bullet penetrating 10% ballistic gelatine, are loaded into MATLAB for automated analysis. The analysis method starts optimising the image for analysis. This is done by removing background noise by cropping the image and masking certain parts of the gelatine to remove the calibration pins. The images are converted from grayscale to black and white. Then, the dataset of images taken from the top view are analysed to find the contour of the temporary cavity. From this contour the cavity volume is calculated. The datasets from both sides are used for the contour detection of the bullet inside the image. These datapoints are processed to reconstruct the 3D path of the bullet. This reconstructed path is corrected for outliers by the fitting of a model. From this model additional data is obtained, namely the velocity, absolute deflection angle, and kinetic energy of the bullet. All results are visualized, to make them more intuitive to understand. The results can be used for the reconstruction of the bullet path on a crime scene to determine the position of the shooter based on the absolute deflection angle of the bullet when passing through the victim. Other applications include evaluating the lethality of the bullet and the possibility of the bullet to break bones at certain depth.
Introduction
The field of wound ballistics experiences a growing demand to understand the effects of projectiles penetrating tissue due to the continued presence of gun violence. Wound ballistics is a diverse field in which scientists with different backgrounds search for answers pertaining to the classification and understanding of wounds in tissue caused by projectiles1. Additionally, with the increase in
information that can be obtained from a crime scene nowadays, it can be hard for a court to distinguish and understand all data that comes their way. Visualisation is a tool that can assist in gaining a better understanding of the presented findings and making a more informed decision as to its value2. Those who already have an understanding of the subject matter can use visualisation to
observe data from another perspective to increase their knowledge2.
One of the topics within this field is the understanding of the temporary wound cavity that is formed after penetration. The mechanics behind the formation of the temporary wound cavity have been known to cause disagreement3. However, with the implementation of high-speed cameras the
formation can be made visible. For the reconstruction of a wound cavity with the intention of studying the formation and effects, ballistic gelatine is an often-used simulant for human soft tissue1,4–7. The volume of the temporary cavity depends on the interaction of the material with itself
and subsequently the interaction with the bullet7. Current and past calculation methods for the
temporary cavity volume include the total crack length method6, the wound profile method6, CT
technology8, ballistic soap7, and overlaying different frames from a high-speed camera to obtain a
maximum cavity picture9. The size of the temporary cavity is also in part representative for the
damage that the victim sustained3. Calculating the maximum temporary cavity volume and
visualizing this in a human gives a more explicit view of what damage was inflicted on the victim and what the effect was of the bullet on the victim.
Besides the volume of the temporary cavity, the penetration and the change in direction of the bullet yields valuable information for forensic purposes. It allows for the reconstruction of the bullet path by finding the deflection of the bullet relative to the shot channel length10–12. Which in turn can
aid in the estimation of the direction from which the shot was fired before entering the victim. For this reconstruction, the absolute deflection angle of the bullet is necessary to make the appropriate estimations. This deflection angle varies depending on the shot channel length. By visualising the bullet path through the victim and calculating at what point the absolute deflection angle increases significantly, the shot channel length before this point can be used for bullet path reconstruction. By using CT technology, a virtual autopsy could suffice to estimate the shooter’s position13. With the
path calculated, the kinetic energy of the bullet at different shot channel lengths can be calculated as well. The kinetic energy of the bullet determines in part its wounding potential6.
In this study, the penetration of a bullet into ballistic gelatine will be analysed. Automated analysis tools will be employed to detect characteristics of the penetration as well as calculate properties pertaining to the penetration. Different points of view of the penetration will be used to optimise the results to encompass a 3D reconstructed path of the bullet. Furthermore, contour detection will be employed to identify and quantify the temporary wound cavity in the ballistic gelatine. The 2D representation of the temporary cavity will allow for the visualisation of how the volume changes with time during the penetration. The found datapoints will be processed to calculate the kinetic energy, absolute deflection angle, and velocity of the bullet. The results will be visualised to increase the understandability of the characteristics and to gain a better perspective of the properties of the bullet during the penetration of ballistic gelatine.
Materials and methods
Experimental set-up
For the calculation of the temporary cavity volume and the properties of the bullet, the dataset of an experimental set-up was used. As a soft tissue
simulant, blocks of 20x20x50cm of 10%wt ballistic gelatine were prepared in accordance with the proposed method of J. Jussila14. Two
high speed cameras were used with a framerate of 15700 frames per second and placed at orthogonal angles towards the gelatine to obtain a dual-sided view (Figure 1). The cameras were operated in tandem, as to synchronize the timestamp of the images. Different high-speed projectiles were fired into the gelatine.
Automated image analysis with MATLAB
MATLAB is used for the automated analysis of the data. Each image is analysed through the steps as seen in Figure 2.
First, the image is cropped to disregard objects outside of the gelatine. Next, the image is optimised by converting the grayscale image to black and white so that in the next analysis step contour detection can be applied. This is done using an adaptive binarization algorithm. This algorithm calculates a locally adaptive threshold based on the local mean intensity in the neighbourhood of each pixel. Additionally, the object of interest, which in other words is the foreground, is specified as being lighter than the background. The sensitivity value is different depending on whether the image should be optimised for detection of the bullet (0.40) or the temporary cavity (0.48). The sensitivity value has a minimum value of 0 and a maximum value of 1. A higher sensitivity value results in more pixels being encompassed with the foreground. The values are determined by trial and error. Should the lighting of the experimental set-up change significantly, they may have to be reevaluated. Edge detection algorithms were tested for further optimisation of the image before detection, these were all found to be insufficient or unnecessary, because they were unable to find only the outline of the cavity. All edge detection methods process the gradients and use thresholds to detect edges in an image. When these gradients are too close together in value to the gradient of the background, edges are not identified or are detected but noise is generated, and edge detection fails. All
conventional edge detection methods failed to consistently find the edge of the cavity in image, because the difference in gradient is to small which is caused by the low contrast difference
between the object of interest and the background. Results of these tests can be found in appendix 1.
x
y z
Figure 1: Representation of coherence of orthogonal views of dataset images Automated detection Processing results Optimise image for detection
MATLAB
Additional black blocks are added to the images to remove background information within the gelatine block, such as the calibration pins, which ensures that these are always kept outside the scope of the analysis. The difference between the original image and the image after optimisation can be seen in Figure 3. Next is the automated detection of either the bullet or the temporary cavity.
Temporary cavity volume
The temporary cavity volume is calculated with MATLAB and is based on the images taken from the top of the gelatine block. The main steps of the automated detection of this method are visualized in Figure 4 and are described in detail in this section. The extended flowchart can be found in appendix 2.
After the initial steps of optimising the image, the outline of the cavity is determined as the outline of the largest object in the image. This is done by identifying all white objects in the binary image. Comparing these objects based on size and selecting the largest one as the temporary cavity. Initially this method was performed as comparing the total area of each object, however it was found that this could result in an unidentified temporary cavity, should this be smaller than the detection limit. This detection limit had to be rather high to prevent the wrong object to be labelled the temporary cavity when multiple large objects are in the image. A mask is constructed of only this largest object in the image, which results in a mask of the temporary cavity (Figure 5).
Figure 3: original image (A) and image after optimisation for analysis of temporary cavity (B) and for bullet detection (C)
A B C
Figure 4: concise flowchart volume calculation
Figure 5: Analyzing of image for the finding of the cavity. Optimised binary image (A), Boundary around larges object, displayed on top of original cropped image (B), Mask of temporary cavity (C)
Bullet Tracking
By using both the image dataset with the high-speed images taken from the side view and taken from the top view, a 3D path was reconstructed of the bullet penetrating the ballistic gelatine. The main steps in this method can be seen in Figure 4 and are described in detail in this chapter. The implementation flowchart is documented in appendix 3.
After the initial steps of image optimisation, all objects in the binary image of the top view are identified. Because the bullet is the fastest moving object in the gelatine, it most often is the object which has penetrated the most in the gelatine. There could be some discrepancies due to lighting and such, which will be discussed later with the results. From the white objects in the image, the bullet is identified as being the most left object. To avoid some of the discrepancies, the area of the bullet is calculated to evaluate whether it is large enough to be the bullet. Should this not be the case, the object which is the second most left will be identified as the bullet. Of this object identified as the bullet, a mask is constructed (Figure 8). An ellipse is fitted on this mask to extract its
properties, such as centre coordinates and orientation. These properties are used for the reconstruction of the 3D path.
For the images taken from the side view, a different approach is necessary, due to a difference in lighting. After the initial steps of image optimisation, the bullet is not always visible in the image, because it is obscured by the temporary cavity. Only when it leaves the temporary cavity, can the bullet be identified as a single object. For each image the position found in the side view is used to specify a narrow region of interest in the top view image in which the bullet is located. If the bullet is still inside the temporary cavity the tip of the bullet is specified as the tip of the temporary cavity (Figure 8A). The centre point is then estimated by subtracting half of the length from the found tip point. Should the bullet have left the cavity then an ellipse is fitted on the bullet and the centre point is extracted (Figure 8B).
Figure 6: Concise flowchart bullet tracking analysis method
Figure 8: Analyzing top view image for bullet. Optimised image for analysis (A) and mask of bullet (B)
B A
Figure 7: Analyzing side view image for bullet when bullet is inside cavity (A) and outside of cavity (B)
B A
Not all images are optimal for identification of the temporary cavity which could cause outliers. These defects in the analysis are partly caused by an unclear outline of the temporary cavity in the input image, for example in Figure 9.
In this image, due to a reflection, there is a light visible at the left of the cavity which distorts the dark outline of the temporary cavity. Therefore, the part left of the light is disregarded as part of the cavity, which in turn means that the volume calculated from this image is an underrepresentation of the actual volume and thus results in an outlier. Several of these images will be part of the dataset and are hardly avoidable. However, to remedy the impact these outliers have on the volume
calculation, a model is constructed to evaluate each point to be either within range of expected data points based on the surrounding data.
The calculated volume is at other points an overestimation of the total volume. This results from the incorporation of the bullet fragment into the volume of the temporary cavity, for example as in Figure 10. A fragment of the bullet can be interpreted as part of the temporary cavity outline, and therefore increase the detected volume.
Figure 9: Image unfit for analysis with boundary detection. Cropped image (A) and image with detected contour(B) B A
Figure 10: Image in which bullet is taken into account with volume calculation
A B
Results
After the detection of both the bullet and the temporary cavity, the results of the analysis are used for the derivation of the properties of the penetration. From the detected temporary cavity, the volume is extracted. From the detected bullet, the 3D path is extracted, which in turn is used for the calculation of the velocity, kinetic energy and absolute deflection angle.
Temporary cavity volume
From the found mask of the temporary cavity (figure 3F), the volume is determined by calculating the number of pixels in each column of the cavity and using this as the diameter at a specific segment. The volume is determined of each individual segment and then summed to find the approximate volume of the entire cavity. So, it is
approximated that the temporary cavity is a collection of discs of the same thickness for which the diameter is the distance between the top and the bottom of the contour. A visual example of this is represented in Figure 11.
The formula with which the total volume of the temporary cavity is calculated:
𝑉 = 𝑓𝑐∙ ∑ 𝜋 · ( 1 2· ∑ 𝑝𝑐 𝑖 ) 2 ∙ 𝛿𝑑
In which fc is the conversion factor from a distance in pixels to a distance in cm. This conversion
factor is specific for a dataset and is calculated before the analysis. The term pc is the number of
pixels that are counted in an individual column and lastly 𝛿𝑑 is the thickness of the disc, which is
always one pixel. The time step size originates from the frame rate (1/5700).
Figure 11: visualization of how a collection of discs make up the temporary cavity
Figure 13: Volume of cavity change over time. red star is maximum volume.
For this dataset, the maximum volume of 4152 cm3 was achieved 4.077ms after the projectile first
penetrated the gelatine. There is a clear gradual increase in volume before this point and a decrease in volume after, as can be seen in Figure 13.
There are discrepancies visible in Figure 13 where detection of the cavity volume fails. There are some underestimations, which are due to the quality of the image as clarified by Figure 9. In which part of the region inside the cavity is not detected and therefore not part of the calculated volume. There is also an overestimation possible as explained by
Figure 10. When this occurs, it is due to the physical appearance of the temporary cavity and not an error in the detection. Local bulges caused by bullet fragments enlarge the diameter of the disk with which the volume is calculated at that point. As illustrated by Figure 14, the darker part is how the volume is calculated where the diameter is the same as the diameter of the cavity at a certain segment. However, when the bullet is added to this diameter, the lighter part is the overestimation of the volume of the cavity. The area with the bullet is only small, making the overestimation limited in the results.
A model is fitted through the volume datapoints. The model helps to smooth out the noise originating from the quantification due to the limiting factor of the pixel ratio in the image resolution. The volume is fitted with a 7th degree polynomial function:
𝑦̂ = 𝑏0+ 𝑏1𝑦 + 𝑏2𝑦2+ 𝑏3𝑦3+ 𝑏4𝑦4+ 𝑏5𝑦5+ 𝑏6𝑦6+ 𝑏7𝑦7
This function was chosen, by determining the significance of each additional order based on its p-value with regard to the sum of mean squares of the model.
The result of this fit, as can be seen in Figure 12, is a smooth graphical representation of the change in volume during the penetration of the bullet in the ballistic gelatine. It shows that there is a slightly sharper increase in volume than the decrease in volume after the maximum has been passed.
Figure 12: Temporary wound cavity volume model during ballistic gelatine penetration of bullet
Figure 14: Visualisation of
overestimation of volume with bullet
overestimated volume ‘real’ cavity volume bullet
Visualisation of temporary cavity volume
The image mask of the found cavities are summed together, to create a mask of the maximum temporary cavity (Figure 15). This
maximum temporary cavity volume gives a representation of the area that is impacted with the penetration of the bullet.
This maximum cavity can be implemented in a simplified overview of a human to get an understanding of the damage an individual could sustain from the analysed
bullet. As can be seen in Figure 16, the bullet would not remain inside of the victim. It is also noteworthy that the initial part of the shot channel is relatively narrow, the bulk of the temporary cavity volume only appears after a few centimetres.
What is visualised in the representation in Figure 16 is the difference in size between the entering and exiting wound. The size of the temporary cavity is much smaller with the entering bullet and only after a short distance starts to increase significantly, making the exit wound that much bigger. The increase in cavity diameter is due to the yawing of the bullet inside the material
This can also be seen when looking at the victim from a different perspective. When the cavity is visualised in a human victim from a front view, as in Figure 17, then it becomes more apparent that there is a difference between the maximum cavity that can be formed inside the person and the maximum cavity that is found in the gelatine. The block of gelatine makes for a longer travel path of the bullet and the maximum diameter of the temporary cavity can therefore fall outside of the victim, depending on the size of the victim. The maximum damage of the bullet can therefore be outside of the victim. The impact the bullet has on the victim is dependent on the size of the victim as well, for this could result in a different maximum diameter for the temporary cavity inside the victim. It also shows that the path of the bullet has a clear deflection after the penetration.
Figure 15: Sum of all temporary cavity masks
Figure 16: Side view of simplified representation of a human with maximum temporary cavity and bullet path.
Shooting direction
Figure 17: maximum cavity in victim, front view. Light blue maximum cavity in victim and dark blue maximum found cavity in gelatine.
Bullet tracking
In the images where the bullet is visible the detection method identifies the bullet. However, the bullet detection fails in some cases due to the quality of the image. When the bullet has moved too far into the plane, or when there is a bubble between the camera and the bullet, the position that is recorded has a significant error. Most images are clear enough for the detection of the bullet, however, some create outliers that later must be removed, like Figure 18A where no bullet is visible in the image or Figure 18B where the bullet is visible, but it is deformed. To account for the
deformation, the centre of the object is measured throughout the images, instead of the tip or the end of the bullet.
Because the images are from orthogonal views, a 3D path can be reconstructed from the found bullet coordinates. The x-coordinate is recorded from both the top view and side view images (Figure 1). This is the only overlapping coordinate. Because the bullet is always visible on the side view, the x-coordinate is selected from this view. There are small differences between the two recorded x-coordinates, most likely caused by the change in refractive index of the gelatine as it starts to expand and the depth at which the bullet is located regarding the camera. The Y-coordinate is recorded from the top view images and the Z-coordinate from the side view images.
Outliers are resolved by fitting a model through each coordinate result individually. The resulting paths of each individual coordinate can be found in Figure 19.
Combining these results, gives a 3D representation of the penetration of the bullet through the ballistic gelatine (Figure 20). In which the bullet deflects toward the lower right corner after entering the ballistic gelatine. The bullet remains inside the gelatine. The bullet deflects in all planes, meaning that there is a significant deviation from the initial entering point in the XY-plane, XZ-plane and YZ-plane.
Figure 20: coordinate paths of a bullet penetrating ballistic gelatine.
Figure 18: No bullet visible(A) and deformed image of bullet (B)
bullet
A B
Figure 19: 3D representation of the bullet path (blue) with XY-plane and XZ-plane (black).
The data collected from this analysis is used for the evaluation of the orientation, velocity, and acceleration of the bullet during the penetration of the gelatine block. The coordinates of the centre of the found bullet object are used for these. First, the pathlength which the bullet travels between each image is calculated and is used for
the calculation of the velocity.
The velocity decreases nonlinearly over time (Figure 21). It starts off with a rather strong deceleration but decreases with time. This is a result of the energy being transferred from the bullet into the gelatine.
The orientation of the bullet is
determined by fitting an ellipse shape on the found object in the black and white image. Since an ellipse is a rather similar shape as a bullet, the orientation
resembles the orientation of the bullet. This orientation is recorded as a deviation from the
horizonal axis. However, should the bullet turn perpendicular to the horizonal axis and the tip turns into the gelatine block, this movement is not recorded. Additionally, this causes the shape of the bullet to transform from ellipse to a more circular shape, since at the extreme only the bottom of the bullet is visible, significant errors occur in the result because of this. So, only when the bullet remains clearly visible and distinguishable as an ellipse, is the calculation valid, unlike Figure 18.
Since the size of the bullet is known, the position of the tip and end of the bullet can be estimated. The tip-, centre-, and endpoint, together with the line parallel to the direction and going through the centre point, the bullet position is followed while propagating through the gelatine block (Figure 23). At some point it starts to tumble, after which it does not return to its initial orientation.
Figure 22: Position properties of the bullet. Line segments the size of the bullet and with the orientation of the bullet at measured positions.
What can be seen from the orientation as it changes throughout the penetration (Figure 24), is that for a short time, the bullet remains horizontal. However, when it starts to turn, it turns rapidly and largely. After which the orientation does not remain the same, but it does not change as fast as before. This slower rate in direction change is due to the decrease in velocity the bullet has when it is deeper in the gelatine. Here, again the robustness of the method must be called into question as the bullet is no longer visible after about 2ms as a bullet and therefore the reliability of the ellipse starts to become questionable. Therefore, this data is not included into the visualised result.
With the position of the bullet in the gelatine, the absolute deflection angle of the bullet with regard to the position the bullet had when first penetrating the gelatine was calculated (Figure 25). The results show that even though there is a relatively small absolute deflection angle at the initial part of the wound channel, there is a rather steep increase near the end. This means that should bullet path reconstruction be necessary in a legal context, only the first part of the wound channel is viable to use to extract a bullet path from with CT technology.
Kinetic energy
The kinetic energy of the bullet is a measurement for the amount of energy that has been
transferred by the bullet into the environment, in this case the gelatine. The energy is what forms the cavity and causes the injury.
The kinetic energy of the bullet is calculated throughout the penetration with the formula:
𝐸𝑘 =
1 2∙ 𝑚 ∙ 𝑣
2
The kinetic energy of the bullet during the penetration through the gelatine, starts high, but decreases as the energy of the bullet is transferred to the gelatine (Figure 26). As for the kinetic energy relative to the path of the bullet, the intensity of the energy transferred decreases as the bullet further penetrates the gelatine. Therefore, less energy can be transferred into deeper tissue and objects that reside there. For example, breaking bones becomes much more unlikely when the pathlength of the bullet is longer than when it is shorter.
Figure 23: Orientation of the bullet as it propagates through the gelatine.
Figure 24: Absolute deflection angle of bullet regarding initial position at different wound channel lengths
Figure 25: kinetic energy of bullet (A) and kinetic energy relative to path (B)
Discussion
Recommendations
Currently, there are a few points of improvement with the MATLAB analysis method. As shown in Figure 2, there are different segments to the analysis of the image. Firstly, the optimisation of the image for the detection method. Due to the difference in lighting between the orthogonal sides, only one side was found to be fit to use for the recognition of the temporary cavity. Both sides were used for the 3D reconstruction of the bullet path. To remedy this problem, the experimental set-up can be changed to optimise the images, since the quality of the images determines in the first instance the robustness of the analysis method. To enhance the images, the lighting of the gelatine block should be changed to optimise the visibility of the cavity from both sides. An additional lighting source could be used, however it should be tested whether this changes the side that is already sufficient for analysis.
Other software improvements for the detection of the temporary cavity in al images, is the incorporation of edge detection. Edge detection as it was tested out, failed because the contrast between the temporary cavity and the surrounding gelatine was insufficient. To be able to employ edge detection, the edges of the cavity have to be made sharpen. This can be done by better lighting or a higher recording rate, because the fuzziness of the edged could be due to motion blur. Other image optimisation tools can be used to enhance the sharpness, such as photoshop. Should it not be found possible to sharpen the edges, other detection methods can be evaluated as fuzzy edge detection and machine learning, depending on whether the images are fit to for those methods. These were briefly evaluated during this study, however no solution was found.
With the automated detection it is possible to find the bullet in 3D and to find the temporary cavity. However, since the volume is not yet analysed in 3D, there could be important information missing which significantly changes the volume that is calculated. With the tracking of the bullet in the images when the bullet is not visible because it is inside the cavity, the tip point of the bullet is determined as the tip point of the cavity. When the bullet starts to tumble and is still inside the cavity, this is neither visible nor considered. A method should be devised with which this tumbling is considered but would mostly be remedied with the improvement of the clarity of the image with the improvements stated earlier. The same goes for the images in which the bullet is clearly visible, but due to turning of the bullet into the plane, the data of the orientation of the bullet becomes unreliable. This is where the orientation of the orthogonal side should take over but was not included into the method.
The datapoints obtained from the automated detection, are measured in pixels and later converted into cm by a conversion factor based on calibration pins inserted into the middle of the gelatine. However, as the material compresses and decompresses during the penetration, there is a local change in density which causes a local change in refractive index. This could influence the translation of the measured position to the real position. However, the investigation of whether this has any effect on the outcome was outside the scope of this research.
With the processing of the resulting datapoints, it is possible to gain various parameters of the penetration. One of these is the volume of the temporary cavity. A model is fitted through this data to smooth out outliers, however this model is chosen by trial and error. Should the data be
significantly different, then a new model will have to be chosen. A method which automatically evaluates the model and chooses the order of the polygon would omit this and is recommended to improve the automation of the method. The same goes for the model constructed to calculate the path of the bullet.
Another parameter that is calculated is the kinetic energy of the bullet in the image. This is
calculated with the mass of the bullet, which is measured before it is shot into the gelatine. Due to fragmentation of the bullet, the mass will decrease during the penetration. The calculated kinetic energy will therefore be an overestimation. However, it is not possible to know the mass of the bullet during the penetration, as there is no equipment that could measure this. It is possible to measure the weight of the fragments after the penetration. Since the mass of the bullet is a relatively small contributor to the kinetic energy as opposed by the velocity, it should have a relatively small impact on the outcome.
Forensic impact
With the automated detection and analysis of the penetration of a bullet through ballistic gelatine, it is possible to reconstruct the bullet path. Additionally, the visualisation of the path through the body gives insight into what happens during the penetration. With the results of this study, various questions originating from a forensic point of view can be answered. One of these, is the question of the location of the shooter during a shooting incident as opposed to the victim. It has been shown in this study and several others that there is a significant deflection angle when the bullet travels through soft tissue. Which results in difficulty to directly correlate the final location where the bullet comes to a full stop and the firing location with a straight line. However, by taking the absolute deflection angle into account a more reliable approximation of the shooter’s position can be obtained.
The shooter’s position can be found by using the result of this study in one of two ways. First a test shot is required for the analysis method to find the absolute deflection angle at various wound channel lengths. This is necessary as Riva et al.10 have shown there can be large differences between
the absolute deflection angle at difference pathlengths. To achieve statistical significance, multiple test shots will have to be fired. With the method discussed in this study, it is observed that the automated detection shows an initial stable penetration in which there is almost no deflection. After this initial pathlength, the absolute deflection angle will increase significantly. By determining the distance, it takes the bullet to develop the significant angle, the wound channel length before this moment can be used to find the shooter’s location. This requires multiple test shots to determine an average distance. Combining the automated analysis method with the results of Riva et al10, a faster
way of analysis is achieved. After the pathlength of the bullet with no deflection is determined, this part of the wound channel in the victim can be further analysed with CT technology to find the angle the bullet had up to the turning point and extrapolate from this the shooter’s location.
A different approach would be necessary should the bullet be no longer be situated in the victim. Additional analysis is needed to obtain the deflection of the bullet due to the exiting the victim. This is done by adjusting the experimental set-up to where the gelatine block is the same length as the victim and measuring the position of the bullet as it leaves the gelatine. Again, Riva et al.10 have
shown the statistical necessity to compare multiple test shot to obtain a significant result. Together with the position of the victim and the absolute deflection angle of the bullet, a straight line can be extrapolated from the victim on which the shooter would have to be located.
Another question that could have to be answered is in a case with multiple shooters and bullet, which of them has caused the decease of the victim. In other words, which of the shooters killed the victim. To obtain a better understanding of the behaviour of the bullet on the surrounding soft tissue of the victim, test shots can be fired and together with the used analysis method, the maximum volume of the temporary cavity can be found. The found temporary cavity will then have to translated to injury, to account for the difference between the gelatine and human tissue. Conversion is possible with conversion factors6. This can give a better understanding as to which
parts of the body of the victim could be affected by the bullet. This becomes even more explicitly when different bullets are fired which will result in different temporary cavities.
Vice versa the volume of the temporary cavity can also be used to estimate the characteristics of the projectile, for example impact velocity and size of bullet in case the projectile has been lost after the incident15. Test shots will have to be fired for the comparison. The deformation pattern of the bullet
could be used in the estimation of the impact velocity16.
Additionally, the physiological impact on the victim can be further investigated. The temporary cavity is representative for the injury potential of the bullet. With the ability to track this cavity, the maximum volume of the cavity can be seen, which can generate new insights into the conditions of the victim5,6,17. This could further the field by deepening the understanding of the connection
between the bullet impact and how this is conceived by the victim. A bullet which generated a small permanent cavity, could be seen as having a low impact on the victim. Of course, depending on where the victim is penetrated. However, should analysis of the penetration show that a large temporary cavity is generated, the impact on the victim can be found to be much larger, which in turn could be considered by the court.
Other information that can be valuable is the correlation between the pathlength of the bullet and the energy it has at a certain depth. This can be used to determine whether the breaking of bones was due to the impact of the bullet or unrelated to the event. Though this would need more information about the victim to be somewhat reliable, like the influence of the clothes.
Conclusion
An automatic analysis method is constructed to analyse images obtained with the experimental set-up. These could be optimised for analysis by transforming them into binary images and masking background information such as the area around the gelatine block and the calibration pins. With the automated detection it is then possible to identify the bullet and the temporary cavity with contour detection. These datapoints are processed to reconstruct the path of the bullet in 3D and calculate the volume of the temporary cavity. These in turn are used for the calculation of the velocity, absolute deflection angle and kinetic energy of the bullet. From these automatically calculated results, various visual representations are made. With this broad spectrum of
visualisations, the analysis of the penetration becomes more intuitive to understand, assisting those who have a need to understand the complicated workings of the penetration as for example the legal court could have.
Acknowledgements
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Appendix 1 – Edge detection
To recognize the temporary cavity in an image, the edges of said cavity must be recognized. There are many methods available for edge detection. Well known algorithms are Sobel, Prewitt. Laplacian of Gaussian, Roberts and Canny edge detection18. Edges in a picture are often detected due to a
discontinuity in depth or surface orientation, a change in the material properties or variations in the illumination of the scene. A combination of these is also possible. Sobel, Prewitt and Laplacian of Gaussian each use a 3x3 convolution matrix to find edges.
Prewitt uses two 3x3 convolution matrices:
𝐺𝑥= [ −1 0 +1 −1 0 +1 −1 0 +1 ] ∗ 𝐴 𝑎𝑛𝑑 𝐺𝑦= [ −1 −1 −1 0 0 0 +1 +1 +1 ] ∗ 𝐴
Where A is the original image. By convolving these matrices with the original image, a separate function is found that describes the change of the image by the matrix. This function is used to calculate the approximation of the direction derivatives (horizontal and vertical). Each point in the image ends up with a gradient vector, which points towards the largest possible intensity increase. The Gx gives a x-coordinate at a given point for the gradient increasing horizontally from right to left.
The Gy gives a y-coordinate for the gradient increasing vertically from the bottom to the top. These
separate derivatives can be combined to a resulting gradient magnitude on each point19.
𝐺 = √𝐺𝑥2+ 𝐺𝑦2
Which in turn can be used to calculate the overall direction of the gradient at each point: 𝛼 = tan−1(𝐺𝑦
𝐺𝑥
)
Should the resulting value, for example, of α, be 0, then α is a vertical edge which is darker on the right side. The edge map is solely constructed from the magnitude of the gradient evaluated with a given threshold value. Each magnitude below the threshold value is disregarded as an edge point. As an example, for a simple image:
𝐼 = [ 150 2 3 4 250 6 7 8 150 4 10 3 150 5 6 1 ] −→ 𝐺𝑥(1,1) = ((3 + 7 + 10) − (150 + 250 + 150)) ∙ 1 4= −132.5 𝐺𝑦(1,1) = ((150 + 4 + 10) − (150 + 2 + 3)) ∙ 1 4= 2.25 The gradient values along the x- and y-axis are:
𝐺𝑥= [−131.75 −0.75−132.5 0.75 ] 𝑎𝑛𝑑 𝐺𝑦= [−25.5 −2.252.25 2 ]
The magnitude of the gradients is:
So should the threshold be set at 100, the edge map will look like: 𝑒𝑑𝑔𝑒 𝑚𝑎𝑝 = [1 0
1 0] −→ So, there is a vertical edge found in the original image.
Sobel uses a similar system, but with different values in the convolution matrices. Laplacian of Gaussian (LoG) also uses a 3x3 convolution matrix with different values, but first reduces the noise in the image by filtering it with a Gaussian lowpass filter. Roberts employs a 2x2 convolution matrix. Canny edge detection goes further than the others, because it first follows the same steps, but it enhances the found edges by using non-maximum suppression to thin the edges. It also uses an additional threshold and connectivity restraint for the final edge map. This
additional threshold is obtained by doubling the original threshold value to evaluate which pixels are then still found to be edges. The restraint of connectivity that Canny edge detection holds on, is that each edge has to be connected to another certain edge, which is called edge tracking by hysteresis20. However, this constitutes to the computational cost of
the detection algorithm. All the algorithms have advantages and disadvantages regarding the results, prompting the case by case
selection of an algorithm depending of the input image. However, Canny edge detection has been shown to have some superiority, be it at a high computational cost18–20.
Optimisation edge detection parameters
The results of the edge detection methods with optimised threshold
value to the point where the outline of the cavity is just visible are listed in Table 1. This threshold was chosen by visual inspection of the resulting edge map. Once the outline of the cavity was visible as a continuous line, the threshold was found to be optimised, since the goal of the edge detection is to find the border of the cavity. The analysed algorithms are the Canny, Prewitt, Sobel, Roberts, Zero cross, approximated Canny and Laplacian of Gaussian filter edge detection. These are the encoded edge detection methods of MATLAB. The percentage of white pixels was calculated to find the method with the least additional points outside of the edge of the cavity.
The detection methods of Prewitt, Sobel, Roberts, zero cross and Laplacian of Gaussian all had similar results with regards to noise. This is to be expected, since these all utilize a 3x3 or 2x2
convolution matrix, be it with different values. Only Laplacian of Gaussian first uses a Gaussian filter, however, this was not found to optimise the edge detection as can be seen in table 1. Additional detected lines are due to irregularities in the images like noise.
The edge detection algorithms with promising results are Canny edge detection and approximated Canny edge detection. Both had lower white percentages than the other methods, however with Canny edge detection having a significant lower white percentage than the others. This led to the conclusion that Canny edge detection is the best fit for the edge detection in the images.
The low amount of noise with Canny edge, can be explained by the connectivity restraint of the method. It disregards found edges, when these do not connect with other certain edges. While the other algorithms have no such constraints.
Gaussian smoothing & gradient filter Hysteresis thresholding Nonmaximum suppression Thresholding Convolution for gradient & Magnitude gradient
Convolution for smoothing Can n y So be l, P re wi tt , R o be rt s LoG
Figure 26: Overview of different edge detection algorithms
Table 1: Different edge detection algorithms with the resulting image and white percentage and the used threshold value. Threshold value was chosen so that the outline of the cavity was just visible.
Algorithm Image Threshold value Percentage white
None (original image) - - Canny 0.36 2.23% Prewitt 0.02 8.77% Sobel 0.02 9.63% Roberts 0.02 13.47% Zero cross 0.001 8.79% Approx. Canny 0.25 6.38% Laplacian of Gaussian 0.001 8.79%
