Original: Mixup for Robust Image Classification - Application in Continuously Transitioning Industrial Sprays
Revised: Mixup for Robust Image Classification - Application in Continuously Transitioning Industrial Sprays

Original: Anonymous Author(s)

Original: AffiliationAddress email

Original: Abstract
Revised: Abstract

Original: Image classification with deep neural networks has seen a surge of technologicalbreakthroughs with promising applications in areas such as face recognition, objectdetection, etc.
Revised: Image classification with deep neural networks has seen a surge of technological breakthroughs with promising applications in areas such as face recognition, object detection, etc.

Original: However, in engineering problems, e.g. high-speed imaging ofengine fuel injector sprays, deep neural networks face a fundamental challengethe availability of adequate and diverse data.
Revised: However, in engineering problems, e.g. high-speed imaging of engine fuel injector sprays, deep neural networks face a fundamental challengethe availability of adequate and diverse data.

Original: Typically, only hundreds or thousandsof samples are available for training.
Revised: Typically, only hundreds or thousands of samples are available for training.

Original: In addition, the transition between differentspray classes is a "continuum" and requires a high level of domain expertise to labelimages accurately.
Revised: In addition, the transition between different spray classes is a "continuum" and requires a high level of domain expertise to label images accurately.

Original: Thus, this work leverages pre-trained Neural Network models tobuild classifiers and employed Mixup to systematically deal with the data scarcityand ambiguous class boundaries found in industrial spray applications.
Revised: Thus, this work leverages pre-trained Neural Network models to build classifiers and employed Mixup to systematically deal with the data scarcity and ambiguous class boundaries found in industrial spray applications.

Original: Comparingto traditional data augmentation methods, Mixup that linear interpolates differentclasses naturally aligns with the continuous transition between different classes in spray applications.
Revised: Comparing to traditional data augmentation methods, Mixup that linear interpolates different classes naturally aligns with the continuous transition between different classes in spray applications.

Original: Results also show that Mixup can train a more accurate androbust deep neural network classifier with only hundreds samples.
Revised: Results also show that Mixup can train a more accurate and robust deep neural network classifier with only hundreds samples.

Original:  Introduction
Revised:  Introduction

Original: Deep Convolutional Neural Networks (CNNs) have led to a series of technological breakthroughs incomputer vision applications [9].
Revised: Deep Convolutional Neural Networks (CNNs) have led to a series of technological breakthroughs in computer vision applications [9].

Original: Among the most important factors that contributed to this tremendous success are publicly available, large, high-quality datasets such as ImageNet [2], CIFAR [6],
Revised: Among the most important factors that contributed to this tremendous success are publicly available, large, high-quality datasets such as ImageNet [2], CIFAR [6],

Original: CelebA [7].
Revised: CelebA [7].

Original: However, pre-trained deep CNNs face unique challenges when directly applied toproblems in scientific domains where datasets are not only very different but also scarce and requireexpert domain knowledge for accurate labeling and annotation.
Revised: However, pre-trained deep CNNs face unique challenges when directly applied to problems in scientific domains where datasets are not only very different but also scarce and require expert domain knowledge for accurate labeling and annotation.

Original: The data scarcity, combined withclass overlap, naturally leads to overfitting and poor model performance.
Revised: The data scarcity, combined with class overlap, naturally leads to overfitting and poor model performance.

Original: Although many strategies such as less complex models, data augmentation, dropout [8] and regularization can be used to prevent overfitting, their effectiveness in small datasets that containonly hundreds of training samples can be limited.
Revised: Although many strategies such as less complex models, data augmentation, dropout [8], and regularization can be used to prevent overfitting, their effectiveness in small datasets that contain only hundreds of training samples can be limited.

Original: In addition, these methods often lack physicalinterpretation, as is critical for model acceptance in scientific applications.
Revised: In addition, these methods often lack physical interpretation, as is critical for model acceptance in scientific applications.

Original: In this work, we aim to apply a pre-trained deep CNNs to build classifiers for such an engineering problem where high speed images of engine fuel sprays need to be classified into different categories.
Revised: In this work, we aim to apply a pre-trained deep CNNs to build classifiers for such an engineering problem where high speed images of engine fuel sprays need to be classified into different categories.

Original: Those images are collected using Mie scattering and are used to help engine experts to understand the mechanisms of spray breakup and mixture formation.
Revised: Those images are collected using Mie scattering and are used to help engine experts to understand the mechanisms of spray breakup and mixture formation.

Original: It is generally accepted that, depending on the macroscopic features of spray images, spray morphology can be classified into three regimes - no collapse, transitional and collapse.
Revised: It is generally accepted that, depending on the macroscopic features of spray images, spray morphology can be classified into three regimes - no collapse, transitional, and collapse.

Original: It is also widely accepted that spray collapse should be avoided atall cost since it can worse engine performance and increase combustion emissions.
Revised: It is also widely accepted that spray collapse should be avoided at all cost since it can worse engine performance and increase combustion emissions.

Original: Unfortunately, the spray collapse phenomenon is not well understood.
Revised: Unfortunately, the spray collapse phenomenon is not well understood.

Original: The detection of spray collapse has so far remained a manual and time consuming process and is highly relied on domain experts
Revised: The detection of spray collapse has so far remained a manual and time consuming process, and is highly relied on domain experts.

Original: To build accurate and robust classifier for such applications, there are two main challenges.
Revised: To build accurate and robust classifier for such applications, there are two main challenges.

Original: First,the transition between different spray classes is not sharp or even perceptibly different, as is shownin Figure 1, where fuel sprays injected into a constant volume chamber were recorded with MieScattering imaging.
Revised: First, the transition between different spray classes is not sharp or even perceptibly different, as is shown in Figure 1, where fuel sprays injected into a constant volume chamber were recorded with MieScattering imaging.

Original: Three spray morphology classes - no collapse, transitional, and collapse areshown in (a), (c), and e), respectively.
Revised: Three spray morphology classes - no collapse, transitional, and collapse are shown in (a), (c), and (e), respectively.

Original: It is clear that the transition between spray morphologyies is a"continuum" and some spray images exhibit features from two different classes, as shown in (b) and(d).
Revised: It is clear that the transition between spray morphologyies is a "continuum" and some spray images exhibit features from two different classes, as shown in (b) and (d).

Original: These mixed images, represent class overlap and are difficult to label even for domain experts.
Revised: These mixed images, represent class overlap and are difficult to label even for domain experts.

Original: For example, (b) can be labeled as no collapse, but its close variant from the next camera frame maybe labeled as transitional.
Revised: For example, (b) can be labeled as no collapse, but its close variant from the next camera frame may be labeled as transitional.

Original: This might unintentionally lead to some "corrupt labels" in the training set,and results in poor model performance despite the remarkable capability of deep learning.
Revised: This might unintentionally lead to some "corrupt labels" in the training set, and results in poor model performance despite the remarkable capability of deep learning.

Original: The second challenge is small data size.
Revised: The second challenge is small data size.

Original: Due to limited testing resources and testing/labelingmanpower, initially only 900 images are collected and labeled from lab.
Revised: Due to limited testing resources and testing/labeling manpower, initially only 900 images are collected and labeled from lab.

Original: The combination of a smalldata set and "corrupt labels" impact data quality and balance, thereby affecting model performance.
Revised: The combination of a small data set and "corrupt labels" impact data quality and balance, thereby affecting model performance.

Original: To overcome those challenges in a physically meaningful manner, the Mixup approach proposedby Zhang et al.
Revised: To overcome those challenges in a physically meaningful manner, the Mixup approach proposed by Zhang et al.

Original: [10] is employed for data augmentation.
Revised: [10] is employed for data augmentation.

Original: Our study suggests that a convex linearinterpolation of Mixup naturally aligns with the continuous class transition observed in the spraydataset.
Revised: Our study suggests that a convex linear interpolation of Mixup naturally aligns with the continuous class transition observed in the spray dataset.

Original: Depending on whether two candidate images belong to a same class or not, Mixup can eitherfunction as a data augmentation technique that reduces overfitting or a label smoothing techniquethat mimics the continuous class transitions.
Revised: Depending on whether two candidate images belong to a same class or not, Mixup can either function as a data augmentation technique that reduces overfitting or a label smoothing technique that mimics the continuous class transitions.

Original: Our study also shows that though traditional dataaugmentation can mitigate overfitting to some degree, it does not bring additional benefits and maynegate the performance boost if stacked with Mixup.
Revised: Our study also shows that though traditional data augmentation can mitigate overfitting to some degree, it does not bring additional benefits and may negate the performance boost if stacked with Mixup.

Original: The key contributions of this work are listed below:
Revised: The key contributions of this work are listed below:

Original: Proposed an explainable training technique to build robust and accurate deep CNN classifier forengineering applications that have limited data, exist continuum between classes and ’corrupt labels’.2.
Revised: Proposed an explainable training technique to build robust and accurate deep CNN classifier for engineering applications that have limited data, exist continuum between classes and ’corrupt labels’.

Original: Showcased that Mixup worked well with small datasets (900 images collected from continuouslytransitioning industrial sprays).
Revised: Showcased that Mixup worked well with small datasets (900 images collected from continuously transitioning industrial sprays).

Original: This benefit has not been discussed in the original work by Zhang etal.
Revised: This benefit has not been discussed in the original work by Zhang et al.

Original: [10], nor such engineering applications have not yet been discussed in literature to our knowledge.
Revised: [10], nor such engineering applications have not yet been discussed in literature to our knowledge.

Original:  Data, methods and results2.1 Introduction of training data and baseline model development
Revised:  Data, methods and results 2.1 Introduction of training data and baseline model development

Original: In this study, the entire dataset is composed of proprietary spray images collected from internal spraylab.
Revised: In this study, the entire dataset is composed of proprietary spray images collected from internal spray lab.

Original: We aim to built classifier that is capable of classifying spray structures over various testingconditions, injection timings, and experimental parameters.
Revised: We aim to built classifier that is capable of classifying spray structures over various testing conditions, injection timings, and experimental parameters.

Original: This allows using this model for sprayimages collected from multiple sources, covering a wide range of operating conditions, injectorgeometries, and measurement events.
Revised: This allows using this model for spray images collected from multiple sources, covering a wide range of operating conditions, injector geometries, and measurement events.

Original: In addition, to cover the entire injection event, an additionalclass named "Pre/Post" (short for pre-injection and post-injection) is added to the dataset so the finalmodel can take any input from the Mie Scattering without human attention.
Revised: In addition, to cover the entire injection event, an additional class named "Pre/Post" (short for pre-injection and post-injection) is added to the dataset so the final model can take any input from the Mie Scattering without human attention.

Original: In total, there are 878 images collected- 173 pre/post, 199 no collapse, 241 transitional, and 265collapse.
Revised: In total, there are 878 images collected- 173 pre/post, 199 no collapse, 241 transitional, andcollapse.

Original: Here, 75% of data is set for training, 15% for validation, and 10% for testing.
Revised: Here, 75% of data is set for training, 15% for validation, and 10% for testing.

Original: Examples ofspray images in each class are shown in Appendix B. Since the data were collected from multiplesources, they are not necessarily the same size.
Revised: Examples of spray images in each class are shown in Appendix B. Since the data were collected from multiple sources, they are not necessarily the same size.

Original: In addition, some images may carry auxiliaryboundary lines and/or text annotations processed by Mie Scattering tool.
Revised: In addition, some images may carry auxiliary boundary lines and/or text annotations processed by Mie Scattering tool.

Original: Those lines were remainedduring the manual labeling process and we anticipate the model would either treat them as noise orrecognize them as useful features.
Revised: Those lines were remained during the manual labeling process and we anticipate the model would either treat them as noise or recognize them as useful features.

Original: Given small dataset, the most feasible starting point is transfer learning by reusing lower layers ofpre-trained models.
Revised: Given small dataset, the most feasible starting point is transfer learning by reusing lower layers of pre-trained models.

Original: This study employed TensorFlow version 2.4.1 [1].
Revised: This study employed TensorFlow version 2.4.1 [1].

Original: Among many availablepre-trained models on Keras, ResNet [4] family is employed after an internal evaluation.
Revised: Among many available pre-trained models on Keras, ResNet [4] family is employed after an internal evaluation.

Original: All imageswere pre-processed as 224 × 224 pixel as expected by ResNet.
Revised: All images were pre-processed as 224 × 224 pixel as expected by ResNet.

Original: Finally, with 5-fold cross validation,the ResNet50 is selected out of 7 ResNet model variants due to its best accuracy and least overfitting.
Revised: Finally, with 5-fold cross validation, the ResNet50 is selected out of 7 ResNet model variants due to its best accuracy and least overfitting.

Original: Detailed model architecture and performance comparison are shown in Appendix C.
Revised: Detailed model architecture and performance comparison are shown in Appendix C.

Original: 2.2 Mixup and data augmentation
Revised: 2.2 Mixup and data augmentation

Original: Mixup is a simple and data-agnostic method proposed by Zhang et al.
Revised: Mixup is a simple and data-agnostic method proposed by Zhang et al.

Original: Given two images, itcan either select one input image as the output or blend both input images and generate a linearlyinterpolated image.
Revised: Given two images, it can either select one input image as the output or blend both input images and generate a linearly interpolated image.

Original: The detailed Mixup introduction is shown in Appendix D.
Revised: The detailed Mixup introduction is shown in Appendix D.

Original: It is noted that thereare many choices of Mixup implementations as suggested by Zhang et al.
Revised: It is noted that there are many choices of Mixup implementations as suggested by Zhang et al.

Original: [10], while this workimplemented the vanilla version
Revised: [10], while this work implemented the vanilla version

Original: Figure 2 shows some examples after Mixup with different α values.
Revised: Figure 2 shows some examples after Mixup with different α values.

Original: Note that we only tested α up to0.6 as Zhang et al.
Revised: Note that we only tested α up to 0.6 as Zhang et al.

Original: [10] found Mixup only improved performance over traditional data augmentationwith α < 0 .
Revised: [10] found Mixup only improved performance over traditional data augmentation with α < 0 .

Original: For larger α values, Mixup leads to underfitting.
Revised: For larger α values, Mixup leads to underfitting.

Original: At α = 0 . 2 , four (circled in
Revised: At α = 0 . 2 , four (circled in

Original: Figure 2,a))
Revised: Figure 2,a))

Original: out of 20 randomly selected images are visually discernible as being augmented by
Revised: out of 20 randomly selected images are visually discernible as being augmented by

Original: Mixup.
Revised: Mixup.

Original: Among those four images, one of them was interpolated between two images belongingto a same class as highlighted by a green circle.
Revised: Among those four images, one of them was interpolated between two images belonging to a same class as highlighted by a green circle.

Original: The resulting image expands data distribution ofthat class and hence Mixup acts as a data augmentation tool.
Revised: The resulting image expands data distribution of that class and hence Mixup acts as a data augmentation tool.

Original: The other three (circled in red) wereinterpolated between two different classes, the resulting labels are no longer one-hot vectors.
Revised: The other three (circled in red) were interpolated between two different classes, the resulting labels are no longer one-hot vectors.

Original: Thisis considered critical to our application as those cross-class augmented images mimic the smoothtransition observed in the spray dataset.
Revised: This is considered critical to our application as those cross-class augmented images mimic the smooth transition observed in the spray dataset.

Original: As α increases, the interpolation becomes stronger, and moreimages can be observed as being interpolated.
Revised: As α increases, the interpolation becomes stronger, and more images can be observed as being interpolated.

Original: Data augmentation is widely used to combat overfitting of deep neural networks.
Revised: Data augmentation is widely used to combat overfitting of deep neural networks.

Original: However, amongmany choices of data augmentation methods such as shifting, rotation, flip, zooming, one must becareful as the effectiveness of data augmentation is dataset dependent and use of domain knowledge isusually needed.
Revised: However, among many choices of data augmentation methods such as shifting, rotation, flip, zooming, one must be careful as the effectiveness of data augmentation is dataset dependent and use of domain knowledge is usually needed.

Original: Although Mixup was found to improve performance over data augmentation [10], theycan easily work together.
Revised: Although Mixup was found to improve performance over data augmentation [10], they can easily work together.

Original: In this work, Mixup is performed before any alternate data augmentationsince it guarantees that there will be only one injector tip located on the top of each augmentedspray image.
Revised: In this work, Mixup is performed before any alternate data augmentation since it guarantees that there will be only one injector tip located on the top of each augmented spray image.

Original: If image augmentation such as rotation and shifting are applied first, then the Mixupaugmented image may have two injector tips, which violates physics pollutes training data.
Revised: If image augmentation such as rotation and shifting are applied first, then the Mixup augmented image may have two injector tips, which violates physics pollutes training data.

Original: To compare different data augmentation techniques, we first fine tuned the baseline model-ResNet50with only tranditional data augmentation (without Mixup).
Revised: To compare different data augmentation techniques, we first fine tuned the baseline model-ResNet with only tranditional data augmentation (without Mixup).

Original: Again, only the last block of ResNet50(i.e. , conv5 block3 ) is retrained with our training data.
Revised: Again, only the last block of ResNet (i.e., conv5 block3 ) is retrained with our training data.

Original: To align with our experiment setup, thefollowing traditional data augmentation is applied: random rotation up to 20 degrees since ourinjector can only be installed at a slightly angled position; random shifting up to 20% as the sprayimage is always centered at the camera window.
Revised: To align with our experiment setup, the following traditional data augmentation is applied: random rotation up to 20 degrees since our injector can only be installed at a slightly angled position; random shifting up to 20% as the spray image is always centered at the camera window.

Original: Horizontal flip but not vertical flip since it gives anupside-down image that makes no physical sense.
Revised: Horizontal flip but not vertical flip since it gives an [Table] upside-down image that makes no physical sense.

Original: Brightness, saturation, hue, or contrast adjustmentsare excluded given Mie
Revised: Brightness, saturation, hue, or contrast adjustments are excluded given Mie

Original: Scattering imaging produces consistent images without much distortion.
Revised: Scattering imaging produces consistent images without much distortion.

Original: The ensemble-averaged training-validation accuracy gaps over the last 50 epochs and the test accuracyfor each final model are reported in Table 1.
Revised: The ensemble-averaged training-validation accuracy gaps over the last 50 epochs and the test accuracy for each final model are reported in Table 1.

Original: Comparing to the baseline model without any dataaugmentation, all single data augmentations lead to improved generalization.
Revised: Comparing to the baseline model without any data augmentation, all single data augmentations lead to improved generalization.

Original: Also, combining two orthree augmentation methods do not bring additional benefits.[Table]
Revised: Also, combining two or three augmentation methods do not bring additional benefits.

Original: Next
Revised: Next

Original: [Table]
Revised: [Table]

Original: we evaluated Mixup without data augmentation.
Revised: we evaluated Mixup without data augmentation.

Original: As shown on Table
Revised: As shown on Table

Original: [Table]
Revised: [Table]

Original: all Mixup tests leadto improved performance over data augmentation.
Revised: all Mixup tests lead to improved performance over data augmentation.

Original: The training-validation accuracy gaps are below1.0% with all three α values.
Revised: The training-validation accuracy gaps are below 1.0% with all three α values.

Original: Larger α leads to better generalization [Table] but under-fits the training set asevidenced by the decreasing ensemble-averaged training accuracies.
Revised: Larger α leads to better generalization, but under-fits the training set as evidenced by the decreasing ensemble-averaged training accuracies.

Original: This finding is consistent withthe work by Zhang et al.
Revised: This finding is consistent with the work by Zhang et al.

Original: [Table] though they used much bigger datasets (ImageNet) [Table]
Revised: [10], though they used much bigger datasets (ImageNet).

Original: In addition, Zhang et al.
Revised: In addition, Zhang et al.

Original: [10] showed Mixup can mitigate the memorization of "corrupted labels" byreplacing up to 80% images with "corrupted" labeled images in the CIFAR dataset.
Revised: [10] showed Mixup can mitigate the memorization of "corrupted labels" by replacing up to 80% images with "corrupted" labeled images in the CIFAR dataset.

Original: In our application,"corrupted labels" are unintentionally introduced because of blurry boundaries between continuousclass transitions.
Revised: In our application, "corrupted labels" are unintentionally introduced because of blurry boundaries between continuous class transitions.

Original: We hypothesize that Mixup can help combat the memorization of those "corruptedlabels" as well.
Revised: We hypothesize that Mixup can help combat the memorization of those "corrupted labels" as well.

Original: For example, if a "collapse/transitional" image is labeled as "collapse" and itsneighbor from the next camera frame is labeled as "transitional", then a neural network without
Revised: For example, if a "collapse/transitional" image is labeled as "collapse" and its neighbor from the next camera frame is labeled as "transitional", then a neural network without

Original: Mixup would learn to memorize those labels and over-fit the data.
Revised: Mixup would learn to memorize those labels and over-fit the data.

Original: On the other hand, all trainingimages are generated from Mixup (although not all of them are interpolated), so those two imagesmay produce a new training image with an interpolated label.
Revised: On the other hand, all training images are generated from Mixup (although not all of them are interpolated), so those two images may produce a new training image with an interpolated label.

Original: This is equivalent to labeling the newlygenerated image as "collapse/transitional", thereby reduces the memorization of "corrupted labels".
Revised: This is equivalent to labeling the newly generated image as "collapse/transitional", thereby reduces the memorization of "corrupted labels".

Original: From the physics point of view, this interpolation aligns with the actual transition in the experiments.
Revised: From the physics point of view, this interpolation aligns with the actual transition in the experiments.

Original: At last, we performed a test with Mixup ( α = 0 . 2 ) followed by the "best-practice" data augmentationi.e. , shifting by 20% plus horizontal flip.
Revised: At last, we performed a test with Mixup ( α = 0 . 2 ) followed by the "best-practice" data augmentation i.e., shifting by 20% plus horizontal flip.

Original: The training accuracy drops to 93.7% and the test accuracyis lower than all Mixup-only tests.
Revised: The training accuracy drops to 93.7% and the test accuracy is lower than all Mixup-only tests.

Original: This indicates additional data augmentation may add excessiveregularization.
Revised: This indicates additional data augmentation may add excessive regularization.

Original:  Conclusion
Revised:  Conclusion

Original: Data scarcity is one of main challenges that large deep neural networks face when applied to scientificproblems.
Revised: Data scarcity is one of main challenges that large deep neural networks face when applied to scientific problems.

Original: In this paper, we showcased a robust and accurate training method for an industrial engineinjector spray classification problem where the transition between classes is a "continuum".
Revised: In this paper, we showcased a robust and accurate training method for an industrial engine injector spray classification problem where the transition between classes is a "continuum".

Original: With
Revised: With

Original: Mixup, a deep CNN classifier (ResNet50) can be built with only hundreds images with 98% accuracyon a real-world spray dataset.
Revised: Mixup, a deep CNN classifier (ResNet50) can be built with only hundreds images with 98% accuracy on a real-world spray dataset.

Original: The study showed that Mixup improved performance over dataaugmentation methods, and can provide benefit of reducing the memorization of "corrupted labels"that unintentionally introduced during manual labeling.
Revised: The study showed that Mixup improved performance over data augmentation methods, and can provide benefit of reducing the memorization of "corrupted labels" that unintentionally introduced during manual labeling.

Original: As we understand, the linear interpolation ofboth data and labels also agrees with the "continuum" nature of class transitions in injector sprays.
Revised: As we understand, the linear interpolation of both data and labels also agrees with the "continuum" nature of class transitions in injector sprays.

Original: As future work, we are interested in incorporating simulation data from high-fidelity computationalfluid dynamics (CFD) tools into the experimental dataset and continue to explore the properties of
Revised: As future work, we are interested in incorporating simulation data from high-fidelity computational fluid dynamics (CFD) tools into the experimental dataset and continue to explore the properties of

Original: Mixup and variants.
Revised: Mixup and variants.

Original: We also wish to understand the impact of Mixup on assisting these models tograsp knowledge that embedded differently in simulation and experiment datasets.
Revised: We also wish to understand the impact of Mixup on assisting these models to grasp knowledge that embedded differently in simulation and experiment datasets.

Original: A Background of fuel injection spray applications
Revised: A Background of fuel injection spray applications

Original: Although the automotive industry appears to be on the verge of transitioning to electric vehicles, thevast majority of passenger cars and commercial vehicles on the road are still powered by Internal
Revised: Although the automotive industry appears to be on the verge of transitioning to electric vehicles, the vast majority of passenger cars and commercial vehicles on the road are still powered by Internal

Original: Combustion Engines (ICE).
Revised: Combustion Engines (ICE).

Original: ICEs are complex systems that convert the energy stored in the hydrocarbon bonds of chemical compounds in fossil fuels to mechanical energy used to power vehicles.
Revised: ICEs are complex systems that convert the energy stored in the hydrocarbon bonds of chemical compounds in fossil fuels to mechanical energy used to power vehicles.

Original: A basic ICE works like follows: the fuel system injects gasoline (or diesel) into the intake port (orcombustion chamber) via high-pressure fuel injectors, the fuel then evaporates and mixes with theinduced fresh air, the fuel-air mixture ignites by spark plug(or auto-ignites by compression), creatinga high temperature, high pressure explosion that provides motive power.
Revised: A basic ICE works like follows: the fuel system injects gasoline (or diesel) into the intake port (or combustion chamber) via high-pressure fuel injectors, the fuel then evaporates and mixes with the induced fresh air, the fuel-air mixture ignites by spark plug(or auto-ignites by compression), creating a high temperature, high pressure explosion that provides motive power.

Original: The fuel injection and mixing with ambient air is one of the most important factors impacting engineperformance (power) as well as engine emissions (such as CO2, and NO).
Revised: The fuel injection and mixing with ambient air is one of the most important factors impacting engine performance (power) as well as engine emissions (such as CO2, and NO).

Original: Therefore, extensivestudies have been carried out in the combustion domain to optimize fuel sprays for maximizing thepower to emissions index.
Revised: Therefore, extensive studies have been carried out in the combustion domain to optimize fuel sprays for maximizing the power to emissions index.

Original: Among the many measurement techniques used in spray testing, Miescattering remains one of the prominent imaging methods for spray visualization [3].
Revised: Among the many measurement techniques used in spray testing, Mie scattering remains one of the prominent imaging methods for spray visualization [3].

Original: Mie scatteringuses a light source (e.g., laser) and a camera to record the macroscopic spray development inside aquiescent chamber filled with pressurized air.
Revised: Mie scattering uses a light source (e.g., laser) and a camera to record the macroscopic spray development inside a quiescent chamber filled with pressurized air.

Original: Light is elastically scattered by fuel droplets similar toor larger than the wavelength of the incident light.
Revised: Light is elastically scattered by fuel droplets similar to or larger than the wavelength of the incident light.

Original: The signal collected by a camera is proportional tothe integral of cubic of droplet diameters along the line of sight.
Revised: The signal collected by a camera is proportional to the integral of cubic of droplet diameters along the line of sight.

Original: Examples of Mie scattering imagingare shown in Figure 1, where the dark color is background and the light color are liquid sprays.
Revised: Examples of Mie scattering imaging are shown in Figure 1, where the dark color is background and the light color are liquid sprays.

Original: Thegrayscale in each image roughly indicates the intensity of liquid volume fractions.
Revised: The grayscale in each image roughly indicates the intensity of liquid volume fractions.

Original: One of many insights gained from Mie scattering is spray morphology which helps engine experts tounderstand the mechanisms of spray breakup and mixture formation.
Revised: One of many insights gained from Mie scattering is spray morphology which helps engine experts to understand the mechanisms of spray breakup and mixture formation.

Original: However, spray developmentis a complicated process affected by many factors such as fuel volatility, fuel temperature, injectorgeometry, ambient conditions, and turbulence.
Revised: However, spray development is a complicated process affected by many factors such as fuel volatility, fuel temperature, injector geometry, ambient conditions, and turbulence.

Original: Despite the continuous efforts in academia andindustry, spray development is still not fully understood.
Revised: Despite the continuous efforts in academia and industry, spray development is still not fully understood.

Original: It is generally accepted that, depending onthe macroscopic features of spray images, spray morphology can be classified into three regimes,namely no collapse, transitional, and collapse.
Revised: It is generally accepted that, depending on the macroscopic features of spray images, spray morphology can be classified into three regimes, namely no collapse, transitional, and collapse.

Original: Characteristics of each regime are listed blow:
Revised: Characteristics of each regime are listed blow:

Original: • No collapse regime:
Revised: • No collapse regime:

Original: Characterized by visually discernible narrow plumes or branches.
Revised: Characterized by visually discernible narrow plumes or branches.

Original: The separations of spray plumes occur very closely to the injector tip (located on the top of the image).
Revised: The separations of spray plumes occur very closely to the injector tip (located on the top of the image).

Original: This is the desirable spray pattern.
Revised: This is the desirable spray pattern.

Original: • Transitional regime:
Revised: • Transitional regime:

Original: Characterized by wide spray plumes that begin to interact with eachother.
Revised: Characterized by wide spray plumes that begin to interact with each other.

Original: The separations of plumes move downstream and the exact locations becomes hard tovisually discern.
Revised: The separations of plumes move downstream and the exact locations becomes hard to visually discern.

Original: The spray structure still resembles a cone shape.
Revised: The spray structure still resembles a cone shape.

Original: • Spray collapse regime:
Revised: • Spray collapse regime:

Original: Characterized by one single prolonged central plume.
Revised: Characterized by one single prolonged central plume.

Original: There may be one or two discernible spray plumes but the majority of them are coalesced.
Revised: There may be one or two discernible spray plumes but the majority of them are coalesced.

Original: It is widely accepted that spray collapse should be avoided at all cost since it can lead to sprayimpingement, reduced total surface area for fuel-air mixing, and poor atomization.
Revised: It is widely accepted that spray collapse should be avoided at all cost since it can lead to spray impingement, reduced total surface area for fuel-air mixing, and poor atomization.

Original: The consequencesof those issues are worsened engine performance and increased combustion emissions.
Revised: The consequences of those issues are worsened engine performance and increased combustion emissions.

Original: Unfortunately,the spray collapse phenomenon is not well understood.
Revised: Unfortunately, the spray collapse phenomenon is not well understood.

Original: The detection of spray collapse has so farremained a manual process requiring many hours of subjective evaluations by domain experts.
Revised: The detection of spray collapse has so far remained a manual process requiring many hours of subjective evaluations by domain experts.

Original: Thischallenge is the main motivation to use deep convolution neural networks for automating robustclassification of spray morphology and detection of spray collapse.
Revised: This challenge is the main motivation to use deep convolution neural networks for automating robust classification of spray morphology and detection of spray collapse.

Original: B Example of training data
Revised: B Example of training data

Original: Examples of spray images in each class are shown in Figure 3.
Revised: Examples of spray images in each class are shown in Figure 3.

Original: C Baseline model network architecture
Revised: C Baseline model network architecture

Original: Given a small dataset, the most feasible starting point is transfer learning by reusing the lower layersof pre-trained models.
Revised: Given a small dataset, the most feasible starting point is transfer learning by reusing the lower layers of pre-trained models.

Original: In this study, TensorFlow version 2.4.1 [1] is used.
Revised: In this study, TensorFlow version 2.4.1 [1] is used.

Original: Among many availablepre-trained models on Keras, ResNet [4] family is employed after an internal evaluation.
Revised: Among many available pre-trained models on Keras, ResNet [4] family is employed after an internal evaluation.

Original: All theimages were pre-processed as 224 × 224 pixel images as expected by ResNet.
Revised: All the images were pre-processed as 224 × 224 pixel images as expected by ResNet.

Original: In addition, thegrayscale images were loaded in Red, Green, and Blue channels.
Revised: In addition, the grayscale images were loaded in Red, Green, and Blue channels.

Original: To select a suitable model for fine tuning, 5-fold cross validation is performed using all 878 availablespray images.
Revised: To select a suitable model for fine tuning, 5-fold cross validation is performed using all 878 available spray images.

Original: Seven variants of ResNet models were tested.
Revised: Seven variants of ResNet models were tested.

Original: Note that we implemented ResNet34from scratch since it is not available from Keras.
Revised: Note that we implemented ResNet from scratch since it is not available from Keras.

Original: For the remaining six models, we reused all thepre-trained lower and mid layers and only made the last block (namely, conv5 block3 ) trainable.
Revised: For the remaining six models, we reused all the pre-trained lower and mid layers and only made the last block (namely, conv5 block3 ) trainable.

Original: Thisleaves about 4.4 million trainable parameters for each model except for ResNet34.
Revised: This leaves about 4.4 million trainable parameters for each model except for ResNet34.

Original: We also removedthe fully connected top layer and replaced it with global average pooling layer, followed by a denseoutput layer with one neuron per class.
Revised: We also removed the fully connected top layer and replaced it with global average pooling layer, followed by a dense output layer with one neuron per class.

Original: For pre-trained ResNet models, we used Adam optimizer [5]and fixed the learning rate, batch size, and total epochs to be 0.001, 32, and 100, respectively.
Revised: For pre-trained ResNet models, we used Adam optimizer [5] and fixed the learning rate, batch size, and total epochs to be 0.001, 32, and 100, respectively.

Original: For
Revised: For

Original: ResNet34, we used stochastic gradient descent with a learning rate of 0.0001 and momentum of 0.9.
Revised: ResNet34, we used stochastic gradient descent with a learning rate of 0.0001 and momentum of 0.9.

Original: The ensemble-averaged test accuracies and standard deviations are reported in Table 2.
Revised: The ensemble-averaged test accuracies and standard deviations are reported in Table 2.

Original: ResNet50outperforms all other models with an impressive test accuracy of 96%, though other models are notfar behind.
Revised: ResNet outperforms all other models with an impressive test accuracy of 96%, though other models are not far behind.

Original: Although ResNet101 and larger models have more representation power than ResNet50,they are prone to overfitting with small training datasets and therefore have slightly poor performanceon the test set.
Revised: Although ResNet101 and larger models have more representation power than ResNet50, they are prone to overfitting with small training datasets and therefore have slightly poor performance on the test set.

Original: On the other hand, ResNet34 seems too shallow to learn all necessary low-leveland/or high-level features.
Revised: On the other hand, ResNet34 seems too shallow to learn all necessary low-level and/or high-level features.

Original: Given its highest accuracy, ResNet50 is used as the base model for furtherexperiments.
Revised: Given its highest accuracy, ResNet50 is used as the base model for further experiments.

Original: D Mixup introduction
Revised: D Mixup introduction

Original: Mixup is a simple and data-agnostic method proposed by Zhang et al.
Revised: Mixup is a simple and data-agnostic method proposed by Zhang et al.

Original: Suppose we have twoinput image vectors, x 1 and x 2 , and their corresponding one-hot label encoding vectors are y 1 and y 2 ,then the Mixup augmented training image vectors are given by:
Revised: Suppose we have two input image vectors, x 1 and x 2 , and their corresponding one-hot label encoding vectors are y 1 and y 2 , then the Mixup augmented training image vectors are given by:

Original: [Table]
Revised: [Table]

Original: [Equation]
Revised: [Equation]

Original: where λ is the interpolation coefficient randomly drawn from the Beta distribution, λ ∼ Beta ( α, α ) .
Revised: where λ is the interpolation coefficient randomly drawn from the Beta distribution, λ ∼ Beta ( α, α ) .

Original: As shown in Figure 4, λ approaches 0 or 1.0 as α → 0 , this essentially eliminates interpolation andselects one input image as the output.
Revised: As shown in Figure 4, λ approaches 0 or 1.0 as α → 0 , this essentially eliminates interpolation and selects one input image as the output.

Original: As α increases, a realization of λ would have a higher chanceof being close to 0.5, leading to strong blending of both input images.
Revised: As α increases, a realization of λ would have a higher chance of being close to 0.5, leading to strong blending of both input images.