# A Robust Approach Towards Distinguishing Natural and Computer Generated
Images using Multi-Colorspace fused and Enriched Vision Transformer

Manjary P. Gangan1, Anoop Kadan2, and Lajish V L1

This work was supported by the Women Scientist Scheme-A (WOS-A) for Research
in Basic/Applied Science from the Department of Science and Technology (DST)
of the Government of India under the Grant SR/WOS-A/PM-62/2018Corresponding
author: Manjary P. Gangan (e-mail: manjaryp_dcs@uoc.ac.in). 1Department of
Computer Science, University of Calicut, India  2School of Psychology, Queen’s
University Belfast, UK

###### Abstract

The works in literature classifying natural and computer generated images are
mostly designed as binary tasks either considering natural images versus
computer graphics images only or natural images versus GAN generated images
only, but not natural images versus both classes of the generated images.
Also, even though this forensic classification task of distinguishing natural
and computer generated images gets the support of the new convolutional neural
networks and transformer based architectures that can give remarkable
classification accuracies, they are seen to fail over the images that have
undergone some post-processing operations usually performed to deceive the
forensic algorithms, such as JPEG compression, gaussian noise, etc. This work
proposes a robust approach towards distinguishing natural and computer
generated images including both, computer graphics and GAN generated images
using a fusion of two vision transformers where each of the transformer
networks operates in different color spaces, one in RGB and the other in YCbCr
color space. The proposed approach achieves high performance gain when
compared to a set of baselines, and also achieves higher robustness and
generalizability than the baselines. The features of the proposed model when
visualized are seen to obtain higher separability for the classes than the
input image features and the baseline features. This work also studies the
attention map visualizations of the networks of the fused model and observes
that the proposed methodology can capture more image information relevant to
the forensic task of classifying natural and generated images.

###### Index Terms:

Digital Image Forensics, Computer generated images, GAN images, Vision
transformers.

##  I Introduction

Most works in the literature that distinguish natural and computer generated
images consider either computer graphics images only or GAN images only in the
category of computer generated images [1, 2, 3, 4, 5]. That is, these works
focus only on one category of computer generated images and not both. However,
these forensic algorithms do not suit the real-world scenario where the
process of image generation is unknown. Also, there could be cases if a
generated image is not computer graphics then maybe it could be a GAN image or
vice-versa. Hence a single forensic classification system is required to
investigate images and understand whether they are natural/real photographs or
the ones created by computer graphics or GAN algorithms, with high accuracy.

With the advent of convolutional neural network architectures (CNN) and
transformer based architectures, the image classification systems are
achieving high classification accuracies. Utilizing these techniques the
forensic algorithms or tools to distinguish natural and computer generated
images while moving to attain some success have been mostly vulnerable to
different variations in images caused due to image quality, resolution,
compression quality, or color which are capable enough to dramatically modify
or restructure the underlying image properties
111https://www.nytimes.com/interactive/2023/06/28/technology/ai-detection-
midjourney-stable-diffusion-dalle.html?auth=register-google&utm_source=pocket-
newtab-intl-en. Image forgeries are almost always followed by these operations
like adding some noise or applying JPEG compression to obscure any traces of
image generation or forgeries and thereby deceiving image forensic algorithms
and tools. Therefore, besides producing a high performance system for
classifying photographs and computer generated images of both categories
(computer graphics and GAN), it is equally essential to review the robustness
of these forensic systems towards various post processing operations. Hence,
unlike the works in the literature that deals the forensic task of
distinguishing natural and computer generated images as a binary-class
classification task either by considering only computer graphics or only GAN
images, our work proposes a generalized forensic algorithm, i.e., a three-
class classification task classifying real, computer graphics and GAN images.
Our methodology focuses on building a classification model such that it
achieves high accuracy and is highly robust against various post-processing
operations.

The major contributions of our work are:

  * •

We propose a transformer based approach for the forensic task of
distinguishing natural images and computer generated images including both
computer graphics and GAN images.

  * •

We majorly focus on building a classification model that is highly robust
against post-processing operations such as JPEG compression, addition of
gaussian noise, etc. and therefore we employ a fusion of two color space
transformations in our approach.

  * •

We compare the performance of our proposed model with a set of baselines and
could observe that the performance of our model outperforms the baselines, is
highly robust against post processing operations, and is also generalizable to
unseen test data.

  * •

We visualize the feature representations of our model and compare with the
input image features and feature representation of a baseline method, where we
could observe that our model provides better separability between the three
different classes, helping towards improved classification performance.

  * •

We also visualize the attention maps of the networks of our fused model to
study the capability of our proposed methodology for the forensic task of
classifying natural and generated images.

The rest of this paper is organized as follows. Section II presents a brief
survey of related works and delineates our proposed work from the related
works in the literature. Section III gives details of the dataset used in this
study. Section IV discusses the methodology of the proposed work along with
the motivation and detailed description of the proposed model. Section V
presents the experimental settings and details of the baseline models used for
comparing our proposed model. Section VI presents the results and discussion
including the results of the experiments for robustness, generalizability,
feature visualization, and the analysis of attention maps. Section VII finally
draws the conclusions.

##  II Related work and Our work in context

The works that distinguish natural and computer graphics images can be seen
since the 1990s. These include statistical feature based works [6, 7, 8],
transform domain features [9, 10, 11], device properties [12, 13, 14], and the
recent works that utilize deep learning architectures such as Convolutional
Neural Networks (CNN) [15, 16, 17, 4]. Whereas, works that distinguish natural
and GAN images are comparatively much more recent than the aforesaid category
of natural versus computer graphics images. These works in the literature that
attempt natural versus GAN images, mostly employ deep learning based
approaches [3, 18, 19], than the handcrafted feature based approaches [20].
Few works are also seen to utilize transformer based architectures to detect
GAN generated videos [21], but these works also only consider the single
category of generation, that is natural versus GAN only.

To the best of our knowledge, there is only a single work that distinguishes
natural versus computer generated images by considering both computer graphics
and GAN images in the category of computer generated images [22], and utilizes
an EfficientNet CNN architecture for the three-class classification task. But,
to the best of our knowledge, no works are seen to be reported using the high
performance recent deep learning architectures i.e., transformer based
architectures for classifying natural images and both categories of computer
generated images, i.e., Graphics and GAN generated images. Our work utilizes
vision transformers and proposes a fusion based approach to distinguish
natural versus computer generated images of both categories, i.e., Graphics
and GAN images. Despite other works in the literature that utilize certain
color space transformations for the task of distinguishing natural images from
computer-generated images of either of the category such as [23, 24], our work
utilizes two color spaces in our methodology, based on our rigorous set of
experiments, one for improving the overall accuracy of the task of
distinguishing natural images from computer-generated images of both
categories and other color space that deals with improving the robustness of
the proposed model against post-processing operations such as JPEG
compression, gaussian noise, etc. Our methodology follows a transfer learning
approach which helps to improve the accuracy of the task without involving the
burdensome process of pre-training and increasing the training complexity.

##  III Dataset

In this work, we utilize the GAN, Graphics, and Real images from the dataset
used in the study [22]. The dataset comprises 12000 images in total, where
each of the classes contains 4000 images. The class GAN consists of images
collected from a variety of generative algorithms such as ProgressiveGAN [25],
StyleGAN [26], StyleGAN2 [27], and StyleGAN2-ADA [28]. Whereas, the images for
the classes Graphics and Real are obtained from the Computer Graphics versus
Photographs dataset [1]. The entire dataset is challenging and contains a
diverse category of images in terms of image content (indoor and outdoor
scenes, animals, objects, etc.), origin (different generative/graphics
algorithms or cameras, etc), and quality. Also, the computer generated images
i.e., both GAN and graphics are photorealistic, i.e., they are not manually
easy to predict as computer generated ones. For the training, validation, and
testing the dataset is proportionally split in the ratio 60:20:20
respectively.

##  IV Methodology

In this work, the forensic task of distinguishing natural and computer
generated images is formulated as a three-class classification task, where the
three classes are GAN, Graphics, and Real. GAN and Graphics images, even
though both being computer generated, are maintained as separate classes as
they have different generation processes. For this three-class classification
problem, we utilize transformer based deep neural networks to find the best-
fit mapping function $M:y=M(x)$ for the train data
${(x_{1},y_{1}),(x_{2},y_{2}),...,(x_{n},y_{n})}$ where for each image $x_{i}$
in the training set, $y_{i}\in(0,1,2)$, indicating either of the classes GAN,
Graphics or Real, respectively.

###  IV-A Motivation

The images transmitted through social media and online platforms are subject
to image compression, mostly JPEG compression, where different online
platforms follow different JPEG compression standards [29, 30, 31]. Also in
the cases of intentionally propagating fake images to support some piece of
fake news to convince the audience, these images are seen to be mostly subject
to multiple image compressions [32, 33]. Hence, any model proposed for
distinguishing natural and computer generated images, apart from obtaining
high classification accuracy must also be highly robust towards compression.
But most of the computational models in the literature proposed for the
forensic task of distinguishing natural and computer generated images, are
less robust to post processing operations, particularly the JPEG compression
[34]. That is, as the compression factor of the images increases (or the
quality factor of the images decreases), the accuracy of the computational
models to distinguish natural and computer generated images decreases. We
analyze the classification accuracies of different computational models to
distinguish GAN, graphics, and real images, at varying levels of JPEG
compression, including the state-of-the-art vision transformer based
architectures ViT-Base and ViT-Large [35], state-of-the-art CNN based
architecture InceptionResNet [36] and a few other baselines that classify
natural and computer generated images [22, 2, 16, 3]. Figure 1 shows the
results of classification accuracies of these models for various compression
factors. As can be seen from the figure, the accuracy of all the models
decreases as the compression increases.

Figure 1: Classification accuracies of the models for various JPEG compression
quality factors

(a) GAN class accuracies

(b) Graphics class accuracies

(c) Real class accuracies

Figure 2: Class accuracies of the models for various JPEG compression quality
factors

To propose a robust model for the task, hence, we further analyze the class
accuracies of these models. Figure 2 shows the individual class accuracies of
the models for varying levels of JPEG compression i.e., accuracies of the
class GAN generated images at varying levels of compression factors in figure
2a, graphics generated images in figure 2b, and real images in figure 2c. We
could observe that, for uncompressed images (zero compression factor or
original images), class accuracies of GAN generated images are always higher
than the graphics and real images, for all the models. But at the same time,
the class GAN is the most affected as the compression increases (as shown in
figure 2a). That is, there is a very high drop/decay in the class GAN
accuracies of the models with even small increments in JPEG compression. For
the class Real in figure 2c, the drop in class accuracies of the models as the
compression increases are comparatively very less and for some compression
rates the accuracies even gets an increase in values. Whereas, for the class
Graphics in figure 2b, there is negligible drop in class accuracies of the
models, it has almost stable accuracies as the compression increases.
Altogether, analyzing the class accuracies shows that the rate of decrease in
class accuracies with the increase in compression differs for different
classes. And hence, how we can exploit this vulnerability of the decrease in
accuracy with an increase in compression, which differs for each class, is the
motivation for our proposed approach of a robust classification model for the
forensic task of distinguishing natural and computer generated images.

###  IV-B Network architecture

Figure 3:  The overall architecture of our Multi-Colorspace fused and Enriched
Vision Transformer (MCE-ViT)

We devise our methodology in such a way that the proposed model should obtain
high classification accuracy and should also be highly robust. We propose a
Multi-Colorspace fused and Enriched Vision Transformer (MCE-ViT) model by
parallely combining two transformer based networks that operates in two
different color spaces, one for obtaining high classification accuracy and the
other network dedicated to improve the robustness of classification. The
entire architecture of our proposed model is shown in figure 3. For obtaining
high classification accuracies we choose as the first network of the fused
model, one of the recent state-of-the-art transformer based models ViT [35].
This network takes as input the RGB images, and we name this first ViT network
as RGB ViT network. We follow a transfer learning strategy where we choose the
ViT network pre-trained on the Imagenet 21-k dataset [37] and fine-tune the
network using the task specific GAN, Graphics and Real images dataset
(detailed in section III). Even though this first RGB ViT network is found to
obtain high classification accuracies for uncompressed images, it also has a
performance decay when the images are JPEG compressed, as already seen in
figure 1. Since the rate of performance decay is different for different
classes (as detailed in section IV-A), allowing the model to also learn about
these differences in performance decay among the classes, would help to better
identify these classes in compressed scenarios. Therefore we design a strategy
for the second network in our fused model in such a way as to make the model
learn these differences and thereby improve the robustness.

In the second network of our fused model, the input RGB images from the
dataset are initially converted to YCbCr color space, the color space commonly
used in the process of JPEG compression [38]. The process of JPEG compression
mainly downsamples the chrominance planes Cb and Cr because the changes
brought up in these planes are less visually discernible [38, 39]. On this
basis, our second Enriched YCbCr ViT network enriches the YCbCr images with
the information on the error of chrominance planes between the original images
and their corresponding JPEG compressed versions as follows.

$\displaystyle\text{YCbCr}\xrightarrow{\text{JPEG
compression}}\text{Y'Cb'Cr'}$
$\displaystyle\text{YCbCr}-\text{Y'Cb'Cr'}\xrightarrow{\text{Error of
chrominance
planes}}\text{\\{\\}Cb\textsuperscript{dif}Cr\textsuperscript{dif}}$
$\displaystyle\text{YCbCr}+\text{\\{\\}Cb\textsuperscript{dif}Cr\textsuperscript{dif}}\xrightarrow{\text{Enrichment}}{\text{YCbCr}}_{\text{enriched}}$
(1)

Our this strategy is motivated by the fact that, since the rate of differences
between original and compressed versions of images are different for different
classes, enriching the images with this information on the rate of differences
would be highly beneficial to distinguish natural and generated images with
high classification accuracies, even for images in post-processed scenarios
thereby improving robustness of the model. Accordingly, the second pre-trained
ViT network is fine-tuned using these enriched YCbCr images.

Both the first RGB ViT network and the second Enriched YCbCr ViT network
produce an output feature vector. Even though the feature vector from the
first RGB ViT network is very powerful to classify gan, graphics, and real
images with high accuracy in uncompressed scenarios, in order to decrease its
effect towards performance decay in compressed scenarios, we perform average
pooling on this feature vector to obtain only the representative feature of
the RGB ViT network. Thus, pooling the feature vector from the RGB ViT network
helps to not affect the robustness of the model in compressed scenarios, as
well as to maintain high model accuracies. Later, to build the fused model,
the feature vectors from both the ViT networks are concatenated to form a
single feature vector which is passed to a fully connected neural network with
a dense layer and a 3-class output layer that determines the class label of
the images.

##  V Experimental Settings

The proposed study utilizes the vision transformer ‘vit-large’ with patch size
16 and input image size 224 x 224, for both RGB and the Enriched YCbCr
networks of the fused model. The Enriched YCbCr ViT network utilizes JPEG
compression with a quality factor of 90. The study follows transfer learning
strategy where both the ‘vit-large’ networks are pre-trained on ImageNet-21k
[37] and fine-tuned on the task specific dataset used in the study. Each ViT
network produces an output feature vector of size 1024. After manually
analysing the results of average pooling of the feature vector from the first
RGB ViT network with various kernel sizes and strides, we use a kernel size of
16 without any stride as a representative setting, and the resultant feature
vector of size 64 is concatenated with the feature vector from the second
Enriched YCbCr ViT network. The entire concatenated feature vector of size
1088 is fed to a dense layer of 512 neurons with ReLU activation function,
followed by an output dense layer of 3 neurons with softmax activation
function, making 559,107 number of trainable parameters. The other
hyperparameters are batch size 16, categorical crossentropy loss function,
Adam optimizer, and 50 epochs.

The experiments are conducted on the deep learning workstation equipped with
Intel Xeon Silver 4208 CPU at 2.10 GHz, 256 GB RAM, and two GPUs of NVIDIA
Quadro RTX 5000 (16GB each), using the libraries Tensorflow (version 2.8.0),
Keras (version 2.8.0), Torch (version 1.13.1+cu116), PyTorch Lightning
(version 1.9.0), Transformer (version 4.17.0), and Albumentations (version
1.3.1).

###  V-A Baselines

We compare the performance of our proposed model with the state-of-the-art
work that classifies GAN, Graphics, and Real images, works that classify
natural and either of the computer generated images (i.e., GAN or Graphics),
and an off-the-shelf deep neural network architecture, by fine-tuning them to
three-class classification task using the dataset used in our study.

  * •

MC-EffNet: Multi-colorspace fused EfficientNet networks proposed in [22]. This
baseline work proposes a fused model by parallely combining three
EfficientNet-B0 networks that operate in three different color spaces RGB,
LCH, and HSV. After converting the images into LCH and HSV color spaces, the
values are rescaled into the range 0 to 255 in order to supply into the
EfficientNet network. The pre-trained EfficientNet-B0 networks are fine-tuned
using the GAN, Graphics, and Real images of the dataset used in [22]. The
feature vectors from all three EfficientNet networks are then concatenated and
supplied to an output dense layer with 3 neurons and a softmax activation
function. This forms the MC-EffNet-1 network. Whereas, the MC-EffNet-2 network
includes an additional preprocessing layer of laplacian of gaussian operation,
before performing the color conversions to LCH and HSV. For both the networks
the hyperparameters are, categorical cross-entropy as loss function, Adam
optimizer with learning rate 0.001, 256 as batch size, and 100 epochs.

  * •

The other baselines chosen for this study include InceptionResNet [36], Quan
et al. [2], Nataraj et al. [3] and Rezende et al. [16] that were chosen as the
baselines in the work of MC-EffNet [22], and the experimental settings of all
these baselines are followed same as mentioned in the work of MC-EffNet [22].

##  VI Results and Discussions

Our proposed model achieves a test accuracy of 94.25 percent. The confusion
matrix of the test results of our proposed model is shown in figure 4. Table I
presents a comparison of the test results of our model and the baselines in
terms of total accuracy and class-wise accuracy. The test results indicate
that our proposed model outperforms the baselines in terms of overall test
accuracy and even in the case of individual class-wise accuracy. Our model
obtains a gain of 4.87 percentage points in terms of overall accuracy when
compared to MC-EffNet-2, the best performing model among the baselines.

Figure 4: Confusion matrix of MCE-ViT TABLE I: Comparison of model performance accuracies in percentage (The highest accuracy is given in boldface) Model | GAN | Graphics | Real | Total accuracy
---|---|---|---|---
MCE-ViT (Our model) | 98.75 | 91.00 | 93.00 | 94.25
MC-EffNet2 [22] | 96.75 | 83.75 | 87.63 | 89.38
MC-EffNet1 [22] | 96.25 | 81.75 | 85.88 | 87.96
InceptionResNet | 85.25 | 73.50 | 79.63 | 79.46
Quan et al. [2] | 56.08 | 72.88 | 69.79 | 66.25
Nataraj et al. [3] | 76.00 | 48.25 | 57.13 | 60.46
Rezende et al. [16] | 59.40 | 52.83 | 57.40 | 56.54

Among the three classes, GAN obtains the highest individual class accuracy of
98.75 percent, achieving a gain of 2 percentage points when compared to the
highest class accuracy of 96.75 percent obtained by MC-EffNet-2 amongst the
baselines. Class Graphics achieves an accuracy of 91.00 percent, a very high
gain of 7.25 percentage points when compared to the highest class accuracy of
83.75 percent for the MC-EffNet-2 model amongst the baselines. Class Real
achieves 93.00 percentage accuracy, i.e., a gain of 5.37 percentage points
when compared to the highest class accuracy of 87.63 percent obtained by MC-
EffNet-2 amongst the baselines.

###  VI-A Robustness against Post-processing

Besides achieving high classification accuracies on original images or images
that are not being post-processed, an efficient image forensic algorithm
should also provide robust classification output over post-processed images.
Hence, the robustness of the proposed model MCE-ViT is evaluated towards the
typical post-processing operation of JPEG compression and is compared against
the baselines. Apart from the baseline models discussed in section V-A, we
also compare the robustness of our proposed model with the off-the-shelf pre-
trained vision transformer networks, ViT-B/16 and ViT-L/16 that are fine-tuned
using the dataset used in this study. Here the ViT-L/16 results will serve as
an ablation study for our methodology that incorporates color space fusion and
enrichment of YCbCr with the error of chrominance planes information using
ViT-L/16.

Every model trained on uncompressed data (or original train data in the
dataset) is tested separately over ten different test data created using
various JPEG compression quality factors within the range 100 to 10, in steps
of 10. Figure 5 shows the robustness test results, where it can be observed
that compared to the baselines, the proposed model achieves improved
robustness towards post-processing based on JPEG compression, for all the
compression quality factors. Here also, similar to the classification results
of original uncompressed images (table I), MC-EffNet-2 is the baseline model
that shows the next improved robustness among all the baselines for different
compression quality factors.

Figure 5: Classification accuracies of our model and the baselines for various
JPEG compression quality factors

Besides analyzing robustness against JPEG compression in terms of overall
accuracy, we also analyze the robustness of our proposed model specifically
for the class GAN, since it is the class that is most affected by post-
processing operations and also the major contributing factor towards the
decrease in overall accuracy, as already discussed in section IV-A. Figure 6
shows the robustness test results of our proposed model and the baselines,
specifically for the class GAN. We can observe that our proposed model
achieves very high class accuracy for all the compression factors. The class
accuracy obtained for our model while classifying original images (no
compression) is 98.75 percent. At the same time, for the images compressed at
a compression factor of 10 (very high compression), the class accuracy of our
model is 85.13 percent. That is, for a very high compression factor of 10, our
model obtains a very high gain of 41.32 percentage points when compared to the
next higher accuracy of 43.81 percent at compression factor 10 for the
baseline Rezende et al. [16] .

The class accuracy of the baseline ViT-L network (ablation) at a compression
factor 10 is only 34.00 percent. That is, our proposed model even being built
using the ViT-L network, but our methodology of color space fusion and the
enrichment of YCbCr with the error of chrominance planes information between
original and compressed images has proven to be highly advantageous in
improving the robustness of the proposed model thereby achieving a class
accuracy of 85.13 percent even at a compression factor of 10, i.e., a very
huge gain of 51.13 percentage points when compared to the ViT-L network
(ablation).

Figure 6: GAN class accuracy of our model and the baselines for various JPEG
compression quality factors

We also find the robustness of our model against other post processing
operations and compare it with the baselines. The accuracy of our proposed
model and the baselines at various standard deviation ($\sigma$) values of
Gaussian noise is shown in figure 7. We can observe that compared to the
baselines our model achieves better robustness against Gaussian noising also.

Figure 7: Classification accuracies of our model and the baselines for various
Gaussian noise standard deviations ($\sigma$)

###  VI-B Generalizability

This study also analyzes the generalizability of our proposed model MCE-ViT by
testing over unseen data. The proposed model MCE-ViT which is fine-tuned on
the dataset used in this study is tested over three other combinations of
unseen GAN, Graphics, Real images, i.e., PG2 versus PRCG versus PIM-Google
[40, 41], PG2 versus PRCG versus PIM-Personal [40, 41], and Cycle GAN versus
Raise versus Level-Design [42, 43, 44] datasets, with 160 images in each of
the class of the three datasets, as experimented in the baseline work [22].
The generalizability test results are shown in table II, where it can be
observed that compared to the baselines our proposed model is able to obtain
higher test accuracies. The results hence prove that our model has better
generalizability, which can even help towards the future challenges in
generated image categories.

TABLE II: Generalizability of the models over three datasets in percentage (The highest accuracies are given in boldface)  Model |  | PG2 $\times$
---
PRCG $\times$
PIM-Google
| PG2 $\times$
---
PRCG $\times$
PIM-Personal
| Cycle GAN $\times$
---
Raise $\times$
Level-Design
MCE-ViT (Our model) | 87.84 | 90.31 | 91.75
MC-EffNet-2 [22] | 81.04 | 85.21 | 84.79
InceptionResNet | 62.08 | 67.16 | 71.74
Quan et al. [2] | 54.22 | 56.27 | 60.01
Rezende et al. [16] | 51.25 | 51.21 | 50.92
Nataraj et al. [3] | 49.17 | 53.63 | 48.75

###  VI-C Feature Visualization

The dimension of images that are input to the proposed MCE-ViT model is 224
$\times$ 224 $\times$ 3, i.e., the length of the raw image features is 150528.
MCE-ViT projects these raw image features into a smaller dimension of length
1088, with an aim to provide better separability between the three classes. We
analyze the separability potential of the feature vector of our model by
comparing against the feature vectors of raw input image pixels and the best
baseline model MC-EffNet-2 that obtains the next higher classification
accuracy among all the baselines. The t-Distributed Stochastic Neighbor
Embedding (t-SNE) [45] dimensionality reduction technique can visualize high
dimensional features into a two-dimensional plane and thereby helps to easily
compare the separability potential of the feature vectors. Using the t-SNE
technique we project the raw image features, feature vector output from the
baseline model MC-EffNet-2 and feature vector output from our proposed model
MCE-ViT, into two-dimensional plots, shown in figure 8. In each of the plots,
three different colors are used to indicate three different classes, green
circles are used to represent GAN image class, blue squares are used to
represent Graphics images class, and pink diamonds are used to represent the
class of Real images. From the t-SNE visualizations, it is clearly
understandable that the raw image features do not have the potential to
separate the classes, all the classes are clustered together, more
particularly towards the center of the plot (figure 8a). The output features
projected from the baseline model MC-EffNet-2 (figure 8b) seem to produce
separability between the classes better than the raw image pixels. The output
features projected from our proposed model MCE-ViT (figure 8c) seem to produce
much better separability between the three classes when compared to both raw
pixels and the best baseline MC-EffNet-2. This demonstrates that our proposed
model MCE-ViT has better capability to transform the raw image pixels to a
much better separable feature space for the forensic task of distinguishing
natural images from computer-generated images including computer graphics and
GAN images.

(a) Raw image features

(b) MC-EffNet-2 features

(c) MCE-ViT features (Our model)

Figure 8: t-SNE visualizations of feature vectors. (  indicate GAN images,
indicate Graphics images and,  indicates Real images)

###  VI-D Attention visualization

While visualizing the attention maps of both the networks of our fused model
i.e., the RGB network and the Enriched YCbCr network, we could observe that
compared to the RGB network, the Enriched YCbCr network could potentially
identify more regions or information in an image that are helpful for
classifying images into the classes GAN, Graphics or Real. Table III shows a
comparison of the attention map visualizations of both the RGB network and the
Enriched YCbCr network for a set of GAN, Graphics and Real images. For example
in the first generated image of a cat in the set of GAN images, the RGB
network mainly captures the edges of the cat, whereas the Enriched YCbCr
network captures some of the information captured by the RGB network and even
more including from the bacground, irrespective of the regions of the object
in the image. Similarly, in the second generated face image, the forehead,
right eye, and the image background are given more attention by the Enriched
YCbCr network than the RGB network.

Similarly in the set of graphics images also, we can observe that the Enriched
YCbCr network is able to capture more relevant image information in detail
than the RGB network, such as the regions of uneven illuminations in the
image. Also, mostly, the attention given to the captured image regions by the
Enriched YCbCr network are higher than the attention given by the RGB network.

In the real class of images also we can observe that the Enriched YCbCr
network could capture more image information than the RGB network. For example
in the first image of the dog and the second image of the cow, the attention
given to the image regions are higher for the Enriched YCbCr network than the
RGB network. Also, more image regions relevant for classification are seen to
be captured by the attention maps of the Enriched YCbCr network.

Thus for all the classes we can observe that the image information captured by
the Enriched YCbCr network for this forensic task is comparatively much more
relevant than the RGB network. This, in fact, shows the powerful nature of our
methodology incorporating the YCbCr color space transformation and enriching
the color space with the information on the rate of differences between
original and corresponding compressed versions of images in different
categories, to capture image information that is highly relevant to the
forensic task of classifying natural and generated images.

TABLE III: Attention map visualizations of the RGB network and the Enriched YCbCr network Original image | Attention map visualizations |  Original image | Attention map visualizations
---|---|---|---
RGB network | Enriched YCbCr network | RGB network | Enriched YCbCr network
GAN
|  |  |  |  |
|  |  |  |  |
Graphics
|  |  |  |  |
|  |  |  |  |
Real
|  |  |  |  |
|  |  |  |  |

##  VII Conclusion

In this work a robust approach towards distinguishing natural and computer
generated images including both, computer graphics and GAN generated images is
proposed, unlike the works in the literature to distinguish natural and
computer generated images that consider only either of the generated images
category. The proposed work utilized a fusion of two vision transformers one
of them operating in RGB color space and the other in YCbCr color space.
Transformer based architectures can provide good classification performance,
while our methodology focuses on improving the robustness of the proposed
model against post processing operations such as JPEG compression by
maintaining a high model accuracy because usually the forensic algorithms and
tools even with high performance accuracies are fooled using these post
processed images. Experiments are conducted to analyze the performance of the
model and are compared against a set of baselines. The proposed model achieves
higher accuracy than the baselines and is found to be highly robust and
generalizable. Visualizing the features showed better separability capability
of the proposed model than the baseline. The work also studied the attention
map visualizations of the networks of the fused model and observed that the
proposed methodology could capture more image information relevant to the
forensic task of classifying natural and generated images. To aid the future
research, the relevant materials of this study including the source code will
be made publicly available at https://github.com/manjaryp/MCE-ViT and
https://dcs.uoc.ac.in/cida/projects/dif/mcevit.html along with the
publication. In the future, we plan to work on other forensic attacks such as
recaptured images and computer generated videos.

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Figure 31: Dust temperature $T_{\mathrm{d}}$ versus grain emissivity index
$\beta$ for $\tau_{160}>5\times 10^{-4}$ ($\rho\simeq 0.00$). Colors code the
distance from $\theta^{1}$ Ori C.

Figure 32: Dust optical depth $\tau_{160}(>5\times 10^{-4})$ versus grain
emissivity index $\beta$ ($\rho\simeq 0.32$). Colors code the distance from
$\theta^{1}$ Ori C.

In Fig. 32, we clearly see that the dust temperature decreases with increasing
distance from the presumably dominant heating source $\theta^{1}$ Ori C.
Points corresponding to lower $\tau_{160}$ tend to be more distant and scatter
around the mean dust temperature.

From Fig. 32, we conclude that also in a free-$\beta$ SED fit there is no
correlation between the resulting dust temperature and optical depth.
Independent of $\tau_{160}$, most of the data points scatter around the mean
dust temperature $T_{\mathrm{d}}\simeq 31.4\,\mathrm{K}$ with a standard
deviation of $\sigma_{T_{\mathrm{d}}}\simeq 4.0\,\mathrm{K}$.

There is no correlation between $T_{\mathrm{d}}$ and $\beta$, as can be seen
from Fig. 32. The mean grain emissivity index is $\beta\simeq 1.33$, but with
significant scatter around this value.

The correlation between $\tau_{160}$ and $\beta$ has a significant slope (Fig.
32), even though there is substantial scatter, which amounts to a correlation
index of only $\rho\simeq 0.32$. Deeper structures tend to have higher
$\beta$, but this is not reflected in dust temperature, as discussed above.
This might be due to the fact that deeper structures also contain colder gas
along with warmer (surface) gas, which leads to a relative suppression of the
long-wavelength tail, resulting in a higher $\beta$.

##  Appendix C SED fits to single points

Figure 34 shows SED fits with $\beta=2$ toward representative points. Fig. 34
shows SED fits where we let $\beta$ vary freely for the same selection of
points.

Figure 33: SED fits to single pixels with $\beta=2$.

Figure 34: SED fits to single pixels with free $\beta$.

##  Appendix D Spectral line fits

###  D.1 M42

Figure 19 shows spectra toward six regions of high [CII] intensity in M42.
Table LABEL:Tab.CII-bright gives the fit parameters of a multi-component
Gaussian fit for each spectrum. Table 15 gives the result of the [13C ii]
analysis, where possible.

Spectrum 1 (Eastern Rim, north) exhibits two [C ii] main components. Both can
be observed in [13C ii], as well. From the fit results, we obtain two rather
different results: The $7.3\,\mathrm{km\,s^{-1}}$ yields a moderate excitation
temperature, while the $10.5\,\mathrm{km\,s^{-1}}$ component seems to arise in
very warm gas. The latter than traces only a very small column, while the
former traces one third of the dust-traced column. Despite the high
temperature, the second component displays a very narrow emission line, where
the line broadening appears to be almost thermal. The origin of this component
is unclear. In channel maps, it seems to be connected to the OMC1 core, that
has a bright eastern extension at that velocity.

The bright [C ii] emission in spectrum 2 (Eastern Rim, south) requires an
incident radiation field of $G_{0}\simeq 10^{4}$ (from models). The excitation
temperatures we derive from the [13C ii] line (two components) are not
extreme. Both components trace about 15% of the dust column. While the [C ii]
components are relatively narrow, the high-velocity 12CO and 13CO components
emit rather broad lines. We do not observe a significant broad [C ii]
component that might stem from the ionized gas, that is seen in H$\alpha$
toward this region. It is not certain how additional possible sources (e.g., T
Ori) affect the excitation and dynamics in this region.

The bright [C ii] emission of spectrum 3 (south of OMC1, north of OMC4)
consists of two components. Despite the strong main [C ii] line, the [13C ii]
line is very weak. This indicates rather low optical depth, but high
temperature. Because of the relatively weak [13C ii] line, it is unlikely that
the main [C ii] line is self- or foreground absorbed. Rather, we fit two
emission components. We can only detect the brighter component in [13C ii].
This [C ii] component traces only a small fraction of the total dust column.
The high temperature is reflected in the associated very bright CO emission
(with a broad 13CO line), that traces a 4 times larger gas column than [C ii]
($A_{\mathrm{V,los}}\simeq 40$). The other CO component, associated with the
fainter [C ii] main component, seems to arise in relatively more moderate
conditions (narrow 13CO line) and seems to trace only a thin
($A_{\mathrm{V,los}}\simeq 3$) layer of gas. In addition to the strong main
line, we observe a very broad component in the [C ii] spectrum at negative
velocities, that possibly stems from ionized gas expanding toward the
observer.

The brighter [C ii] components require very extreme conditions, according to
the standard models of the PDR Toolbox (Kaufman et al. 2006; Pound & Wolfire
2008). Also in the central regions of the Orion Nebula, the [C ii] intensity
is higher than expected from standard PDR models. Constant pressure models, as
opposed to constant density models, might hold clues to the reason for this
behavior.

In spectrum 4 (west of Orion S), we observe a single bright [C ii] main
component, well separated from two weak low-velocity components. Also the CO
spectra reveal only one component. In the region of spectrum 4, we observe the
lower branch of the [C ii]-FIR correlation in the ISF (although this region
lies adjacent to the main spine). Despite the face-on geometry in this area,
the [C ii] emission lies above the model predictions. We cannot exclude a
tilted surface, however. If we assume optically thick [C ii] emission, we
compute an excitation temperature of $T_{\mathrm{ex}}=64\,\mathrm{K}$. The CO
excitation temperature is only slightly lower and both emissions need rather
high radiation field and density (from the models). The 13CO line is rather
broad, which hints at elevated turbulence. The CO emission traces a large
column of gas, $A_{\mathrm{V,los}}\simeq 20$, which is 1/5 of the dust-traced
column. The dust temperature is rather moderate
($T_{\mathrm{d}}=27\,\mathrm{K}$), the background consisting of a large column
of cold dust. From the FIR intensity we estimate a radiation field of
$G_{0}\simeq 4\times 10^{3}$, which is 2-3 times lower than required for the
[C ii] and CO intensity according to the models.

In spectra 5 and 6 (south of OMC4 in the ISF), we notice that the CO
excitation temperature is further decreasing with distance from the Trapezium.
The CO column density remains constant, CO tracing a column of
$A_{\mathrm{V,los}}\simeq 10$. From comparison with the [C ii] emission, we
see that $G_{0}$ is dropping, but $n$ remains approximately constant, $n\simeq
1\text{-}5\times 10^{4}\,\mathrm{cm}^{-3}$.

###  D.2 M43

Figure 19 shows six spectra toward the shell of M43. Table LABEL:Tab.M43-shell
gives the fit parameters of a multi-component Gaussian fit for each spectrum.
Table 16 gives the result of the [13C ii] analysis, where possible.

All spectra have too strong [C ii] emission as to be consistent with face-on
geometry. The column traced by [C ii] corresponds to $A_{\mathrm{V,los}}\simeq
15$ in most cases. This clearly indicates an edge-on illuminated gas column,
given the rather moderate radiation field in M43. Most spectra, both [C ii]
and CO, consist of at least two components. Spectrum 5 is the most enigmatic.
The [C ii] spectrum can be fitted only with four components plus one component
that we attribute to [13C ii] emission (it could be a red-shifted [12C ii]
component, as well). However, the [13C ii] component (if it is such and not an
additional [12C ii] component) appears to be rather strong compared to the
[12C ii] component, which yields a very high [C ii] optical depth. The 12CO
spectrum clearly comprises two components, but cannot be fitted satisfactorily
with Gaussian profiles, while the 13CO spectrum can. We note that spectrum 5
lies in a region where the shell surrounding the M43 H ii region seems to be
interrupted, possibly allowing for ionized gas flowing out of the cavity.
Outflows may lead to irregular line shapes in the surface layers of a
molecular cloud. However, we do not observe a broad component in the [C ii]
spectrum, that might stem from the ionized gas itself. The fact that most
spectra comprise more than one emission component may indicate that the gas
layers along the line of sight experience shear due to stellar feedback. We
judge that the spectra in M43 can be explained by emitting components only,
rather than invoking additional absorbing layers.

###  D.3 NGC 1977

Figure 19 shows six spectra toward the shell of NGC 1977. Table
LABEL:Tab.NGC1977-shell gives the fit parameters of a multi-component Gaussian
fit for each spectrum. Table 17 gives the result of the [13C ii] analysis,
where possible.

The CO component at $8\,\mathrm{km\,s^{-1}}$ in spectrum 2 corresponds to a
weak [C ii] component, that cannot be fitted properly because it is just above
the noise level. Again, it is unlikely that 13CO is self-absorbed, hence we
conclude that there are two emitting CO components within the line of sight.

The [C ii] line in spectrum 3 is almost Gaussian, but slightly asymmetric. In
a two-component fit the [C ii] components line up with the CO components. This
might indicate that the shell around NGC 1977 is indeed moving at differential
velocities and that CO emission arises within the shell at low density. The
cloud depth derived from the 13CO line is about $A_{\mathrm{V,los}}\simeq
0.1\text{-}0.4$.

The [C ii] line in spectrum 4 is slightly asymmetric. The line widths in a
two-component fit are close to the thermal line width, as in spectrum 3. We do
not find a good fit with an absorbing component instead of a second emitting
component. Since we expect the region to be in dynamic expansion, we may
expect line asymmetries, and the Gaussian two-component fit may be misleading.

Also the [C ii] line in spectrum 5 has a relatively (close to thermal) line
width, but an additional broad wing. Spectrum 5 is taken toward the [C
ii]-faint region, where the shell may be breaking open. The broad wing might
be a signature of an ionized outflow or increased turbulence in the neutral
gas due to the rupture (as in M43). The narrow line in spectrum 5 is blue-
shifted with respect to the lines in other [C ii] spectra toward NGC 1977,
possibly reflecting an increased backward pressure in this region.

The [C ii] line in spectrum 6 is slightly asymmetric, as well, and can be
fitted with two Gaussian components.

###  D.4 Spectra behind the Bar

Fig. 24 shows nine spectra toward the region southeast of the Orion Bar. Table
LABEL:Tab.behind-Bar gives the fit parameters of a multi-component Gaussian
fit for each spectrum. Table 18 gives the result of the [13C ii] analysis,
where possible.

Spectra with bright [C ii] emission, where we can detect the [13C ii]
$F=2\text{-}1$ line, can be interpreted as exhibiting a significant absorbing
component. However, invoking an absorbing component gives rise to rather
extreme derived excitation condition, which we do not expect behind the Orion
Bar and in the Eastern Rim. As the [13C ii] line is often only marginally
detected, fit uncertainties are large. Deeper observations are needed to
investigate this matter further (Kabanovic et al. in prep.). All spectra along
the line cut behind the Orion Bar show multiple features, that are enigmatic
in origin. A more detailed study, comparing with velocity-resolved data sets
like CO rotational lines, optical and dust emission, would be needed to
understand the structure of the background PDR and the Eastern Rim. We report
here that the relation between [C ii] and CO(2-1) emission is complex, as
components in the respective spectra are not easy to match with each other.

Table 8: Line fits to [C ii]-bright spectra 1-6 in M42. spectrum | line | comp. | $T_{\mathrm{P}}$ | $v_{\mathrm{P}}$ | $\Delta v_{\mathrm{FWHM}}$
---|---|---|---|---|---
|  | # | [K] | [$\mathrm{km\,s^{-1}}$] | [$\mathrm{km\,s^{-1}}$]
1 | [C ii] | 1 | 35.1 | 7.4 | 2.3
|  | 2 | 56.0 | 10.4 | 1.4
| [13C ii] | 1 | 1.3 | 7.1 | 5.2
|  | 2 | 0.7 | 10.6 | 3.0
|  12CO | 1 | 12.8 | 7.3 | 2.5
|  | 2 | 47.1 | 11.0 | 3.0
|  13CO | 1 | 4.2 | 6.7 | 2.3
|  | 2 | 28.9 | 11.2 | 1.8
2 | [C ii] | 1 | 4.3 | 2.1 | 1.6
|  | 2 | 50.7 | 7.9 | 1.5
|  | 3 | 19.0 | 11.7 | 1.7
| [13C ii] | 2 | 1.4 | 7.7 | 2.3
|  | 3 | 0.6 | 10.6 | 2.0
|  12CO | 1 | 23.4 | 8.8 | 3.9
|  | 2 | 28.2 | 12.5 | 3.6
|  13CO | 1 | 4.5 | 7.5 | 1.4
|  | 2 | 3.7 | 11.9 | 3.7
3 | [C ii] | 1 | 2.6 | -0.6 | 14.0
|  | 2 | 7.5 | 1.2 | 3.5
|  | 3 | 76.3 | 7.8 | 3.0
|  | 4 | 32.9 | 10.6 | 2.5
| [13C ii] | 2 | 1.0 | 8.3 | 2.5
|  12CO | 1 | 2.2 | -0.3 | 2.4
|  | 2 | 83.5 | 8.4 | 3.7
|  | 3 | 41.8 | 11.3 | 2.1
|  13CO | 1 | 29.4 | 9.1 | 3.5
|  | 2 | 12.0 | 11.1 | 1.1
4 | [C ii] | 1 | 4.5 | -1.0 | 4.4
|  | 2 | 2.2 | 3.2 | 2.4
|  | 3 | 25.7 | 9.1 | 3.3
|  12CO | 1 | 52.5 | 9.3 | 4.2
|  13CO | 1 | 19.5 | 9.4 | 3.4
5 | [C ii] | 1 | 10.7 | 7.3 | 2.2
|  | 2 | 3.4 | 8.9 | 0.8
|  12CO | 1 | 36.7 | 7.8 | 3.3
|  | 2 | 9.5 | 10.6 | 2.0
|  13CO | 1 | 15.0 | 8.0 | 2.9
6 | [C ii] | 1 | 1.2 | -2.9 | 4.6
|  | 2 | 6.3 | 8.0 | 1.8
|  12CO | 1 | 27.4 | 8.2 | 3.8
|  13CO | 1 | 15.8 | 8.0 | 2.8
Notes: Line fit uncertainties are of the order $\sigma_{T_{\mathrm{P}}}\simeq
0.5\,\mathrm{K}$, $\sigma_{v_{\mathrm{P}}}\simeq 0.1\,\mathrm{km\,s^{-1}}$,
and $\sigma_{v_{\mathrm{FWHM}}}\simeq 0.1\,\mathrm{km\,s^{-1}}$.
Table 8: Continued. Table 9: Parameters and results of [13C ii] analysis in
M42.

spectrum, | $T_{\mathrm{P}}([{}^{12}\mathrm{C\,\textsc{ii}}])$ | $T_{\mathrm{P}}([{}^{13}\mathrm{C\,\textsc{ii}}])$ | $\Delta v$ | $T_{\mathrm{d}}$ | $\tau_{160}$ | $\tau_{[\mathrm{C\,\textsc{ii}}]}$ | $T_{\mathrm{ex}}$ | $N_{\mathrm{C^{+}}}$ | $N_{\mathrm{C^{+}}}/\mathcal{A}_{\mathrm{C}}/N_{\mathrm{H}}$
---|---|---|---|---|---|---|---|---|---
comp. | [K] | [K] | [$\mathrm{km\,s^{-1}}$] | [K] |  |  | [K] | [$\mathrm{cm^{-2}}$] |
1, 1 | 35 | 1.3 | 2.3 | 37 | $1\times 10^{-2}$ | 3.9 | 81 | $3.0\times 10^{18}$ | 0.32 ($A_{\mathrm{V,los}}\simeq 10$)
1, 2 | 56 | 0.7 | 1.4 | 37 | $1\times 10^{-2}$ | 0.6 | 171 | $6.3\times 10^{17}$ | 0.07 ($A_{\mathrm{V,los}}\simeq 2$)
2, 2 | 51 | 1.4 | 1.5 | 34 | $1\times 10^{-2}$ | 2.8 | 100 | $1.7\times 10^{18}$ | 0.18 ($A_{\mathrm{V,los}}\simeq 5$)
2, 3 | 19 | 0.6 | 1.7 | 34 | $1\times 10^{-2}$ | 3.3 | 61 | $1.4\times 10^{18}$ | 0.15 ($A_{\mathrm{V,los}}\simeq 4$)
3 | 76 | 1.0 | 3.0 | 29 | $5\times 10^{-2}$ | 0.7 | 192 | $1.8\times 10^{18}$ | 0.04 ($A_{\mathrm{V,los}}\simeq 6$)

151515Line fit uncertainties are of the order $\sigma_{T_{\mathrm{P}}}\simeq
0.5\,\mathrm{K}$. $T_{\mathrm{P}}([{}^{13}\mathrm{C\,\textsc{ii}}])$ is barely
above the noise level and is uncertain by $\sigma_{T_{\mathrm{P}}}\simeq
0.3\,\mathrm{K}$.

Table 10: Line fits to spectra 1-6 in M43. spectrum | line | comp. | $T_{\mathrm{P}}$ | $v_{\mathrm{P}}$ | $\Delta v_{\mathrm{FWHM}}$
---|---|---|---|---|---
|  | # | [K] | [$\mathrm{km\,s^{-1}}$] | [$\mathrm{km\,s^{-1}}$]
1 | [C ii] | 1 | 73.9 | 8.7 | 3.9
|  | 2 | 29.5 | 9.8 | 1.5
| [13C ii] | 1 | 2.7 | 8.7 | 2.0
|  12CO | 1 | 19.9 | 8.7 | 2.6
|  | 2 | 9.4 | 11.2 | 2.8
|  13CO | 1 | 3.1 | 9.2 | 3.4
|  | 2 | 0.4 | 11.1 | 2.1
2 | [C ii] | 1 | 21.8 | 5.5 | 3.5
|  | 2 | 82.7 | 9.1 | 3.6
| [13C ii] | 2 | 2.1 | 8.5 | 2.3
|  12CO | 1 | 85.4 | 10.0 | 3.7
|  13CO | 1 | 19.6 | 10.1 | 2.6
3 | [C ii] | 1 | 17.5 | 5.6 | 3.6
|  | 2 | 67.3 | 10.0 | 3.7
| [13C ii] | 2 | 1.0 | 9.5 | 3.4
|  12CO | 1 | 3.1 | 6.8 | 1.9
|  | 2 | 59.4 | 10.8 | 2.5
|  13CO | 1 | 0.8 | 7.8 | 1.7
|  | 2 | 15.2 | 10.6 | 1.6
4 | [C ii] | 1 | 32.4 | 8.7 | 5.5
|  | 2 | 45.2 | 11.0 | 2.6
|  12CO | 1 | 9.0 | 10.6 | 4.3
|  | 2 | 42.9 | 10.7 | 1.4
|  13CO | 1 | 1.8 | 10.5 | 3.6
|  | 2 | 6.8 | 10.7 | 1.1
5 | [C ii] | 1 | 20.9 | 6.9 | 4.1
|  | 2 | 22.9 | 10.3 | 3.0
| [13C ii] | 1 | 2.1 | 6.2 | 1.7
|  12CO | 1 | 13.1 | 9.7 | 3.9
|  | 2 | 0.97 | 11.4 | 1.3
|  13CO | 1 | 3.2 | 9.3 | 2.6
|  | 2 | 1.2 | 11.2 | 1.4
6 | [C ii] | 1 | 3.7 | 5.4 | 1.6
|  | 2 | 72.1 | 9.7 | 3.5
|  | 3 | 5.3 | 12.6 | 5.6
| [13C ii] | 2 | 1.7 | 9.6 | 2.3
|  12CO | 1 | 2.4 | 6.2 | 1.8
|  | 2 | 57.9 | 9.4 | 2.5
|  | 3 | 7.2 | 12.4 | 1.5
|  13CO | 1 | 1.0 | 7.3 | 2.0
|  | 2 | 18.8 | 9.4 | 1.5
|  | 3 | 2.0 | 10.2 | 3.4
Notes: Line fit uncertainties are of the order $\sigma_{T_{\mathrm{P}}}\simeq
0.5\,\mathrm{K}$, $\sigma_{v_{\mathrm{P}}}\simeq 0.1\,\mathrm{km\,s^{-1}}$,
and $\sigma_{v_{\mathrm{FWHM}}}\simeq 0.1\,\mathrm{km\,s^{-1}}$.
Table 10: Continued. Table 11: Parameters and results of [13C ii] analysis in
M43.

spectrum | $T_{\mathrm{P}}([{}^{12}\mathrm{C\,\textsc{ii}}])$ | $T_{\mathrm{P}}([{}^{13}\mathrm{C\,\textsc{ii}}])$ | $\Delta v$ | $T_{\mathrm{d}}$ | $\tau_{160}$ | $\tau_{[\mathrm{C\,\textsc{ii}}]}$ | $T_{\mathrm{ex}}$ | $N_{\mathrm{C^{+}}}$ | $N_{\mathrm{C^{+}}}/\mathcal{A}_{\mathrm{C}}/N_{\mathrm{H}}$
---|---|---|---|---|---|---|---|---|---
| [K] | [K] | [$\mathrm{km\,s^{-1}}$] | [K] |  |  | [K] | [$\mathrm{cm^{-2}}$] |
1 | 74 | 2.7 | 3.9 | 37 | $1\times 10^{-2}$ | 3.8 | 124 | $7.7\times 10^{18}$ | 0.61 ($A_{\mathrm{V,los}}\simeq 25$)
2 | 83 | 2.1 | 3.6 | 36 | $2\times 10^{-2}$ | 2.5 | 139 | $5.2\times 10^{18}$ | 0.36 ($A_{\mathrm{V,los}}\simeq 15$)
3 | 67 | 1.0 | 3.7 | 38 | $9\times 10^{-3}$ | 1.1 | 149 | $2.6\times 10^{18}$ | 0.30 ($A_{\mathrm{V,los}}\simeq 10$)
5 | 21 | 2.1 | 1.7 | 37 | $5\times 10^{-3}$ | 11 | 64 | $5.0\times 10^{18}$ | 1.03 ($A_{\mathrm{V,los}}\simeq 15$)
6 | 72 | 1.7 | 3.5 | 34 | $1\times 10^{-2}$ | 2.2 | 127 | $4.2\times 10^{18}$ | 0.36 ($A_{\mathrm{V,los}}\simeq 15$)

161616Line fit uncertainties are of the order $\sigma_{T_{\mathrm{P}}}\simeq
0.5\,\mathrm{K}$.

Table 12: Line fits to spectra 1-6 in NGC 1977. spectrum | line | comp. | $T_{\mathrm{P}}$ | $v_{\mathrm{P}}$ | $\Delta v_{\mathrm{FWHM}}$
---|---|---|---|---|---
|  | # | [K] | [$\mathrm{km\,s^{-1}}$] | [$\mathrm{km\,s^{-1}}$]
1 | [C ii] | 1 | 141.2 | 11.7 | 2.9
|  | 2 | -101.1 | 12.0 | 2.2
| [13C ii] | 1 | 3.0 | 11.6 | 2.0
|  12CO | 1 | 15.6 | 11.7 | 2.1
|  | 2 | 33.2 | 12.7 | 1.4
|  13CO | 1 | 5.0 | 11.1 | 1.0
|  | 2 | 20.2 | 12.6 | 1.1
2 | [C ii] | 1 | (1.0) | (8.0) | (2.0)
|  | 2 | 32.8 | 11.4 | 2.6
|  12CO | 1 | 0.3 | 8.0 | 1.5
|  | 2 | 1.0 | 11.0 | 1.1
|  | 3 | 1.1 | 11.5 | 3.0
|  13CO | 1 | 0.09 | 8.7 | 2.6
|  | 2 | 0.38 | 11.1 | 1.2
|  | 3 | 0.22 | 12.7 | 1.2
3 | [C ii] | 1 | 12.7 | 11.2 | 1.6
|  | 2 | 27.4 | 12.7 | 1.9
|  12CO | 1 | 0.61 | 11.7 | 3.1
|  | 2 | 0.52 | 12.6 | 1.5
|  13CO | 1 | 0.14 | 11.1 | 2.4
|  | 2 | 0.12 | 12.7 | 0.7
4 | [C ii] | 1 | 11.1 | 11.6 | 1.3
|  | 2 | 19.0 | 12.7 | 2.0
5 | [C ii] | 1 | 2.1 | 11.6 | 5.1
|  | 2 | 3.8 | 13.7 | 1.5
6 | [C ii] | 1 | 22.8 | 11.6 | 3.1
|  | 2 | 5.2 | 12.7 | 1.0
Notes: Line fit uncertainties are of the order $\sigma_{T_{\mathrm{P}}}\simeq
0.5\,\mathrm{K}$, $\sigma_{v_{\mathrm{P}}}\simeq 0.1\,\mathrm{km\,s^{-1}}$,
and $\sigma_{v_{\mathrm{FWHM}}}\simeq 0.1\,\mathrm{km\,s^{-1}}$.
Table 12: Continued. Table 13: Parameters and results of [13C ii] analysis in
NGC 1977.

spectrum | $T_{\mathrm{P}}([{}^{12}\mathrm{C\,\textsc{ii}}])$ | $T_{\mathrm{P}}([{}^{13}\mathrm{C\,\textsc{ii}}])$ | $\Delta v$ | $T_{\mathrm{d}}$ | $\tau_{160}$ | $\tau_{[\mathrm{C\,\textsc{ii}}]}$ | $T_{\mathrm{ex}}$ | $N_{\mathrm{C^{+}}}$ | $N_{\mathrm{C^{+}}}/\mathcal{A}_{\mathrm{C}}/N_{\mathrm{H}}$
---|---|---|---|---|---|---|---|---|---
| [K] | [K] | [$\mathrm{km\,s^{-1}}$] | [K] |  |  | [K] | [$\mathrm{cm^{-2}}$] |
1 | 141 | 3.0 | 2.9 | 31 | $1\times 10^{-2}$ | 2.0 | 211 | $5.2\times 10^{18}$ | 0.42 ($A_{\mathrm{V,los}}\simeq 15$)

171717Line fit uncertainties are of the order $\sigma_{T_{\mathrm{P}}}\simeq
0.5\,\mathrm{K}$.

Table 14: Line fits to spectra 1-10 in the southeast of the Orion Bar. spectrum | line | comp. | $T_{\mathrm{P}}$ | $v_{\mathrm{P}}$ | $\Delta v_{\mathrm{FWHM}}$
---|---|---|---|---|---
|  | # | [K] | [$\mathrm{km\,s^{-1}}$] | [$\mathrm{km\,s^{-1}}$]
1 | [C ii] | 1 | 35.3 | 9.1 | 5.1
|  | 2 | 117.8 | 10.9 | 3.0
| [13C ii] | 2 | 3.4 | 11.0 | 2.5
|  12CO | 1 | 115.6 | 9.9 | 4.0
|  | 2 | 35.3 | 11.3 | 1.9
|  13CO | 1 | 7.6 | 9.9 | 4.2
|  | 2 | 35.3 | 10.1 | 2.1
2 | [C ii] | 1 | 52.1 | 9.9 | 4.4
|  | 2 | 62.3 | 11.5 | 2.6
| [13C ii] | 2? | 3.0 | 10.6 | 1.9
|  12CO | 1 | 93.5 | 9.5 | 3.7
|  | 2 | 23.0 | 10.9 | 2.2
|  13CO | 1 | 1.4 | 7.0 | 1.2
|  | 2 | 27.4 | 9.8 | 2.4
3 | [C ii] | 1 | 54.0 | 10.6 | 4.0
|  | 2 | 30.4 | 12.0 | 2.0
|  12CO | 1 | 55.3 | 9.0 | 2.1
|  | 2 | 49.0 | 10.9 | 2.3
|  13CO | 1 | 8.0 | 8.9 | 1.2
|  | 2 | 10.1 | 10.6 | 2.0
4 | [C ii] | 1 | 3.1 | 2.2 | 15.9
|  | 2 | 61.7 | 11.1 | 3.1
|  12CO | 1 | 50.6 | 10.0 | 3.6
|  | 2 | 12.0 | 11.6 | 1.8
|  13CO | 1 | 6.4 | 10.2 | 3.2
|  | 2 | 4.2 | 11.3 | 1.5
5 | [C ii] | 1 | 2.3 | -0.9 | 16.2
|  | 2 | 56.4 | 10.9 | 2.9
|  12CO | 1 | 27.7 | 8.9 | 4.3
|  | 2 | 24.5 | 11.5 | 2.5
|  13CO | 1 | 3.2 | 9.4 | 4.3
|  | 2 | 2.2 | 11.7 | 2.0
6 | [C ii] | 1 | 1.8 | -0.6 | 19.6
|  | 2 | 28.7 | 10.3 | 3.7
|  12CO | 1 | 7.1 | 7.2 | 2.3
|  | 2 | 25.8 | 10.6 | 4.5
|  13CO | 1 | 0.6 | 6.9 | 2.1
|  | 2 | 2.3 | 10.4 | 3.7
7 | [C ii] | 1 | 4.4 | 7.5 | 3.2
|  | 2 | 19.7 | 10.5 | 2.7
|  | 3 | 2.3 | 14.3 | 1.1
|  12CO | 1 | 7.0 | 6.9 | 2.1
|  | 2 | 28.6 | 10.4 | 2.6
|  | 3 | 24.2 | 14.4 | 4.3
|  13CO | 1 | 0.8 | 7.0 | 1.9
|  | 2 | 2.0 | 10.3 | 2.9
|  | 3 | 2.7 | 14.8 | 2.9
8 | [C ii] | 1 | 14.1 | 8.3 | 4.8
|  | 2 | 13.1 | 10.7 | 1.8
|  | 3 | (1.0) | (13.0) | (4.0)
|  12CO | 1 | 7.3 | 7.7 | 3.0
|  | 2 | 45.8 | 10.8 | 1.9
|  | 3 | 21.4 | 13.1 | 3.5
|  13CO | 1 | 0.8 | 7.8 | 2.9
|  | 2 | 7.7 | 10.9 | 1.5
|  | 3 | 2.5 | 13.5 | 2.6
9 | [C ii] | 1 | 9.5 | 5.9 | 7.8
|  | 2 | 26.7 | 6.1 | 1.8
|  | 3 | 49.6 | 8.0 | 1.7
| [13C ii] | 2/3 | 2.3 | 6.8 | 4.1
|  12CO | 1 | 30.6 | 7.2 | 1.6
|  | 2 | 4.8 | 10.6 | 4.8
|  13CO | 1 | 6.9 | 7.3 | 1.1
|  | 2 | 0.5 | 9.7 | 6.0
10 | [C ii] | 1 | 20.2 | 7.0 | 4.5
|  | 2 | 26.4 | 8.0 | 1.8
| [13C ii] | 2 | 3.0 | 7.9 | 1.6
|  12CO | 1 | 66.0 | 7.3 | 1.8
|  | 2 | 4.2 | 11.1 | 3.0
|  | 1 | 23.1 | 7.4 | 1.3
|  13CO | 2 | 0.6 | 10.9 | 2.6
Notes: Line fit uncertainties are of the order $\sigma_{T_{\mathrm{P}}}\simeq
0.5\,\mathrm{K}$, $\sigma_{v_{\mathrm{P}}}\simeq 0.1\,\mathrm{km\,s^{-1}}$,
and $\sigma_{v_{\mathrm{FWHM}}}\simeq 0.1\,\mathrm{km\,s^{-1}}$.
Table 14: Continued. Table 15: Parameters and results of [13C ii] analysis of
spectra to the southeast of the Orion Bar.

spectrum | $T_{\mathrm{P}}([{}^{12}\mathrm{C\,\textsc{ii}}])$ | $T_{\mathrm{P}}([{}^{13}\mathrm{C\,\textsc{ii}}])$ | $\Delta v$ | $T_{\mathrm{d}}$ | $\tau_{160}$ | $\tau_{[\mathrm{C\,\textsc{ii}}]}$ | $T_{\mathrm{ex}}$ | $N_{\mathrm{C^{+}}}$ | $N_{\mathrm{C^{+}}}/\mathcal{A}_{\mathrm{C}}/N_{\mathrm{H}}$
---|---|---|---|---|---|---|---|---|---
| [K] | [K] | [$\mathrm{km\,s^{-1}}$] | [K] |  |  | [K] | [$\mathrm{cm^{-2}}$] |
1 | 118 | 3.4 | 2.5 | 38 | $3.0\times 10^{-2}$ | 2.9 | 175 | $5.4\times 10^{18}$ | 0.32 ($A_{\mathrm{V,los}}\simeq 15$)
2 | 62 | 1.9 | 2.9 | 37 | $1.8\times 10^{-2}$ | 3.1 | 113 | $4.3\times 10^{18}$ | 0.25 ($A_{\mathrm{V,los}}\simeq 15$)
9 | 50 | 1.8 | 1.7 | 33 | $0.9\times 10^{-2}$ | 3.8 | 95 | $2.6\times 10^{18}$ | 0.30 ($A_{\mathrm{V,los}}\simeq 10$)
10 | 26 | 1.1 | 1.8 | 30 | $1.0\times 10^{-2}$ | 4.4 | 67 | $2.2\times 10^{18}$ | 0.23 ($A_{\mathrm{V,los}}\simeq 10$)

181818Line fit uncertainties are of the order $\sigma_{T_{\mathrm{P}}}\simeq
0.5\,\mathrm{K}$.