上了一週的latex培訓課，很水，只知道了有這個軟體，直到今天交期末作業才把它完整走一遍。一個小時足夠搞定所有基本操作（題目，摘要，圖片，表格，公式）。但如果所投期刊有具體要求，並且你是個完美主義，那就另當別論了。

然後就是開啟你所需要修改的論文，開啟-所有程式-CteX-WinEdt,如下圖

風格類似於matlab，然後就是下載你論文所需要的模板在B區域塗塗改改就行了。如果只是單純想學學，要自己寫可以用下面我給的程式碼。可以省去你很多時間找資源，不用下載任何package放到B區執行出來，就可以明白Latex用於寫論文的基本操作。唯一需要改的是圖片名這裡是1.png。

我想說的：

1.注意選單欄可以直接用，省去好多程式碼

2.遇到bug時很有可能是你沒有新增\usepackage{##}

3.很多錯誤網上都有解決方法，不要去群裡問同學，除非你們很熟或者他很厲害。

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{authblk}
\usepackage{geometry}
\usepackage{graphicx}
\usepackage{subfigure}
\usepackage{indentfirst}
\usepackage{latexsym}
\usepackage{amsmath}
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\usepackage{makecell}
\title{\textbf{Automatic Color Correction for Multisource Remote Sensing Images with Wasserstein CNN}}
\author[1,2,3]{Jiayi Guo}
\author[1,2,3]{Zongxu Pan}
\author[1,2,3]{Bin Lei}
\author[1,2,3]{Chibiao Ding}
\affil[1]{School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of
Sciences, Huairou District, Beijing 101408, China;}
\affil[2]{Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China}
\affil[3]{Key Laboratory of Geo-spatial Information Processing and Application System Technology,Beijing 100190, China}
\renewcommand\Authands{ and }
\begin{document}
\maketitle
\begin{abstract}
Abstract: In this paper a non-parametric model based on Wasserstein CNN is proposed for color
correction. It is suitable for large-scale remote sensing image preprocessing from multiple sources
under various viewing conditions, including illumination variances, atmosphere disturbances,
and sensor and aspect angles. Color correction aims to alter the color palette of an input image
to a standard reference which does not suffer from the mentioned disturbances. Most of current
methods highly depend on the similarity between the inputs and the references, with respect to
both the contents and the conditions, such as illumination and atmosphere condition. Segmentation
is usually necessary to alleviate the color leakage effect on the edges. Different from the previous
studies, the proposed method matches the color distribution of the input dataset with the references
in a probabilistic optimal transportation framework. Multi-scale features are extracted from the
intermediate layers of the lightweight CNN model and are utilized to infer the undisturbed
distribution. The Wasserstein distance is utilized to calculate the cost function to measure the
discrepancy between two color distributions. The advantage of the method is that no registration
or segmentation processes are needed, benefiting from the local texture processing potential of the
CNN models. Experimental results demonstrate that the proposed method is effective when the
input and reference images are of different sources, resolutions, and under different illumination and
atmosphere conditions.
\\\textbf{Keywords}: remote sensing image correction; color matching; optimal transport; CNN
\end{abstract}
\section{Introduction}

Large-scale remote sensing content providers aggregate remote sensing imagery from different
platforms, providing a vast geographical coverage with a range of spatial and temporal resolutions.
One of the challenges is that the color correction task becomes more complicated due to the
wide difference in viewing angles, platform characteristics, and light and atmosphere conditions
(see Figure 1). For further processing purposes, it is often desired to perform color correction to the
images. Histogram matching [1,2] is a cheap way to address this when a reference image with no color
errors is available that shares the same coverage of land and reflectance distribution.

To gain a deeper insight, first we would like to place histogram matching in a broader context
as the simplest form of color matching [3]. These methods try to match the color distribution of the
input images to a reference, also known as color transferring. They can either work by matching low order statistics [3–5] or by transferring the exact distribution [6–8]. Matching the low order
statistics is sensitive to the color space selected [9]. The performances of both methods are highly
related to the similarity between the contents of the input and the reference. Picking an appropriate
reference requires manual intervention and may become the bottle neck for processing. A drawback
of such methods is that the colors on the edges of the targets would be mixed up [10–12]. Methods
exploiting the spatial information were proposed to migrate the problem, but segmentation, spatial
matching, and alignment are required [13,14]. Matching the exact distribution is not sensitive to the
color space selection, but has to work in an iterative fashion [8]. Both the segmentation and the iteration
increase the computation burden and are not suitable for online viewing and querying. For video
and stereo cases, extra information from the correlation between frames can be exploited to achieve
better color harmony [15,16]. The holography method is introduced into color transfer to eliminate
the artifacts [17]. Manifold learning is an interesting framework to find the similarity between the
pixels, so that the output color can be more natural and it can suppress the color leakage as well [18].
Another perspective to comprehend the problem is image-to-image translation. Convolutional neural
networks have proven to be successful for such applications [19], for example, the auto colorization
of grayscale images [20,21]. Recently, deep learning shows its potential and power in hyper-spectral
image understanding applications [22].
\begin{figure}[h]

\centering
\includegraphics[scale=0.35]{1}
\caption{Color discrepancy in remote sensing images. (a,b) Digital Globe images on different dates
from Google Earth; (c,d) Digital Globe (bottom, right) and NASA (National Aeronautics and Space
on the same date from Google Earth; (e) GF1 (Gaofen-1) images from different sensors, same area and date.}
\end{figure}

Unfortunately, for large-scale applications, it is too strict a requirement that the whole
reflectance distribution should be the same between the reference image and the ones to be processed.
As a result, such reference histograms are usually not available and have greatly restricted the
applications of these sample-based color matching methods. In [23] the authors choose a color
correction plan that minimizes the color discrepancy between it and both the input image and the
reference image. This is a good solution in stitching applications. However, the purpose of this paper
is to eliminate the errors raised by atmosphere, light, etc., so that the result can be further employed
in ground reflectance retrieval or atmosphere parameters retrieval. We hope that the output is as
close as possible to the reference images, rather than modifying the ground truth values as in [23].
Since it is usually infeasible the reference images, rather than modifying the ground truth values as in [23]. Since it is usually
infeasible to find such a reference, a natural question is, can we develop a universal function which
can automatically determine the references directly according to the input images? Once this function
is obtained, we can combine it with simple histogram matching or other color transfer methods into
a very powerful algorithm. In this paper, a Wasserstein CNN model is built to infer the reference
histograms for remote sensing image color correction applications. The model is completely data
driven, and no registration or segmentation is needed in both the training phase and the inferring
phase. Besides, as will be explained in Section 2, the input and the reference can be of different
scales and sources. In Section 2, the details of the proposed method are elaborated in an optimal
transporting framework [24,25]. In Section 3, the experiments are conducted to validate the feasibility
of the proposed method, in which images from the GF1 and GF2 satellites are used as the input and
the reference datasets accordingly. Section 4 comprises the discussions and comparisons with other
color matching (correcting) methods. And finally, Section 5 gives the conclusion and points out our
future works.
\section{Materials and Methods}
\subsection{Analysis}

Given an input image $I^{'}$ and a reference image $I^{'}$ with $N_{c}$ channels, an automatic color matching
algorithm aims to alter the color palette of I to that of $I^{'}$, the reference. Some of the algorithms
require that the reference image is known, which are called sample-based methods. Of course
an ideal algorithm should work without knowing $I^{'}$. The matching can be operated either in the
Nc-dimensional color space at once, or in each dimension separately [8,26]. The influence of the light
and the atmosphere conditions and other factors can be included into a function \emph{h}($I^{'}$, \emph{x, y)} that acts on
the grayscale value of the pixel located at \emph{(x, y)}. Under such circumstances, the problem is converted
to learning an inverse transfer function \emph{f (I, x, y)} that maps the grayscale values of the input image \emph{I}
back to that of the reference image $I^{'}$, where \emph{(x, y)} denotes the location of the target pixel inside \emph{I}.

When the input image is divided into patches that each possess a relatively small geographical
coverage, the spatial variance of the color discrepancy inside each patch is usually small enough to be
neglected. Thus \emph{h($I^{'}$, x, y) }should be the same with \emph{h($I^{'}$, $x^{'}$, $y^{'}$)} as long as \emph{(x, y)} and \emph{($x^{'}$, $y^{'}$)} share the
same gray scale values. Let $u_{x,y}$ and $v_{x,y}$ be the gray scale values of the pixels located at (x, y) in \emph{I} and $I^{'}$
accordingly, and \emph{h($I^{'}$, x, y)} can be rewritten as \emph{h($I^{'}$, $v_{x,y}$)}, because the color discrepancy function is not
related to the location of the pixel but only to its value. The three assumptions of the transformation
from the input images to the reference images are made as follows, and some properties which\emph{ f}
should satisfy can be derived from them.
\\\textbf{Assumption 1}: $v_{x,y}$  = $v_{x^{'},y^{'}}$ $\Rightarrow$ $u_{x,y}$  = $u_{x^{'},y^{'}}$

Assumption 1 suggests that when two pixels in $I^{'}$ have the same grayscale value, so do the
corresponding pixels in \emph{I}. This assumption is straight forward since in general cases the cameras
are well calibrated and the inhomogeneity of light and atmosphere is usually small within a small
geographical coverage. It is true that when severe sensor errors occur this assumption may not hold,
however that is not the focus of this paper.
\\\textbf{Assumption 2}: $u_{x,y}$  = $u_{x^{'},y^{'}}$ $\Rightarrow$ $v_{x,y}$  = $v_{x^{'},y^{'}}$

Assumption 2 indicates that when two pixels in \emph{I} have the same grayscale, so are their
corresponding pixels in $I^{'}$. The assumption is based on the fact that the pixel value the sensor
recorded is not related to its context or location, but only to its raw physical intensity.
\\\textbf{Assumption 3}:$u_{x,y}$  > $u_{x^{'},y^{'}}$ ,$v_{x,y}$  > $v_{x^{'},y^{'}}$

Assumption 3 implies that the transformation is order preserving, or a brighter pixel in \emph{I} should
also be brighter in $I^{'}$, and vice versa.

According to the above assumptions, we expect the transfer function \emph{f }to possess the
following properties.
\\\textbf{Property 1:}$u_{x,y}$  = $u_{x^{'},y^{'}}$ $\Rightarrow$ \emph{f(I,$u_{x,y}$)}=\emph{f(I,$u_{x^{'},y^{'}}$)}
\\\textbf{Property 2:}$u_{x,y}$  > $u_{x^{'},y^{'}}$ \emph{f(I,$u_{x,y}$)}>\emph{f(I,$u_{x^{'},y^{'}}$)}
\\\textbf{Property 3:}$I_{1}$ $\not=$ $I_{2}$ $\Rightarrow$ \emph{f($I_{1}$,$\bullet$) $\not=$ f($I_{2}$,$\bullet$)}

Consider that even when two pixels inside $I_{1}$and$I_{2}$ share the same grayscale values, the corrected
values can still be different according to their ground truth values in the references. Property 3 is to say
that f should be content related. In other words, for different input images, the transfer function values
should be different to maintain the content consistency. To better explain the point, consider that two
input images having different contents, the grassland and the lake so to speak, happen to be of similar
color distributions. The pixel in the lake should be darker and the other pixel in the grassland should
be brighter in the corresponding reference images. If \emph{f }is only related to the grayscale values while
discarding the input images (the contexts of the pixels), this cannot be done because similar pixels in
different input images have to be mapped to similar output levels.
An issue to take into account is whether the raw image or its histogram of the input and reference
images should be made use of for the matching. Table 1 lists all possible cases, each of which will
be discussed.
\begin{center}
\textbf{Table 1.} Different color matching schemes according to the input form and the reference form.
\end{center}
\begin{center}
\begin{tabular}{c|c|c} \Xhline{0.8pt}
Input & Reference & Scheme \\ \Xhline{0.6pt}
Histogram &Histogram  &A \\
Image & Image & B  \\
Image & Histogram  & C  \\
Histogram & Image  & D  \\  \Xhline{0.8pt}
\end{tabular}
\end{center}

Scheme A is the case when both the input and reference are histograms, and this is essentially
histogram matching. Many previous studies employ this scheme for simplicity, for example, histogram
matching and low order statistics matching in various color spaces. Since histograms do not contain
the content information, the corresponding histogram matching is not content related. Concretely
speaking, two pixels that belong to two regions with different contents but with the same grayscale fall
into the same bin of the histogram, and have to be assigned to the same grayscale value in the output
image, which does not meet Property 3. In order for one distribution with different contexts to be
correctly matched to different corresponding distributions, we cannot enclose different transformations
in one unified mapping (see Figure 2). This should not be appropriate for large scale datasets that
demand a high degree of automation.

Scheme B corresponds to the case where both the input and output are images, which is usually
referred to as image to image translation. The image certainly contains much more information than
its histogram, thus providing a possibility that the mapping is content related. Although Property 3
can be satisfied, this scheme emphasizes the content of the image, and the consequence is that the
pixels with same grayscales may be mapped to different grayscales as their contexts could be different,
and in this case Property 1 is violated (see Figure 3).
\subsection{Optimal Transporting Perspective of View}
\subsection{The Model Structure}
\subsection{Data Augmentation}
\subsection{Algorithm Flow Chart}

\section{Results}

\section{Discussion}

\section{Conclusion}

This paper presents a nonparametric color correcting scheme in a probabilistic optimal transport
framework, based on theWasserstein CNN model. The multi-scale features are first to be extracted from
the intermediate layers, and then are used to infer the corrected color distribution which minimizes
the errors with respect to the ground truth. The experimental results demonstrate that the method is
able to handle images of different sources, resolutions, and illumination and atmosphere conditions.
With high efficiency in computing speed and memory consumption, the proposed method shows its
prospects for utilization in real time processing of large-scale remote sensing datasets.

We are currently extending the global color matching algorithm to take the local inhomogeneity
of illumination into consideration, in order to enhance the precision. Local histogram matching of
each band could serve for reflectance retrieval and atmospheric parameter retrieval purposes, and the
preliminary results are encouraging.
\\\textbf{Acknowledgments}: This work was supported by the National Natural Science Foundation of China (Grant
No. 61331017.)
\\\textbf{Author Contributions}: Jiayi Guo and Bin Lei conceived and designed the experiments; Jiayi Guo performed
the experiments; Jiayi Guo analyzed the data; Bin Lei and Chibiao Ding contributed materials and computing
resources; Jiayi Guo and Zongxu Pan wrote the paper.
\\\textbf{Conflicts of Interest}: The authors declare no conflict of interest.
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\end{document}