[Mod] Grammarly verification gaoxiang12#4

TODO_Review.md

@@ -18,7 +18,7 @@
 - [ ] Grammarly verification
   - [x] \include{chapters/preface-en}
   - [x] \include{chapters/preface}
-  - [ ] \include{chapters/whatSlam}
+  - [x] \include{chapters/whatSlam}
   - [ ] \include{chapters/rigidBody}
   - [ ] \include{chapters/lieGroup}
   - [ ] \include{chapters/cameraModel}

chapters/cameraModel.tex

@@ -282,16 +282,16 @@ \subsubsection{Install OpenCV}
 
 Since we use a newer version of OpenCV, we must install it from the source code. First, you can adjust some compilation options to match the programming environment (for example, whether you need GPU acceleration, etc.); furthermore, from the source code installation we can use some additional functions. OpenCV currently maintains two major versions, divided into OpenCV 2.4 series and OpenCV 3 series \footnote{In 2020 we can also use version 4.0 or higher.}. This book uses the OpenCV \textbf {3} series.
 
-Because the OpenCV project is relatively large, it will not be placed under 3rdparty in this book. Readers can download it from ~ \url{http://opencv.org/downloads.html}~ and select the OpenCV for Linux version. You will get a compressed package like opencv-3.1.0.zip. Unzip it to any directory, we found that OpenCV is also a cmake project.
+Because the OpenCV project is relatively large, it will not be placed under 3rdparty in this book. Readers can download it from ~ \url{http://opencv.org/downloads.html}~ and select the OpenCV for Linux version. You will get a compressed package like opencv-3.1.0.zip. Unzip it to any directory, we found that OpenCV is also a CMake project.
 
 Before compiling, first install the dependencies of OpenCV:
 \begin{lstlisting}[language=sh, caption=Terminal input:]
 sudo apt-get install build-essential libgtk2.0-dev libvtk5-dev libjpeg-dev libtiff4-dev libjasper-dev libopenexr-dev libtbb-dev
 \end{lstlisting}
 
-In fact, OpenCV has many dependencies, and the lack of certain compilation items will affect some of its functions (but we will not use all the functions). OpenCV will check whether the dependencies will be installed during cmake and adjust its own functions. If you have a GPU on your computer and the relevant dependencies are installed, OpenCV will also enable GPU acceleration. But for this book, the above dependencies are sufficient.
+In fact, OpenCV has many dependencies, and the lack of certain compilation items will affect some of its functions (but we will not use all the functions). OpenCV will check whether the dependencies will be installed during CMake and adjust its own functions. If you have a GPU on your computer and the relevant dependencies are installed, OpenCV will also enable GPU acceleration. But for this book, the above dependencies are sufficient.
 
-Subsequent compilation and installation are the same as ordinary cmake projects. After make, please call ``sudo make install'' to install OpenCV on your machine (instead of just compiling it). Depending on the machine configuration, this compilation process may take from 20 minutes to an hour. If your CPU is powerful, you can use commands like ``make -j4'' to call multiple threads to compile (the parameter after -j is the number of threads used). After installation, OpenCV is stored in the /usr/local directory by default. You can look for the installation location of OpenCV header files and library files to see where they are. In addition, if you have installed the OpenCV 2 series before, it is recommended that you install OpenCV 3 elsewhere (think about how this should be done).
+Subsequent compilation and installation are the same as ordinary CMake projects. After make, please call ``sudo make install'' to install OpenCV on your machine (instead of just compiling it). Depending on the machine configuration, this compilation process may take from 20 minutes to an hour. If your CPU is powerful, you can use commands like ``make -j4'' to call multiple threads to compile (the parameter after -j is the number of threads used). After installation, OpenCV is stored in the /usr/local directory by default. You can look for the installation location of OpenCV header files and library files to see where they are. In addition, if you have installed the OpenCV 2 series before, it is recommended that you install OpenCV 3 elsewhere (think about how this should be done).
 
 \subsection{Basic OpenCV Images Operations}
 Now let's go through the basic image operations in OpenCV from a simple example.
@@ -370,7 +370,7 @@ \subsection{Basic OpenCV Images Operations}
 }
 \end{lstlisting}
 
-In this example, we demonstrated the following operations: image reading, displaying, pixel vising, copying, assignment, etc. When compiling the program, you need to add the OpenCV header file in your CMakeLists.txt, and then link the program to the OpenVC's library. At the same time, due to the use of C ++ 11 standards (such as nullptr and chrono), you also need to set up the c++ standard in compiler flag:
+In this example, we demonstrated the following operations: image reading, displaying, pixel vising, copying, assignment, etc. When compiling the program, you need to add the OpenCV header file in your ``CMakeLists.txt'', and then link the program to the OpenVC's library. At the same time, due to the use of C ++ 11 standards (such as nullptr and chrono), you also need to set up the c++ standard in compiler flag:
 
 \begin{lstlisting}[language=Python,caption=slambook/ch5/imageBasics/CMakeLists.txt]
 # use c++11 standard
@@ -397,7 +397,7 @@ \subsection{Basic OpenCV Images Operations}
 \item In line 10 \textasciitilde to 18, use the cv::imread function to read the image, and display the image and basic information.
 \item In line 35 \textasciitilde 46, we iterate over all pixels in the image and calculates the time spent in the entire loop. Please note that the pixel visiting method is not unique, and the method given by the example is not the most efficient way. OpenCV provides an iterator of cv::Mat, you can traverse the pixels of the image through the iterator. Or, cv::Mat::data provides a raw pointer to the beginning of the image data, you can directly calculate the offset through this pointer, and then get the actual memory location of the pixel. The method used in the example is to facilitate the reader to understand the structure of the image.
 
-On the author's machine (virtual machine), it takes about 12.74ms to traverse this image. You can compare the speed on your machine. However, we are using the default debug mode of cmake, which is much slower than the release mode.
+On the author's machine (virtual machine), it takes about 12.74ms to traverse this image. You can compare the speed on your machine. However, we are using the default debug mode of CMake, which is much slower than the release mode.
 
 \item OpenCV provides many functions for manipulating images, we will not list them one by one, otherwise this book will become an OpenCV operation manual. The example shows the most common things like image reading and displaying, as well as the deep copy function in cv::Mat. During the programming process, readers will also encounter operations such as image rotation and interpolation. At this time, you should refer to the corresponding documentation of the function to understand their principles and usage.
 \end{enumerate}
@@ -519,7 +519,7 @@ \subsection{RGB-D Vision}
 \label{sec:join-point-cloud}
 Finally, we demonstrate an example of RGB-D vision. The convenience of RGB-D cameras is that they can obtain pixel depth information through physical methods. If the internal and external parameters of the camera are known, we can calculate the position of any pixel in the world coordinate system, thereby creating a point cloud map. Now let's demonstrate how to do it.
 
-We have prepared 5 pairs of images, located in the slambook2/ch5/rgbd folder. There are 5 RGB images from 1.png to 5.png under the color/ directory, and 5 corresponding depth images under the depth/. At the same time, the pose.txt file gives the camera poses of the 5 images (in the form of $ \mathbf{T}_\mathrm{wc} $). The form of the pose record is the same as before, with the translation vector plus a rotation quaternion:
+We have prepared 5 pairs of images, located in the slambook2/ch5/rgbd folder. There are 5 RGB images from 1.png to 5.png under the color/ directory, and 5 corresponding depth images under the depth/. At the same time, the ``pose.txt'' file gives the camera poses of the 5 images (in the form of $ \mathbf{T}_\mathrm{wc} $). The form of the pose record is the same as before, with the translation vector plus a rotation quaternion:
 \[
 [x, y, z, q_x, q_y, q_z, q_w],
 \]

chapters/lieGroup.tex

@@ -478,7 +478,7 @@ \subsection{Derivative on $\mathrm{SE}(3)$}
 
 \section{Practice: Sophus}
 \subsection{Basic Usage of Sophus}
-We have introduced the basic knowledge of Lie algebra, and now it is time to consolidate what we have learned through practical exercises. Let's discuss how to manipulate Lie algebra in a program. In Lecture 3, we saw that Eigen provided geometry modules, but did not provide support for Lie algebra. A better Lie algebra library is the Sophus library maintained by Strasdat (\url{https://github.com/strasdat/Sophus})\footnote{Sophus Lie first proposed the Lie algebra. The library is named after him.}. The Sophus library supports $\mathrm{SO}(3)$ and $\mathrm{SE}(3)$, which are mainly discussed in this chapter. In addition, it also contains two-dimensional motion $\mathrm{SO}(2), \mathrm{SE} (2) $ and the similar transformation of $\mathrm{Sim}(3)$. It is developed directly on top of Eigen and we don't need to install additional dependencies. Readers can get Sophus directly from GitHub, or the Sophus source code is also available in our book's code directory ``slambook2/3rdparty''. For historical reasons, earlier versions of Sophus only provided double-precision Lie group/Lie algebra classes. Subsequent versions have been rewritten as template classes, so that different precision of Lie group/Lie algebra can be used in the Sophus from the template class, but at the same time it increases the difficulty of use. In the second edition of this book, we use the Sophus library of \textbf{with templates}. The Sophus provided in the 3rdparty of this book is the \textbf{template} version, which should have been copied to your computer when you downloaded the code for this book. Sophus itself is also a cmake project. Presumably you already know how to compile the cmake project, so I won't go into details here. The Sophus library only needs to be compiled, no need to install it.
+We have introduced the basic knowledge of Lie algebra, and now it is time to consolidate what we have learned through practical exercises. Let's discuss how to manipulate Lie algebra in a program. In Lecture 3, we saw that Eigen provided geometry modules, but did not provide support for Lie algebra. A better Lie algebra library is the Sophus library maintained by Strasdat (\url{https://github.com/strasdat/Sophus})\footnote{Sophus Lie first proposed the Lie algebra. The library is named after him.}. The Sophus library supports $\mathrm{SO}(3)$ and $\mathrm{SE}(3)$, which are mainly discussed in this chapter. In addition, it also contains two-dimensional motion $\mathrm{SO}(2), \mathrm{SE} (2) $ and the similar transformation of $\mathrm{Sim}(3)$. It is developed directly on top of Eigen and we don't need to install additional dependencies. Readers can get Sophus directly from GitHub, or the Sophus source code is also available in our book's code directory ``slambook2/3rdparty''. For historical reasons, earlier versions of Sophus only provided double-precision Lie group/Lie algebra classes. Subsequent versions have been rewritten as template classes, so that different precision of Lie group/Lie algebra can be used in the Sophus from the template class, but at the same time it increases the difficulty of use. In the second edition of this book, we use the Sophus library of \textbf{with templates}. The Sophus provided in the 3rdparty of this book is the \textbf{template} version, which should have been copied to your computer when you downloaded the code for this book. Sophus itself is also a CMake project. Presumably you already know how to compile the CMake project, so I won't go into details here. The Sophus library only needs to be compiled, no need to install it.
 
 Let's demonstrate the SO(3) and SE(3) operations in the Sophus library:
 
@@ -545,17 +545,17 @@ \subsection{Basic Usage of Sophus}
 }
 \end{lstlisting}
 
-The demo is divided into two parts. The first half introduces the operation on $\mathrm{SO}(3)$, and the second half is $\mathrm{SE}(3)$. We demonstrate how to construct $\mathrm{SO}(3), \mathrm{SE}(3)$ objects, exponentially, logarithmically map them, and update the lie group elements when we know the update amount. If the reader has a good understanding of the content of this lecture, then this program should not be difficult for you. In order to compile it, add the following lines to CMakeLists.txt:
+The demo is divided into two parts. The first half introduces the operation on $\mathrm{SO}(3)$, and the second half is $\mathrm{SE}(3)$. We demonstrate how to construct $\mathrm{SO}(3), \mathrm{SE}(3)$ objects, exponentially, logarithmically map them, and update the lie group elements when we know the update amount. If the reader has a good understanding of the content of this lecture, then this program should not be difficult for you. In order to compile it, add the following lines to ``CMakeLists.txt'':
 
 \begin{lstlisting}[caption=slambook/ch4/useSophus/CMakeLists.txt]
-# we use find_package to make cmake find sophus
+# we use find_package to make CMake find sophus
 find_package( Sophus REQUIRED )
 include_directories( ${Sophus_INCLUDE_DIRS} ) # sohpus is header only
 
 add_executable( useSophus useSophus.cpp )
 \end{lstlisting}
 
-The find\_package is a command provided by cmake to find the header and library files of a library. If cmake can find it, it will provide the variables for the directory where the header and library files are located. In the example of Sophus, it is Sophus\_INCLUDE\_DIRS. The template-based Sophus library, like Eigen, contains only header files and no source files. Based on them, we can introduce the Sophus library into our own cmake project. Readers are asked to see the output of this program on their own, which is consistent with our previous derivation.
+The \textit{find\_package} is a command provided by CMake to find the header and library files of a library. If CMake can find it, it will provide the variables for the directory where the header and library files are located. In the example of Sophus, it is Sophus\_INCLUDE\_DIRS. The template-based Sophus library, like Eigen, contains only header files and no source files. Based on them, we can introduce the Sophus library into our own CMake project. Readers are asked to see the output of this program on their own, which is consistent with our previous derivation.
 
 \subsection{Example: Evaluating the trajectory}
 In practical engineering, we often need to evaluate the difference between the estimated trajectory of an algorithm and the real trajectory to evaluate the accuracy of the algorithm. The real (or ground-truth) trajectory is often obtained by some higher precision systems, and the estimated one is calculated by the algorithm to be evaluated. In the last lecture we demonstrated how to display a trajectory stored in a file. In this section we will consider how to calculate the error of two trajectories. Consider an estimated trajectory $\mathbf{T}_{\mathrm{esti}, i}$ and the real trajectory $\mathbf{T}_{\mathrm{gt},i}$, where $i=1,\cdots, N$; then we can define some error indicators to describe the difference between them.
@@ -579,7 +579,7 @@ \subsection{Example: Evaluating the trajectory}
 \mathrm{RPE}_{\mathrm{trans}} = \sqrt{ \frac{1}{N-\Delta t} \sum_{i=1}^{N-\Delta t} \| \mathrm{trans } \left( \left(\mathbf{T}_{\mathrm{gt},i}^{-1} \mathbf{T}_{\mathrm{gt},i+\Delta t} )\right)^ {-1} \left(\mathbf{T}_{\mathrm{esti},i}^{-1} \mathbf{T}_{\mathrm{esti},i+\Delta t}\right)\right ) \|_2^2}.
 \end{equation}
 
-This part of the calculation is easy to implement with the Sophus library. Below we demonstrate the calculation of the absolute trajectory error. In this example, we have two trajectories: groundtruth.txt and estimated.txt. The following code will read the two trajectories, calculate the error, and display it in a 3D window. For the sake of brevity, the code for the trajectory plotting has been omitted, as we have done similar work in the previous section.
+This part of the calculation is easy to implement with the Sophus library. Below we demonstrate the calculation of the absolute trajectory error. In this example, we have two trajectories: ``groundtruth.txt'' and ``estimated.txt''. The following code will read the two trajectories, calculate the error, and display it in a 3D window. For the sake of brevity, the code for the trajectory plotting has been omitted, as we have done similar work in the previous section.
 
 \begin{lstlisting}[language=c++,caption=slambook/ch4/example/trajectoryError.cpp]
 #include <iostream>
@@ -744,5 +744,5 @@ \section*{Exercises}
         \end{array}} \right].
     \end{equation}
     \item Follow the derivation of the left perturbation and derives the derivatives of $\mathrm{SO}(3)$ and $\mathrm{SE}(3)$ under the right perturbation.
-    \item Search how cmake's find\_package works. What optional parameters does it have? What are the prerequisites for cmake to find a library?
+    \item Search how CMake's \textit{find\_package} works. What optional parameters does it have? What are the prerequisites for CMake to find a library?
 \end{enumerate}

chapters/mapping.tex

@@ -858,7 +858,7 @@ \subsection{八叉树地图}
 有了对数概率，我们就可以根据RGB-D数据更新整个八叉树地图了。假设我们在RGB-D图像中观测到某个像素带有深度$d$，这说明了一件事：我们\textbf{在深度值对应的空间点上观察到了一个占据数据，并且，从相机光心出发到这个点的线段上，应该是没有物体的}（否则会被遮挡）。利用这个信息，可以很好地对八叉树地图进行更新，并且能处理运动的结构。
 
 \subsection{实践：八叉树地图}
-下面通过程序演示一下octomap的建图过程。首先，请读者安装octomap库：\url{https://github.com/OctoMap/octomap}。Octomap库主要包含octomap地图与octovis（一个可视化程序），二者都是cmake工程。其主要依赖doxygen，可通过如下命令安装：
+下面通过程序演示一下octomap的建图过程。首先，请读者安装octomap库：\url{https://github.com/OctoMap/octomap}。Octomap库主要包含octomap地图与octovis（一个可视化程序），二者都是CMake工程。其主要依赖doxygen，可通过如下命令安装：
 \begin{lstlisting}
 sudo apt-get install doxygen 
 \end{lstlisting}

chapters/preface-en.tex

@@ -1,5 +1,5 @@
 \chapter*{Preface for English Version}
-A lot of friends at Github asked me about this English version. I'm really sorry it takes so long to do the translation, and I'm glad to make it publicly available to help the readers. I encountered some issues with math equation on the web pages. Since the book is originally written in LaTeX, I'm going to release the LaTeX source along with the compiled pdf. You can directly access the pdf version for the English book, and probably the publishing house is going to help me do the paper version.
+A lot of friends at Github asked me about this English version. I'm really sorry it takes so long to do the translation, and I'm glad to make it publicly available to help the readers. I encountered some issues with the math equations on the web pages. Since the book is originally written in LaTeX, I'm going to release the LaTeX source along with the compiled pdf. You can directly access the pdf version for the English book, and probably the publishing house is going to help me do the paper version.
 
 As I'm not a native English speaker, the translation work is basically based on Google translation and some afterward modifications. If you think the quality of translation can be improved, and you are willing to do this, please contact me or send an issue on Github. Any help will be welcome!