$$\begin{aligned}\mathrm{x}_{P Y} &=\left[\theta, \phi, \omega_\theta, \omega_\phi\right]^{\top} \text { and } \\\mathbf{f}_{P Y}\left(\mathbf{x}_{P Y}\right) &=\left[\begin{array}{c}\theta+\omega_\theta \Delta t \\\phi+\omega_\phi \Delta t \\\omega_\theta \\\omega_\phi\end{array}\right]+\mathbf{w}_{P Y},\end{aligned}$$
where $\omega_\theta$ and $\omega_\phi$ are the angular velocity of pitch and yaw angles and $\mathbf{w}_{P Y}=\left[0,0, w_\theta, w_\phi\right]^{\top}$ is a noise variable of the system model with the normal distribution $\mathcal{N}\left(0, \mathbf{W}_{P Y}\right)$.
Using the NGC-VD orthogonality, a measurement model $h_{P Y}$ for the pitch and yaw angle estimation is defined as
where $\mathbf{n}$ is an $\mathrm{NGC}$ of $\mathrm{l} \in \mathcal{L}_c$ and $q_{P Y}$ is a noise variable of the measurement model with the normal distribution $\mathcal{N}\left(0, Q_{P Y}\right)$.
The state vector $\mathrm{x}_{P Y}$ are estimated by $\mathrm{EKF}$ as follows: For simplicity, $\mathrm{x}_{P Y}$ is abbreviated as $\mathrm{x}$. Then let $\mathrm{x}_{t-1}$ and $\mathbf{P}_{t-1}$ denote the state estimate and its covariance at time $t-1$. The prediction of the state $\hat{\mathbf{x}}_t$ and its covariance $\hat{\mathbf{P}}_t$ is calculated as follows.
where $\mathbf{F}_t$ is a Jacobian of the system model. For all the inliers in $\mathcal{L}_c$, the residuals of the measurements are computed using (11) and concatenated as follows.
The Kalman gain $\mathrm{G}_t$ for update is computed as follows.
$\mathbf{G}_t=\hat{\mathbf{P}}_t \mathbf{H}_t^{\top} \mathbf{S}_t^{-1}$, where $\mathbf{S}_t=\mathbf{H}_t \hat{\mathbf{P}}_t \mathbf{H}_t^{\top}+\mathbf{Q}_t$. Here, $\mathrm{H}_t$ and $\mathrm{Q}_t$ denote a Jacobian of the measurement model, i.e., $\mathbf{H}_t=\left[\cdots,\left.\frac{\partial h_{P Y}^{\mathrm{n}}}{\partial \mathbf{x}}\right|_{\hat{\mathbf{x}}_t} ^{\top}, \cdots\right]^{\top}$, and a measurement noise covariance at time $t$, respectively. From the residuals and the Kalman gain, the predicted state and covariance are updated as follows.
Finally, temporally consistent IPM is possible with the extrinsic camera parameter estimates $\theta, \phi, \psi$, and $h$. A homography matrix $\mathbf{H}_{W C}$ from the camera coordinates to the world (or ground) coordinates is calculated as follows.
where $a_X$ and $a_Z$ are the scale parameters that determine the resolution of a BEV image, $b_X$ and $b_Z$ are the size parameters of $X$-axis and $Z$-axis in the world coordinate system, and $\mathbf{R}_{r_1}$ is the $i$-th row of the matrix $\mathbf{R}(\theta, \phi, \psi)$ which is computed by
本文解读 NeRF（神经辐射场）论文，介绍如何用 MLP 神经网络将静态 3D 场景隐式表示为连续的 5D 函数，输出各点的体积密度与视角相关颜色，并沿相机光线做可微体素渲染。文章重点讲解了场景表示、基于分段随机采样的离散近似渲染算法，以及位置编码、多层级采样等训练技巧，最终实现从任意视角合成逼真的新视图。
以连续辐射场隐式建模场景，任意视角皆可渲染
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Nerf论文学习2026-08-25T13:18:00.971Zguoben
本文总结 SLAM 中常用的角点检测算法：先介绍人工设计特征点应具备的可重复性、可区别性、高效率与本地性，以及关键点和描述子的组成；再逐一讲解 FAST、Harris、Shi-Tomas、ORB、SIFT、SURF 的原理、优缺点及其在 SLAM 中的适用性。
小而稳定的特征，撑起整个位姿估计
特征点
人工设计的特征点该具有的特性
可重复性（Repeatability）：相同的“区域”可以在不同的图像中被找到。
可区别性（Distinctiveness）：不同的“区域”有不同的表达。
高效率（Efficiency）：同一图像中，特征点的数量应远小于像素的数量。
本地性（Locality）：特征仅与一小片图像区域相关。
组成
关键点
描述子
描述子设计原则：外观相似的特征应该又相似的描述子；
常用角点检测算法
SLAM中常用的角点检测算法整理如下：
本文根据ORBSLAM3中的综述表格进行总结：
FAST关键点
单纯的FAST关键点，没有描述子
FAST 是一种角点，主要检测局部像素灰度变化明显的地方，以速度快著称。它的思 想是：如果一个像素与它邻域的像素差别较大（过亮或过暗）, 那它更可能是角点。相比于其他角点检测算法，FAST 只需比较像素亮度的大小，十分快捷。它的检测过程如下（见图7-3 ）：
在图像中选取像素p，假设它的亮度为$I_p$。
设置一个阈值T(比如$I_p$ 的20%)。
以像素p 为中心, 选取半径为3 的圆上的16 个像素点。
假如选取的圆上，有连续的N 个点的亮度大于Ip + T 或小于Ip - T，那么像素p可以被认为是特征点(N 通常取12，即为FAST-12。其它常用的N 取值为9 和11，他们分别被称为FAST-9，FAST-11)。
循环以上四步，对每一个像素执行相同的操作。
在FAST-12 算法中，为了更高效，可以添加一项预测试操作，以快速地排除绝大多数不是角点的像素。具体操作为，对于每个像素，直接检测邻域圆上的第1，5，9，13 个像素的亮度。只有当这四个像素中有三个同时大于Ip + T 或小于Ip T 时，当前像素才有可能是一个角点，否则应该直接排除。这样的预测试操作大大加速了角点检测。此外，原始的FAST 角点经常出现“扎堆”的现象。所以在第一遍检测之后，还需要用非极大值抑制（Non-maximal suppression），在一定区域内仅保留响应极大值的角点，避免角点集中的问题。
OPENCV描述：In the last chapter, we saw that corners are regions in the image with large variation in intensity in all the directions. One early attempt to find these corners was done by Chris Harris & Mike Stephens in their paper A Combined Corner and Edge Detector in 1988, so now it is called the Harris Corner Detector. He took this simple idea to a mathematical form. It basically finds the difference in intensity for a displacement of (u,v) in all directions.
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https://grobenis.github.io/2022/05/31/2022-05-31-SLAM_Feature_detecter/2022-05-31T13:38:32.000Z
本文总结 SLAM 中常用的角点检测算法：先介绍人工设计特征点应具备的可重复性、可区别性、高效率与本地性，以及关键点和描述子的组成；再逐一讲解 FAST、Harris、Shi-Tomas、ORB、SIFT、SURF 的原理、优缺点及其在 SLAM 中的适用性。
构造函数中还有一个默认参数flags，默认值为 std::regex::ECMAScript，该参数可以用来设置正则表达式所采用的语法，如 std::regex::grep, std::regex::awk 等，也可以设置 case insensitive。flags 的多个值用比特位 OR 操作|连接，如
In the last month, how often have you been upset because of something that happened unexpectedly? In the last month, how often have you felt that you were unable to control the important things in your life? In the last month, how often have you felt nervous and "stressed"? In the last month, how often have you dealt successfully with irritating life hassles? In the last month, how often have you felt that you were effectively coping with important changes that were occurring in your life? In the last month, how often have you felt confident about your ability to handle your personal problems? In the last month, how often have you felt that things were going your way? In the last month, how often have you found that you could not cope with all the things that you had to do? In the last month, how often have you been able to control irritations in your life? In the last month, how often have you felt that you were on top of things? In the last month, how often have you been angered because of things that happened that were outside of your control? In the last month, how often have you found yourself thinking about things that you have to accomplish? In the last month, how often have you been able to control the way you spend your time? In the last month, how often have you felt difficulties were piling up so high that you could not overcome them?
Get ready for measurement. Get into a comfortable position where you can record your measurement. You can stand or sit - it doesn’t matter. For the best result we recommend to rest your arms on a table or in your lap while you take a measurement with the Apple Watch facing up. Keep your wrist flat, and hold as still as you can. If you were physically active just before the measurement, take a break for 10 minutes before the measurement.
A better fit means better readings. Make sure that your Apple Watch is snug but comfortable on your wrist. If your Apple Watch doesn’t stay in place, or the sensors aren’t reading your heart rate, tighten the band a bit. The back of your Apple Watch needs to be touching your wrist.
Breathe in Breathe app for 2 min.
Press the Digital Crown to go to the Home screen, then open the Breathe app.
Turn the Digital Crown to set the session’s length. We recommend to breath for 2 min for the best result.
Tap Start when you’re ready. Breath normally, ignoring the instructions.
Remember to stay still while you breathe. The data may not be saved if you move while breathing.
Wait until the session ends and your watch taps you twice and chimes. When you’re done, you can see your heart rate.
We’ll show your stress result as soon as the data, that your Apple Watch recordedbecomes available in Apple Health. Usually it takes about 30 sec to get the data. To speed up the process we highly recommend to lock and unlock the screen of your iPhone right after you finish breathing.
intStrToInt(string str){ int len = str.length(); if (len == 0) return0; int i = 0; while (i < len && str[i] == ' ') ++i; // 排除开头的空格 if (i == len) return0;
if (!isdigit(str[i]) && str[i] != '+' && str[i] != '-') return0; //判断第一个符号 bool neg = str[i]=='-' ? true : false; i = isdigit(str[i]) ? i : i+1; longlong ans = 0L;
while (i < len && isdigit(str[i])) { ans = ans * 10 + (str[i++]-'0'); if (!neg && ans > INT_MAX) { ans = INT_MAX; break; } if (neg && ans > 1L + INT_MAX) { ans = 1L + INT_MAX; break; } } if (i != len) return0; // 不要此处，就是atoi()库函数的实现 return !neg ? static_cast<int>(ans) : static_cast<int>(-ans); }
classSolution { public: intfindMaxForm(vector<string>& strs, int m, int n){ vector<vector<int>> dp(m+1,vector<int>(n+1,0)); for(auto str:strs) { int zero = 0; int one = 0; for(int i = 0;i<str.length();i++) { zero += str[i]=='0'?1:0; one += str[i]=='1'?1:0; } for(int i = m;i>=zero;i--) for(int j = n;j>=one;j--) { dp[i][j] = max(dp[i-zero][j-one]+1,dp[i][j]); } } return dp[m][n]; } };
1 begin intialize: c,\hat{c} <- n, D_i <- {x_i}, i = 1,...,n 2 do \hat{c}<-\hat{c}-1 3 求最接近的聚类，如D_i和D_j 4合并D_i和D_j 5 until c = \hat{c} 6return c个聚类 7 end
1 begin intialize: c,\hat{c} <- n, D_i <- {x_i}, i = 1,...,n 2 do \hat{c}<-\hat{c}-1 3 寻找其合并类，将准则函数改变为最小的聚类，例如D_i和D_j 4合并D_i和D_j 5 until c = \hat{c} 6return c个聚类 7 end
SELECT COUNT(*) FROM students; #查询students表一共有多少条记录 COUNT(*)表示查询所有列的行数，要注意聚合的计算结果虽然是一个数字，但查询的结果仍然是一个二维表，只是这个二维表只有一行一列，并且列名是COUNT(*)。 SELECT COUNT(*) num FROM students; #通常，使用聚合查询时，我们应该给列名设置一个别名，便于处理结果： SELECT COUNT(*) boys FROM students WHERE gender = 'M'; #聚合查询同样可以使用WHERE条件，因此我们可以方便地统计出有多少男生、多少女生、多少80分以上的学生等：
SELECT AVG(score) average FROM students WHERE gender = 'M';要统计男生的平均成绩，我们用下面的聚合查询： SELECT AVG(score) average FROM students WHERE gender = 'X'; #如果聚合查询的WHERE条件没有匹配到任何行，COUNT()会返回0，而SUM()、AVG()、MAX()和MIN()会返回NULL： 输出NULL
分组
可以用SELECT COUNT(*) num FROM students WHERE class_id = 1;。如果要继续统计二班、三班的学生数量，难道必须不断修改WHERE条件来执行SELECT语句吗？对于聚合查询，SQL还提供了“分组聚合”的功能。我们观察下面的聚合查询：
1 2
SELECT class_id, COUNT(*) num FROM students GROUP BY class_id;#对于聚合查询，SQL还提供了“分组聚合”的功能。 SELECT name, class_id, COUNT(*) num FROM students GROUP BY class_id;#，GROUP BY子句指定了按class_id分组，因此，执行该SELECT语句时，会把class_id相同的列先分组，再分别计算，因此，得到了3行结果。
GROUP BY子句指定了按class_id分组，因此，执行该SELECT语句时，会把class_id相同的列先分组，再分别计算，因此，得到了3行结果。
1 2 3
SELECT class_id, COUNT(*) num FROM students GROUP BY class_id;#执行这个查询，COUNT()的结果不再是一个，而是3个，这是因为，GROUP BY子句指定了按class_id分组，因此，执行该SELECT语句时，会把class_id相同的列先分组，再分别计算，因此，得到了3行结果。 SELECT name, class_id, COUNT(*) num FROM students GROUP BY class_id;#结果集就可以一目了然地看出各个班级的学生人数。 SELECT class_id, COUNT(*) num FROM students GROUP BY class_id;#我们再试试把name放入结果集：
7 多表查询
SELECT查询不但可以从一张表查询数据，还可以从多张表同时查询数据。查询多张表的语法是：SELECT * FROM <表1> <表2>。
1
SELECT * FROM students, classes; # 从students表和classes表的“乘积”，即查询数据，可以这么写；
-- 从id=1的账户给id=2的账户转账100元 -- 第一步：将id=1的A账户余额减去100 UPDATE accounts SET balance = balance - 100 WHERE id = 1; -- 第二步：将id=2的B账户余额加上100 UPDATE accounts SET balance = balance + 100 WHERE id = 2;
