深度图转激光原理

深度图转激光在ROS包depthimage_to_laserscan中实现，本篇讲解其计算过程。关于点云转激光数据的思路也是类似的，只需要将一定高度范围内的数据进行投影即可。

1. 深度图转激光原理

原理如图（1）所示。深度图转激光中，对任意给定的一个深度图像点(m(u,v,z))，其转换激光的步骤为：

a.将深度图像的点(m(u,v,z))转换到深度相机坐标系下的坐标点(M(x,y,z))，具体求解过程请参考“深度图转点云的原理”；

b.计算直线(AO)和(CO)的夹角(AOC)，计算公式如下：

　　( heta = atan(x/z))

c.将角(AOC)影射到相应的激光数据槽中.已知激光的最小最大范围([alpha,eta]),激光束共细分为(N)分，那么可用数组(laser[N])表示激光数据。那么点(M)投影到数组laser中的索引值(n)可如下计算：

　　(n=( heta - alpha)/((eta - alpha)/N) =N( heta - alpha)/(eta - alpha))

(laser[n])的值为(M)在x轴上投影的点(C)到相机光心(O)的距离(r)，即

(laser[n] = r=OC=sqrt{z^{2}+x^{2}})

图（1）

2. 代码

以下为添加注释说明的实现代码（另可参阅原始代码），

/**
    * Converts the depth image to a laserscan using the DepthTraits to assist.
    * 
    * This uses a method to inverse project each pixel into a LaserScan angular increment.  This method first projects the pixel
    * forward into Cartesian coordinates, then calculates the range and angle for this point.  When multiple points coorespond to
    * a specific angular measurement, then the shortest range is used.
    * 
    * @param depth_msg The UInt16 or Float32 encoded depth message.
    * @param cam_model The image_geometry camera model for this image.
    * @param scan_msg The output LaserScan.
    * @param scan_height The number of vertical pixels to feed into each angular_measurement.
    * 
    */
    template<typename T>
    void convert(const sensor_msgs::ImageConstPtr& depth_msg, const image_geometry::PinholeCameraModel& cam_model, 
         const sensor_msgs::LaserScanPtr& scan_msg, const int& scan_height) const{
      // Use correct principal point from calibration
      float center_x = cam_model.cx();//图像中心位置x
      float center_y = cam_model.cy();//图像中心位置y

      // Combine unit conversion (if necessary) with scaling by focal length for computing (X,Y)
      double unit_scaling = depthimage_to_laserscan::DepthTraits<T>::toMeters( T(1) );
      float constant_x = unit_scaling / cam_model.fx();
      float constant_y = unit_scaling / cam_model.fy();
      
      const T* depth_row = reinterpret_cast<const T*>(&depth_msg->data[0]);
      int row_step = depth_msg->step / sizeof(T);

      int offset = (int)(cam_model.cy()-scan_height/2);
      depth_row += offset*row_step; // Offset to center of image

      for(int v = offset; v < offset+scan_height_; v++, depth_row += row_step){
        for (int u = 0; u < (int)depth_msg->width; u++) // Loop over each pixel in row
        {    
          T depth = depth_row[u];
          
          double r = depth; // Assign to pass through NaNs and Infs
          double th = -atan2((double)(u - center_x) * constant_x, unit_scaling); // 计算夹角AOC，Atan2(x, z),实际上这里省略了深度值，因为分子分母都有，所以就略去了 but depth divides out
          int index = (th - scan_msg->angle_min) / scan_msg->angle_increment;//计算对应激光数据的索引
          
          if (depthimage_to_laserscan::DepthTraits<T>::valid(depth)){ // Not NaN or Inf
            // Calculate in XYZ,计算XYZ
            double x = (u - center_x) * depth * constant_x;
            double z = depthimage_to_laserscan::DepthTraits<T>::toMeters(depth);
            
            // Calculate actual distance，计算激光的真实距离
            r = sqrt(pow(x, 2.0) + pow(z, 2.0));
          }
      
      // Determine if this point should be used.判断激光距离是否超出预设的有效范围
      if(use_point(r, scan_msg->ranges[index], scan_msg->range_min, scan_msg->range_max)){
        scan_msg->ranges[index] = r;
      }
    }
      }
    }
    
    image_geometry::PinholeCameraModel cam_model_; ///< image_geometry helper class for managing sensor_msgs/CameraInfo messages.
    
    float scan_time_; ///< Stores the time between scans.
    float range_min_; ///< Stores the current minimum range to use.
    float range_max_; ///< Stores the current maximum range to use.
    int scan_height_; ///< Number of pixel rows to use when producing a laserscan from an area.
    std::string output_frame_id_; ///< Output frame_id for each laserscan.  This is likely NOT the camera's frame_id.
  };