# Normal Estimation Using Integral Images

In this tutorial we will learn how to compute normals for an organized point cloud using integral images.

# The code

Then, create a file, let’s say, `normal_estimation_using_integral_images.cpp` in your favorite editor, and place the following inside it:

``` 1#include <pcl/visualization/pcl_visualizer.h>
2#include <iostream>
3#include <pcl/common/io.h>
4#include <pcl/io/pcd_io.h>
5#include <pcl/features/integral_image_normal.h>
6
7int
8main ()
9{
11    pcl::PointCloud<pcl::PointXYZ>::Ptr cloud (new pcl::PointCloud<pcl::PointXYZ>);
13
14    // estimate normals
15    pcl::PointCloud<pcl::Normal>::Ptr normals (new pcl::PointCloud<pcl::Normal>);
16
17    pcl::IntegralImageNormalEstimation<pcl::PointXYZ, pcl::Normal> ne;
19    ne.setMaxDepthChangeFactor(0.02f);
20    ne.setNormalSmoothingSize(10.0f);
21    ne.setInputCloud(cloud);
22    ne.compute(*normals);
23
24    // visualize normals
25    pcl::visualization::PCLVisualizer viewer("PCL Viewer");
26    viewer.setBackgroundColor (0.0, 0.0, 0.5);
28
29    while (!viewer.wasStopped ())
30    {
31      viewer.spinOnce ();
32    }
33    return 0;
34}
```

# The explanation

Now, let’s break down the code piece by piece. In the first part we load a point cloud from a file:

```    pcl::PointCloud<pcl::PointXYZ>::Ptr cloud (new pcl::PointCloud<pcl::PointXYZ>);
```

In the second part we create an object for the normal estimation and compute the normals:

```    // estimate normals
pcl::PointCloud<pcl::Normal>::Ptr normals (new pcl::PointCloud<pcl::Normal>);

pcl::IntegralImageNormalEstimation<pcl::PointXYZ, pcl::Normal> ne;
ne.setMaxDepthChangeFactor(0.02f);
ne.setNormalSmoothingSize(10.0f);
ne.setInputCloud(cloud);
ne.compute(*normals);
```

The following normal estimation methods are available:

```enum NormalEstimationMethod
{
COVARIANCE_MATRIX,
AVERAGE_DEPTH_CHANGE,
};
```

The COVARIANCE_MATRIX mode creates 9 integral images to compute the normal for a specific point from the covariance matrix of its local neighborhood. The AVERAGE_3D_GRADIENT mode creates 6 integral images to compute smoothed versions of horizontal and vertical 3D gradients and computes the normals using the cross-product between these two gradients. The AVERAGE_DEPTH_CHANGE mode creates only a single integral image and computes the normals from the average depth changes.

In the last part we visualize the point cloud and the corresponding normals:

```    // visualize normals
pcl::visualization::PCLVisualizer viewer("PCL Viewer");
viewer.setBackgroundColor (0.0, 0.0, 0.5);