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Accurate Volumes

We have a lot of images of landscapes and we are interested in finding the volumes of the rocks and forest located on them. The volume tools don’t seem to do a very accurate job, many of the measurements have a large margin of error because of the human error of clicking the points around the object to be the base surface. I noticed all the different volume options, which is best for calculating volume on a sloping hill? Is it the change in elevation that is making these measurements inaccurate? Is there anything to be done to make the measurements more accurate or to edit the volume once you have calculated it?

The accuracy of a volume measurement depends on the quality of the reconstruction and on how well the base surface is defined. 

This means that I would first make sure that the project itself is well reconstructed by checking the quality report and the point cloud. The point cloud can be checked directly in the rayCloud view: is there noise? are there more than a single layer? how is the reprojection of a point in the images? 

The volume measurement accuracy can also be increased by adding Ground Control Points (GCPs) in the area you measure or by adding a scale constraint as reference to the project: 
How to scale a project 

If you have made sure that the project is well reconstructed, you can have a look at these articles for more information: 
How Pix4Dmapper calculates the Volume?
Accuracy of Pix4Dmapper Outputs

As for the definition of the base surface, the “Triangulated (default)” or “Fit plane” surface option seems most adapted for your use case, as the other options will not keep the angle of the slope in the base surface. As you noted, the base surfaces will still need to be clicked carefully so that the right area will be measured.