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Does anyone know how, or even if it is possible, to estimate the necessary number (and placement) of photos to achieve a certain final digital elevation model resolution (X points per square meter) generated using structure form motion?

I would like to do yearly follow-up surveys of a Brook that we have a longitudinal profile of, and have not been able (so far) to find any literature that discuss optimal picture number, placement, resolution, overlap, etc., given a certain terrain X with characteristics Y, over a length Z.

Any ideas?

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Structure from Motion is based on;

1) Feature identification (e.g. SIFT)

2) Matching features from two or more images

3) Bundle (block) adjustment

The matched and bundle adjusted features are essentially what the points are, so the point density depends on the texture of the target and how well the initial features (part 1) can be matched between images (part 2 & 3). Distance from the target and the camera model (sensor resolution) ultimately defines what is the level of detail you are able to capture and what the features are. Check this publication by Dandois et al. for further information.

I'll assume that you are using a drone for SfM. Here is a link to a spreadsheet that can calculate the ground sampling distance (GSD) for you. From the GSD you can easily calculate the points per square meter too (100/GSD = x^2, where x is the points per meter). Furthermore, you should consider image overlap when planning you project. Overlap can be divided to frontal and side overlap. For traditional photogrammetry the (frontal) overlap is ~ 60 % between images, but for computer vision based SfM, a higher overlap is used depending on target properties. For a good texture, bare ground target, e.g. quarry, something like 70 % would suffice. For a difficult target, e.g dense vegetation and steep topography, something like ~ 85-90 % would be better. Side overlap can be less than this, here is another study regarding overlap, altitude etc. by Dandois et al, for further reading.

I think in your case the you can safely fly as high as the regulations let you fly (120 m a.g.l.?), and you would still have decent GSD for your purposes. I can update my answer too, if you wish to provide more details about your project (e.g. what is the size of you study area, what hardware and software are you using and so on).

Please be aware of this book too, especially if you are using hand-held camera for SfM.

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