Number of plots and number of tress needed to measure in order to get needed precision of estimates depends on heterogeneity of stand as regards heterogeneity in tree age,  tree development classes or tree sizes as well as on tree distribution on site  and also on terrain heterogeneity. It could be variety of combinations. If terrain heterogeneity is high then more sample plots are needed. If heterogeneity of age or/and tree development classes or/and tree sizes is high then larger sample plots with more trees are needed. Based on this you have to choose right method. If you  set thresholds to only measure trees within a certain distance from the camera then each sample plot will have irregular number of trees especially if distribution of trees is hetorogenous 

Hallo Harley,

You want to estimate dbh (average) and density (which index?) of stands with photos. If you want to test a new methode you should first test it in a pure and very unique stand to verify your method. So you can campare your results on your plot also with yield tables. When you get good results you can test your methode in different stands without measure all trees.

Your plots should not be to large because otherwise you will not find differences between your plots. In provenance trials we use 3 plots per provenance with (16) to 50 plants each (50 is usual now). In agriculture more than 3 plots (3 to 10) are usual. If we test tree populations in genetic investigations we seample 50 to 100 plants of each population. For statistic investigations e.g. ANOVA it is useful to have more than 30 plants and 3 repetions (plots) (minimum).

For more recommondations more information about your data is neccessary

Literatur: you will find sime information about test design and trialplaning in: Grundlagen der Waldwachstumsforschung (2002) from Prof. Dr. Pretzsch. There is also a book in english language with similar content - Forest Dynamics, Growth and Yield (2009)

with best regards

and good success

Gerhard

I guess your photos are from ground level so that you can see some tree trunks, but don't have a full 360deg photo.  I don't think you can get tree density from a simple photo, but you talk of plots, so maybe you will be on site to do the work?

Two options come to mind:

1.  Basal area using a relascope (cross sectional area of tree trunks in m sq/ha)

Maybe this will work for you:

https://play.google.com/store/apps/details?id=ee.deskis.adnroid.relascope&hl=en_GB

2.  Plotless sample from a point within the forest (several methods) will give you an estimate of density and dbh of trees in the sample if you measure them.  Two handy URLs:

http://faculty.clintoncc.suny.edu/faculty/michael.gregory/files/BIO%20206/206%20Laboratory/Point-Quarter%20Method/point-quarter%20instructions.htm

http://www.academia.edu/3515156/Point_Centered_Quarter-_Plotless_sampling_methods

Mike Swaine

What you are attempting to do is extremely hard and will require far more time and effort than a simple BAF (Basal Area Factor) cruise of the stand, using a relascope, or prism.

Wayne Shepperd

First of all, thank you very much for your responses.

Alfas, I have done some preliminary work in the forests and have a good feel for the heterogeneity of the area. Now that I have some early data I need to work on the details and determine what my sample sizes need to be. I am trying to avoid doing field work and then having someone tell me that I didn't sample enough or that I wasted too much time doing too many samples. The guidelines for forests in my area suggest four plots of 400 m2 in a forest greater than 2 hectares however these guidelines do not reveal how this was calculated. I would like to know so I can do the calculations myself.

Gerhard, I am after the density per hectare. I think you are correct that I should use a very uniform stand which is what Alfas was suggesting. I just downloaded the book you referred to me. It seems like a useful resource. Thank you very much. Perhaps my answer will be in that.

Thanks Swaine. Yes, it is trunks I can see. Generally I don't use a 360 degree view, but if that is the most appropriate way to do it, then I can modify my technique. The relascope you referred to me is similar to what I am doing, although I use the images to build a digital model and make my measurements from the desktop. I had considered plotless measurement techniques however there are so many trees in my models that it seems a waste to only measure 4. That is why I went for plots.

Thanks for the feedback Wayne. Like most things, I have since realised the difficulty of what I am doing but am determined to see it through. Taking the measurements is the part I have confidence in. It is comparing them to other methods to show that it is a sound technique that I am trying to do.

Perhaps if I propose a hypothetical it will make it easier. What if I had a 5 hectare patch of forest with approximately 100-200 mixed age trees per hectare. For argument sake, lets assume they are relatively evenly distributed and there isn't a large amount of terrain variability. Is there a calculation I can use to determine how much area, or how many trees I should sample per hectare knowing that my sample method is a photo set (plot)? The photo plots are approximately 200 m2 but they can be larger or smaller if necessary. Judging by the feedback, it is more complicated than I had originally assumed. 

Harley,

Given your example, you could expect  each tree to occupy from 50 - 100 m2. With your current plot size, you could expect to sample an average of less than 2 trees/plot, with a fair number of non-stocked plots occurring. To increase the statistical reliability of your sample you should probably aim for an average of at least  of 4 trees/plot, which would require doubling  your plot size. Of course this assumes a spatially uniform population. Irregular spacing of the trees will require further adjustment of plot size or shape.

I'm curious how you are dealing with trees that are hidden from view in a fixed photo point. Are you shifting camera position to see them? Or, grabbing images from moving video where you know all trees in the plot are visible?

Thanks for your help Wayne. Aiming for 4 trees per plot sounds like a good target. I typically get more than that but trees that are closer to the camera are resolved better. How many plots would I require per hectare? Is this something I should test in the field and see when the estimate levels off when graphed? Or is there a calculation I can make based on the variance i get?

During the proposed trials, I am testing the techniques in grassy woodlands and other non-shrubby forests so that eucalypt trunks are clearly visible. There are two methods I wish to compare to standard tape measurements or Bitterlich plots: stereophotogrammetric images (measuring disparity) and photo (or video) transects of minimum 10 photos (to build 3d models from point clouds similar to a ground based LiDAR). My aim is to do these using standard digital or mobile phone cameras and have the measurements rapidly made from the office. 

I face significant occlusion issues with the stereophotogrammetry method and would rely on some kind of predictive model that infers the existence of some trees (i have read some papers on this), but the photo (or video) transect avoids this almost entirely.

You should take a number of trees to be found between 20 to 30 within each plot. As for the amount of parcels you should take into account the variance of the population with which you work to calculate the minimum sample size.

another literature: T.E. Avery and H.E Burghart 2002: Forest Measurements, Fifth Edition,  McGraw Hill ISBN 0-07-366176-7pp. 271-294.