Understanding resolution in vector maps?
The term resolution refers to the smallest details that can be distinguished. It is mainly used for raster data (resolution in time, in space or in spectral domain).
For a vector map, two other concepts are more broadly used: the scale and the minimum mapping unit.
The scale is related to the spatial precision of the boundaries of your entities. It comes from the time of paper maps, where boundaries were drawn and the width of the pencil was the limit of the precision of the representation of the entities on the paper map. Assuming that the pencil is about 0.2 mm, the precision of the line was about equal to the scale factor multiplied by 0.1 to 0.3 mm (0.2 mm on average). For example, a scale of 1:10 000 correspond to approximately 1 to 3 m of maximum precision. With vector data, you can zoom in or out as you wish, so the "scale" of the data doesn't have the same meaning. However, you need to define a scale of reference (stored in the metadata) so that your data is used in an appropriate way (you must be careful to combine entities from different scales).
The minimum mapping unit is the minimum size of representation of an object. For instance, you could map all the gaps in a forest, or only map large gaps to avoid complex polygons. For very different scales, the geometry of your object could also change (e.g. a river would be a polygon with small scale factors and a line with large scale factors). This is also related to the resolution of your product (What is the smallest distinguishable object), but not in terms of planimetric precision.
So, in your case, the resolution has two components:
- what is the smallest entity that you can map?
- what is the precision of delineation of your entities?
You MMU is problably a few cm (are some poles to small to be mapped?)
Your precision is a function of your point density (you can roughly assume the average spacing between the closest points of your xyz point cloud is equal to your resolution).
Finally, for a complete information about data quality, your should also consider the accuracy of this data. Indeed, because you do not have GCPs, there is a risk that all your dataset is shifted or rotated away from the "true" location, or that it doesn't have the same scale.
From stereo camera, the accuracy will depend on the accuracy of the position of the camera, the accuracy of the viewing angles of the camera (called external orientation), and the accuracy of the corrections of deformations of the lens. There are hardware solution (RTK DGPS, high quality INS for accurate exterior orientation) as well as calibration procedure for interior orientation (calibrated camera lenses or structure from motion algorithm for multiple overlap), so that it is now possible to have good results without GCP. However, I would recommend you ta have some GCP in any case (in order to compute your absolute error, even if it is difficult to find GCP for this resolution).
Hm.... where I come from, resolution in the context of vector data usually means that the data has the same level of detail as an equivalent raster or in some otherway prerendered map. For example, we have a vector database with resolution 1:5000 which means that this database includes such features and level of detail, that can be found on a typical raster map of such scale. So you would probably have for example a railway caracterized by a single polyline, not 2 polyline for each rail, because on the scale 1:5000 it would not make sense to do that.
Please note like I said, this is how we sometimes interpret "vector resolution" in our country. It could also be something completely different (for example, precision of coordinated, or something like that)
Not a geographer but I believe that you could evaluate what your original point cloud can distinguish. For instance, can your point cloud identify the thickness of the lamp post? Can it identify finer objects?
Then, in the old-days of paper maps, the smallest feature could be represented by 0.2mm (bellow that we just can't see). So, if the smallest feature of your point cloud has 20 cm and that is represented as 0.2mm, the scale would be 0,2 mm / 200 mm = 0.001 or 1:1000 scale. But this was for paper maps and might not be applicable.
Another option is to take a look at a rule from Waldo Tobler on scale and map resolution. That might give you some hints. From his rule, if you need a detectable size of 10cm, you would need a scale of 1:100 and a raster resolution of 5 cm.