If you are using Axes Constraints, you have to have a photo with the correct perspective. With Axes Constraints you can solve for focal length if you have a strong two or three point perspective and you can solve for focal length and principal point if you have a strong three point perspective.
A single point perspective photo has just one vanishing point and the horizon is near the center of the photo. If a photographer was standing in the middle of some train tracks and took a photo looking down these tracks and the tracks vanish in the distance to a point near the center of the photo, then that is a single perspective photo and Inverse Camera will not work.
A two-point perspective photo has two vanishing points. A photo taken at 45 degrees to the corner of a building but the camera still parallel to the ground plane (which makes the vertical edges appear vertical in the photo) is a two point perspective photo. If the perspective is strong enough PhotoModeler can solve for the camera position and focal length for this photo. You would mark two sets of lines or edges and set up two Axes Constraints.
A three-point perspective photo has three vanishing points. A photo taken at 45 degrees to the corner of a building with the camera pointed towards the top of the building (which makes the vertical edges appear to vanish to a point near the top of the photo) is a three point perspective photo. If the perspective is strong enough PhotoModeler can solve for the camera position, focal length and principal point for this photo. You would mark three sets of lines or edges and set up three Axes Constraints.
Good example: You are modeling a building or a room and the camera was at a sharp angle to all surfaces (perhaps a video surveillance camera pointing down and way from the corner). This photo is perhaps in three-point perspective and you may be able to solve for focal length and principal point.
Bad example: You have a single photograph of a road taken right down the middle. The camera was parallel to the ground and the horizon is close to the center of the photograph. This photograph is probably in single point perspective and no Inverse Camera solution can be done.
Note: axes constraints cannot be used to solve for Inverse Camera in a multi-photo project. Instead work with each photographs individually and then combine the results (camera parameter solutions and photos) into a multi-photo project.
If you managed to get through this review and answer positively to all of the questions you will have a good chance of getting the 3D measurements you want. If some of the aspects are weak or poor, you might still be able to do something. If the reference count check is bad and there is no source of good control, then you are probably out of luck and these photographs cannot be used to get 3D measurements.