This tool does a cylinder fit to find cylinders in 3D Point Cloud - Scorpion 3D Image

3D coordinate system

• Reference - select a 3D reference for position and results

ROI

• See the term 3D ROI (Note: Sphere ROI is not supported for this tool)

Note that the axis of a cylinder found must fall within a cylinder described by the center of the ROI (x direction) and the initial guess radius in its entire (x) extent. This means:

• If you have a cylinder ROI, a found cylinder will have its axis close to the ROI axis, within the boundary set by the initial guess radius (not the inner or outer ROI radii)
• With a box ROI, the ROI axis is defined as the center (in y and z) of the box. This means you must make the ROI box wide enough to enclose the axis of the cylinder you want to find. Specifically, if your data set contains only points from one "side" of the cylinder (as is common with GCPS), your ROI should include the "other" (hidden) side of the cylinder as well.

Fit algorithm

• Fit only - run (possibly multipass - see Advanced) the fit algorithm given by Method
• RANSAC only - run a single RANSAC fit only
• RANSAC + fit - run a single RANSAC fit, followed by (possibly multipass - see Advanced) the fit algorithm given by Method
• Exhaustive - run RANSAC followed by a complete iterative fit based on the algorithm given by Method
• Method -
  • Random (10) - Naive implementation used primarily for testing and debugging. It simply tests randomly in a region assumed to contain a minimum. If the random point tested actually produces a smaller error, the method jumps there and then continues. By slowly reducing the randomness and size of the region, one increases the chance of stumbling upon a global minimum. The method will converge, but not necessarily fast.
  • Conjugate gradients - This is a class of methods based on the availability of derivatives of the error function, i.e., a gradient. In its simplest con guration, this method performs the classic Steepest Decent search for a minimum, which works by moving in the direction in which the error decreases most rapidly, and moving an amount in this direction which is foreseen to bring us to a point from which it is no longer useful to continue in said direction. This is then repeated. For many problems this can work just nicely, but the classic and simple example for which this breaks down is the error function looking like a long and slightly slanting valley . For this problem, Steepest Decent will (from a high point) head straight towards the valley, overshoot/undershoot slightly, and then in the next step also head directly for the bottom of the valley , doing a much smaller step. The sensible thing to do, take a long stride along the valley, will never be a favoured move by this method, hence a very slow convergence. This particular problem is eliminated by the conjugate gradient methods (of which Steepest Decent is not a true case, rather a very reduced special case). But still - these methods need the gradient, and a numerical gradient will destroy some of the nice convergence properties of the methods. There are three variations, documented in e.g. Numerical Recipes:
    • Fletcher-Reeves (20) - a proper conjugate gradient method
    • Polak-Ribiere (21) - a proper conjugate gradient method
    • Steepest descent (22) - see above
  • Nelder Mead - This algorithm is not based on a gradient or other derivative of the error function. In a sense, it can be compared to the RandomMinimizer, except that it moves around in a much more smart fashion than purely random. The method is based on having a simplex in the search space for which the corners are evaluated. The simplex is moved and transformed so as to continually shrink simultaneously with the corner evaluations also decreasing, thus converging on what is hoped to be a (global) minimum. How this transformation of the simplex is done is not without freedom, there are some parameters to tweak, giving variations of the method. With parameters as close to the original work by Nelder and Mead as we have been able to figure out, we have made a Classic Nelder-Mead , and with some more recent choices of parameters we have found published on the internet, we made Variation I.
    • Original (30) - see above
    • Variation (31) - see above
• Radius - initial guess
• Tolerance - max deviation from initial guess
• Decimations - max number of iterations (for Exhaustive search)
• RANSAC count - max RANSAC iterations
• Min dist - minimum distance between points considered for a RANSAC search
• Max dist - maximum distance between points considered for a RANSAC search

Advanced

Passes

The cylinder fit can run a multipass fit procedure. The first option is used to turn this on or off.  (This is not available for the Exhaustive search.)

• Multipass fit - selects single or multiple passes
• Max iteration count - never exceed this number of passes
• Stop if RMS improvement less than - do not process further if RMS does not improve more than the threshold
• Stop if RMS less than - do not process further if RMS has reached the threshold
• Stop if active point count below - do not process further if less than the specified number of points remain
• Stop if active point percentage below - do not process further if less than the specified percentage of points within the ROI remain
• Stop if RMS deteriorates - do not process further, and ignore last pass, if RMS increases

Constraints

• Point accept distance - used to filter outliers in multipass fit and for the result (this is not used by the Exhaustive search)
• Max fit RMS for accept - RMS filter to accept/decline the result
• Minimum points for accept - point count filter to accept/decline the result
• Minimum percentage for accept - point percentage filter (within ROI) to accept/decline the result

Point cloud decimation (x & y)

• Factor - keep only every nth sample in x and y directions

Point cloud filter

• Contrast - element 4 in a 5-element point cloud; set min and max allowable value

Visualisation

Cylinder	Found cylinder
FittedPoints	Accepted points within the ROI
InitialGuess	Initial cylinder guess
Points	All points within the ROI
ROI	The ROI cube/cylinder segment

Results

CenterLine.p.x	Point p and extent v form the axis within the found
CenterLine.p.y	cylinder segment.
CenterLine.p.z
CenterLine.v.x
CenterLine.v.y
CenterLine.v.z
Cylinder radius	Radius of found cylinder
RMS	Quality of fit
Loop count	Total number of loops
Point count	Total number of points within ROI
Fit count	Used points
Fit percent	Percentage of points used