A case study : basis for development of a curriculum based on images of self and environment.

<p><b>(a)</b> Right-handed twofold helical chain in 1 linked by intermolecular C–H···π interactions (red dotted line); <b>(b)</b> 3D supramolecular architecture construcated by C–H···π, O–H···O and C–H···O interactions.</p

Potential multiple primitive detection (Dataset I).

<p>(<b>a</b>) Two detected peaks of planar parameter sets (<b>b</b>) Four detected peaks of spherical parameter sets <b>(c)</b> Four detected peaks of cylindrical parameter sets.</p

BaySAC process flowchart for the fitting of primitive model <i>i</i>.

<p>Use n data points with the highest inlier probabilities as the hypothesis set to fit primitive model <i>i</i>; evaluate all data points w.r.t. primitive model <i>i</i> and update the inlier probabilities of each data point concerning primitive model <i>i</i> in the hypothesis set via Bayes’ rule; update the multiple inlier probabilities using the new inlier probabilities for model <i>i</i> as well as the new inlier probabilities for other models updated through other BaySAC processes running in parallel; repeat the hypothesis testing process until the sampling number reaches the defined threshold; using all inlier points, compute the optimal model parameters through least-squares adjustment.</p

The 2D histogram of a sphere.

<p>The horizontal and vertical axes denote the distance between the hypothesis center point and coordinate system origin and the hypothesis radius respectively; the upright axis represents the convergence degree of each candidate parameter set. This degree of candidate parameter set convergence in the histogram is calculated as the number of parameter sets that converge to the candidate parameter set divided by the total number of parameter sets.</p

Potential multiple primitive detection

<p>(Dataset IV and V) (<b>a</b>) 2D point-density images: Dataset IV (Left) and Dataset V (Right); (b) Segmentation results: Dataset IV (Left) and Dataset V (Right); (c) Statistical testing of candidate model parameters for the highlighted segment of Dataset IV.</p

Description of test point clouds.

<p>Description of test point clouds.</p

Primitive parameterization.

<p>The primitive parameterization is described as follows <b>(a)</b> A singularity free representation (Hesse form) of a plane: the planar primitive is represented by the normal vector and perpendicular distance from the origin <b>(b)</b> An infinite cylinder represented by the axis of the cylinder, the point closest to the origin and the radius <b>(c)</b> A sphere defined by its center point and radius.</p

The 2D histogram of a plane.

<p>The horizontal and vertical axes denote the angle between the normal vector n of a plane and horizontal plane and the perpendicular distance from the origin respectively; the upright axis represents the convergence degree of each candidate parameter set. This degree of candidate parameter set convergence in the histogram is calculated as the number of parameter sets that converge to the candidate parameter set divided by the total number of parameter sets.</p

Test point clouds.

<p>(<b>a</b>) Synthetic Dataset I includes two planes, four spheres and four cylinders;(<b>b</b>) Real Dataset II includes two planes and five cylinders <b>(c)</b> Real Dataset III includes several planar primitives and one spherical primitive <b>(d)</b> Real Dataset IV includes several planar primitives <b>(e)</b>Real Dataset V consists of an airborne point cloud with planar roofs.</p

An example of the proposed multiBaySAC.

<p>(<b>a</b>) Fifteen candidate points for fitting two lines that contain three outliers, i.e. points 13, 14 and 15 (<b>b</b>) The detection of potential lines using the hypothesis model parameters histogram.</p