Three-Dimensional Pose Estimation and Segmentation Methods - 3D Computer Vision: Efficient Methods and Applications - page 105

of tubes, this includes elasticity, length, radius, and sometimes the mounting posi-
tion, depending on the application. The model information is introduced into the
optimisation process in two ways. The first is by adding additional energy terms,
the second by using a constrained optimisation algorithm. Additional model-based
energy terms that favour a certain shape of the contour can be added to E con .For
example, the approximate radius of a cable is known, but it may vary at some places
due to labels or constructive changes.
As a first approach, we utilise a three-dimensional ribbon snake to detect the
cable shape and position. Hence, E con =

2 can be used as
a 'spring energy' to favour contours with a radius r close to a model radius given
by the function r model (s) . However, adding constraint terms to the objective func-
tion may result in an ill-posed problem with poor convergence properties and adds
more weight factors that need to be tuned for a given scenario (Fua and Brechbüh-
ler, 1996 ). The second approach is to enforce model constraints through optimiser
constraints. In the greedy algorithm this is achieved by intersecting the parameter
search region H and the region C permitted by the constraints to obtain the allowed
search region H c =

E rib =[ r(s) − r model (s) ]

C . This ensures that these constraints cannot be violated
(they are also called hard constraints).
For some applications like glue line detection, the surface in which the contour
is located is known, for example from CAD data. In other cases, the bounding box
of the object can be given. This knowledge can be exploited by a constraint that
restricts the optimisation to the corresponding surface or volume. Model information
can also be used to create suitable initial contours—for example, tubes are often
fixed with brackets to other parts. The pose of these brackets is usually given a priori
when repeated quality inspection tasks are performed or can be determined by using
pose estimation algorithms for rigid objects (cf. Sect. 2.1 ). These points can be used
as starting and end points, i.e. boundary conditions, for three-dimensional ziplock
ribbon snakes.

H ∪

2.2.2.3 Experimental Results on Synthetic Image Data

As a first test, the described algorithm has been applied to synthetically generated
image data, for which the ground truth is inherently available. For all examples, a
three-dimensional ribbon snake was used. The weight factors of ( 2.5 ) were set to
α =

0. Additionally, a hard constraint has been placed
on the minimum and maximum ribbon width, which avoids solutions with neg-
ative or unrealistically large width. To estimate the reconstruction quality, a syn-
thetically rendered scene was used as a test case, as this allows a direct compari-
son to the known ground truth. Figures 2.4 a and b show the example scene and its
three-dimensional reconstruction result. The start and end points of the object and
their tangents were specified. In a real-world application these could either be taken
from a CAD model, or estimated by pose estimation of the anchoring brackets. The
ground truth used to produce the image is known and is compared to the segmented
contour. The utilised error measure is the root-mean-square error (RMSE) of the

1, β = 1, γ = 3, and δ =