Registration of Six Degrees of Freedom Data with Proper Handling of Positional and Rotational Noise. Franaszek M - J Res Natl Inst Stand Technol (2013) Bottom Line: The mismatch can be formally corrected by dividing the positional component by some scale factor with units of length.However, the scale factor is set arbitrarily and, depending on its value, more or less importance is associated with the positional component relative to the rotational component.This may result in a poorer registration. View Article: PubMed Central - PubMed Affiliation: National Institute of Standards and Technology, Gaithersburg, MD 20899. ABSTRACTWhen two six degrees of freedom (6DOF) datasets are registered, a transformation is sought that minimizes the misalignment between the two datasets. Commonly, the measure of misalignment is the sum of the positional and rotational components. This measure has a dimensional mismatch between the positional component (unbounded and having length units) and the rotational component (bounded and dimensionless). The mismatch can be formally corrected by dividing the positional component by some scale factor with units of length. However, the scale factor is set arbitrarily and, depending on its value, more or less importance is associated with the positional component relative to the rotational component. This may result in a poorer registration. In this paper, a new method is introduced that uses the same form of bounded, dimensionless measure of misalignment for both components. Numerical simulations with a wide range of variances of positional and rotational noise show that the transformation obtained by this method is very close to ground truth. Additionally, knowledge of the contribution of noise to the misalignment from individual components enables the formulation of a rational method to handle noise in 6DOF data. No MeSH data available. Related in: MedlinePlus © Copyright Policy - open-access Related In: Results  -  Collection License getmorefigures.php?uid=PMC4487304&req=5 .flowplayer { width: px; height: px; } f2-jres.118.013: The diagram showing which of the three methods delivered most frequently the best registration. In method 1, Eloc was minimized using only the positional data; in method 2, Erot was minimized using only the rotational data; in method 3, Epose was minimized using full 6DOF data. For each pair of noise parameters (g, h), a total of Ntot = 1,600 registrations of different data pairs were performed. Mentions: Figures 1–5 show the results of simulations obtained for 200 × 200 pairs of noise parameters (g, h). On average, 5–9 iterative steps were needed for the DFP minimization procedure to converge. The length of each dataset (primary or secondary) is N = 10, Nnoise = 16, Mdata = 10, Ktrans = 10, so there are Ntot = 1,600 pairs of (primary, secondary) data requiring registration for each (g, h). Figure 1 shows the mean ratio averaged over all Ntot cases and displayed in a logarithmic scale(26)α¯=1Ntot∑l=1Ntotαl,αl=Eloc(vpose(l))Erot(vpose(l)),where is the solution obtained by minimizing Epose for the l-th pair of data. Figure 2 shows which method most frequently delivered the smallest deviation from ground truth dk as defined in (24). Figure 3 displays how often a given method delivered the best results.

Registration of Six Degrees of Freedom Data with Proper Handling of Positional and Rotational Noise.

Franaszek M - J Res Natl Inst Stand Technol (2013)

Related In: Results  -  Collection

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f2-jres.118.013: The diagram showing which of the three methods delivered most frequently the best registration. In method 1, Eloc was minimized using only the positional data; in method 2, Erot was minimized using only the rotational data; in method 3, Epose was minimized using full 6DOF data. For each pair of noise parameters (g, h), a total of Ntot = 1,600 registrations of different data pairs were performed.
Mentions: Figures 1–5 show the results of simulations obtained for 200 × 200 pairs of noise parameters (g, h). On average, 5–9 iterative steps were needed for the DFP minimization procedure to converge. The length of each dataset (primary or secondary) is N = 10, Nnoise = 16, Mdata = 10, Ktrans = 10, so there are Ntot = 1,600 pairs of (primary, secondary) data requiring registration for each (g, h). Figure 1 shows the mean ratio averaged over all Ntot cases and displayed in a logarithmic scale(26)α¯=1Ntot∑l=1Ntotαl,αl=Eloc(vpose(l))Erot(vpose(l)),where is the solution obtained by minimizing Epose for the l-th pair of data. Figure 2 shows which method most frequently delivered the smallest deviation from ground truth dk as defined in (24). Figure 3 displays how often a given method delivered the best results.

Bottom Line: The mismatch can be formally corrected by dividing the positional component by some scale factor with units of length.However, the scale factor is set arbitrarily and, depending on its value, more or less importance is associated with the positional component relative to the rotational component.This may result in a poorer registration.

View Article: PubMed Central - PubMed

Affiliation: National Institute of Standards and Technology, Gaithersburg, MD 20899.

ABSTRACT
When two six degrees of freedom (6DOF) datasets are registered, a transformation is sought that minimizes the misalignment between the two datasets. Commonly, the measure of misalignment is the sum of the positional and rotational components. This measure has a dimensional mismatch between the positional component (unbounded and having length units) and the rotational component (bounded and dimensionless). The mismatch can be formally corrected by dividing the positional component by some scale factor with units of length. However, the scale factor is set arbitrarily and, depending on its value, more or less importance is associated with the positional component relative to the rotational component. This may result in a poorer registration. In this paper, a new method is introduced that uses the same form of bounded, dimensionless measure of misalignment for both components. Numerical simulations with a wide range of variances of positional and rotational noise show that the transformation obtained by this method is very close to ground truth. Additionally, knowledge of the contribution of noise to the misalignment from individual components enables the formulation of a rational method to handle noise in 6DOF data.

No MeSH data available.

Related in: MedlinePlus