Bounds on the quality of the PCA bounding boxes

Dimitrov, Darko; Knauer, Christian; Kriegel, Klaus; Rote, Günter

doi:10.1016/j.comgeo.2008.02.007

Cited by 39 publications

(22 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The following lower and upper bounds on the quality of the PCA bounding boxes were shown in (Dimitrov et al, 2007a) and (Dimitrov et al, 2007b). Theorem 2.1…”

Section: Continuous Pcamentioning

confidence: 99%

“…In (Dimitrov et al, 2007b), it was shown that λ d,i = ∞ for any d ≥ 4 and any 1 ≤ i < d − 1. This way, there remain only two interesting cases for a given d: the factor λ d,d−1 corresponding to the boundary of the convex hull, and the factor λ d,d corresponding to the full convex hull.…”

Section: Continuous Pcamentioning

confidence: 99%

“…The popularity of this heuristic, besides its speed, lies in its easy implementation and in the fact that usually PCA bounding boxes are tight fitting. Recently, (Dimitrov et al, 2007b) presented examples of discrete points sets in the plane, showing that the worst case ratio of the volume of the PCA bounding box to the volume of the minimum-volume bounding box tends to infinity (see Figure 1 for an illustration in R 2 ). It has been shown in (Dimitrov et al, 2007a) that the continuous PCA version on convex point sets in R 3 guarantees a constant approximation factor for the volume of the resulting bounding box.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Experimental Study of Bounding Box Algorithms

Dimitrov

Holst

Knauer

et al. 2008

Proceedings of the Third International Conference on Computer Graphics Theory and Applications

View full text Add to dashboard Cite

The computation of the minimum-volume bounding box of a point set in R 3 is a hard problem. The best known exact algorithm requires O(n 3) time, so several approximation algorithms and heuristics are preferred in practice. Among them, the algorithm based on PCA (Principal Component Analysis) plays an important role. Recently, it has been shown that the discrete PCA algorithm may fail to approximate the minimum-volume bounding box even for a large constant factor. Moreover, this happens only for some very special examples with point clusters. As an alternative, it has been proven that the continuous version of PCA overcomes these problems. Here, we study the impact of the recent theoretical results on applications of several PCA variants in practice. We give the closed form solutions for the case when the point set is a polyhedron or a polyhedral surface. To the best of our knowledge, the continuous PCA over the volume of a 3D body is considered for the first time. We analyze the advantages and disadvantages of the different variants on realistic inputs, randomly generated inputs, and specially constructed (worst case) instances. The results reveal that for most of the realistic inputs the qualities of the discrete PCA and the continuous PCA bounding boxes are comparable. As it was expected the discrete PCA versions are much faster, but behave bad on the clustered inputs. In addition, we evaluate and compare the performances of several existing bounding box algorithms.

show abstract

“…The following lower and upper bounds on the quality of the PCA bounding boxes were shown in (Dimitrov et al, 2007a) and (Dimitrov et al, 2007b). Theorem 2.1…”

Section: Continuous Pcamentioning

confidence: 99%

Section: Continuous Pcamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Experimental Study of Bounding Box Algorithms

Dimitrov

Holst

Knauer

et al. 2008

Proceedings of the Third International Conference on Computer Graphics Theory and Applications

View full text Add to dashboard Cite

show abstract

“…Of the 700 DA models, approximately 50 -60% were not acceptable because they presented small, loosely connected or poorly defined DA "domains." The selection of the DA model was done by first computing a tight boundary around each DA model using principal components analysis (28) and then removing the DA models that presented an increase in one of the bounding-box lengths of more than 2 to 5% from the average value. For each accepted DA model, dummy atoms were clustered in two groups (each group representing a single hexamer), and the center of each cluster was calculated from the mean of the DA coordinates that belong to the cluster.…”

Section: Methodsmentioning

confidence: 99%

Structural Basis of the Lactate-dependent Allosteric Regulation of Oxygen Binding in Arthropod Hemocyanin

Hirota

Tanaka

Mičetić

et al. 2010

Journal of Biological Chemistry

View full text Add to dashboard Cite

Hemocyanin (Hc) is an oxygen carrier protein in which oxygen binding is regulated by allosteric effectors such as H؉ and L-lactate. Isothermal titration calorimetric measurements showed that L-lactate binds to dodecameric and heterohexameric Hc and to the CaeSS3 homohexamer but not to the CaeSS2 monomer. The binding of lactate caused no change in the optical absorption and x-ray absorption spectra of either oxy-or deoxy-Hc, suggesting that no structural rearrangement of the active site occurred. At pH 6.5, the oxygen binding rate constant k obs obtained by flash photolysis showed a significant increase upon addition of L-lactate, whereas L-lactate addition had little effect at pH 8.3. Lactate binding caused a concentration-dependent shift in the interhexameric distances at pH 6.5 based on small angle x-ray scattering measurements. These results show that L-lactate affects oxygen affinity at pH 6.5 by modulating the global structure of Hc without affecting its binuclear copper center (the active site). In contrast to this, the active site structure of deoxy-Hc is affected by changes in pH (Hirota, S., Kawahara, T., Beltramini, M., Di Muro, P., Magliozzo, R. S., Peisach, J., Powers, L. S., Tanaka, N., Nagao, S., and Bubacco, L. (2008) J. Biol. Chem. 283, 31941-31948). Upon addiction of lactate, the kinetic behavior of oxygen rebinding for Hc was heterogeneous under low oxygen concentrations at pH 6.5 due to changes in the T and R state populations, and the equilibrium was found to shift from the T toward the R state with addition of lactate.

show abstract

“…The principal components of discrete point sets can be strongly influenced by point clusters (Dimitrov, Knauer, Kriegel & Rote (2009)). To avoid the influence of the distribution of the point set, often continuous sets, especially the convex hull of a point set is considered, which lead to so-called continuous PCA.…”

mentioning

confidence: 99%

Bounds on the quality of the PCA bounding boxes

Cited by 39 publications

References 11 publications

Experimental Study of Bounding Box Algorithms

Experimental Study of Bounding Box Algorithms

Structural Basis of the Lactate-dependent Allosteric Regulation of Oxygen Binding in Arthropod Hemocyanin

Computing and Updating Principal Components of Discrete and Continuous Point Sets

Contact Info

Product

Resources

About