English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this note, we show that the L2 optimal solutions to most real multipleview L2 triangulation problems can be efficiently obtained by two-stageNewton-like iterative methods, while the difficulty of such problems mainlylies in how to verify the L2 optimality. Such a working two-stage bundleadjustment approach features: first, the algorithm is initialized by symmedianpoint triangulation, a multiple-view generalization of the mid-point method;second, a symbolic-numeric method is employed to compute derivativesaccurately; third, globalizing strategy such as line search or trust region issmoothly applied to the underlying iteration which assures algorithm robustnessin general cases.  Numerical comparison with tfml method shows that the local minimizersobtained by the two-stage iterative bundle adjustment approach proposed hereare also the L2 optimal solutions to all the calibrated data sets availableonline by the Oxford visual geometry group. Extensive numerical experimentsindicate the bundle adjustment approach solves more than 99% the realtriangulation problems optimally. An IEEE 754 double precision C++implementation shows that it takes only about 0.205 second tocompute allthe4983 points in the Oxford dinosaur data setvia Gauss-Newton iteration hybridwith a line search strategy on a computer with a 3.4GHz Intel i7 CPU.

Newton-Type Iterative Solver for Multiple View $L2$ Triangulation