By Wolfgang Förstner, Bernhard P. Wrobel
This textbook bargains a statistical view at the geometry of a number of view research, required for digicam calibration and orientation and for geometric scene reconstruction in response to geometric snapshot gains. The authors have backgrounds in geodesy and in addition lengthy event with improvement and examine in computing device imaginative and prescient, and this can be the 1st ebook to give a joint procedure from the converging fields of photogrammetry and laptop imaginative and prescient.
Part I of the publication offers an creation to estimation thought, protecting elements corresponding to Bayesian estimation, variance elements, and sequential estimation, with a spotlight at the statistically sound diagnostics of estimation effects crucial in imaginative and prescient metrology. half II offers instruments for 2nd and 3D geometric reasoning utilizing projective geometry. This comprises orientated projective geometry and instruments for statistically optimum estimation and try out of geometric entities and differences and their relations, instruments which are valuable additionally within the context of doubtful reasoning in aspect clouds. half III is devoted to modelling the geometry of unmarried and a number of cameras, addressing calibration and orientation, together with statistical review and reconstruction of corresponding scene gains and surfaces in accordance with geometric photograph good points. The authors offer algorithms for numerous geometric computation difficulties in imaginative and prescient metrology, including mathematical justifications and statistical research, hence permitting thorough reviews. The chapters are self-contained with a number of figures and exercises, and they're supported by means of an appendix that explains the elemental mathematical notation and a detailed index.
The booklet can function the root for undergraduate and graduate classes in photogrammetry, computer imaginative and prescient, and special effects. it's also applicable for researchers, engineers, and software program builders within the photogrammetry and GIS industries, quite these engaged with statistically dependent geometric machine imaginative and prescient methods.
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Additional info for Photogrammetric Computer Vision: Statistics, Geometry, Orientation and Reconstruction
155) and the relative bias of the mean of the product, σx σy . bµ rµz = z = ρxy . 156) The relative bias of the mean is the product of the relative accuracies σx /µx and σy /µy multiplied with the correlation coefficient. The bias is zero if the random variables are uncorrelated, which is often the case when constructing a geometric entity from two others. 154), p. 45 uses E((x − µx )2 (y − µy )2 ) = (1 + 2ρxy )σx2 σy2 . 34 σz = µ2y σx2 + µ2x σy2 + 2µx µy σxy σz = σz + (1 + ρ2xy )σx2 σy2 .
Stochastic Processes . . . . . . . . . . . . . . . . . . . . . . . . Generating Random Numbers . . . . . . . . . . . . . . . . . . . Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 22 24 28 36 40 40 48 55 56 This chapter collects the basic terms from probability theory and statistics. It motivates the axiomatic approach for the concept of probability, introduces the concept of a random variable, describes the key properties of the main distributions of random variables occurring when modelling observational uncertainties and testing hypotheses, and provides an introduction to stochastic processes.
Continuous and Discrete Random Variables . . . . . . . . . . Vectors and Matrices of Random Variables . . . . . . . . . . . Statistical Independence . . . . . . . . . . . . . . . . . . . , a colour, it is useful to map the experimental outcome to a real value and describe the probabilistic properties of the experiment using a real-valued random variable. Since such a mapping in a natural way can be defined for experiments with discrete or continuous outcome, random variables in a unifying manner play a central role in stochastic modelling.
Photogrammetric Computer Vision: Statistics, Geometry, Orientation and Reconstruction by Wolfgang Förstner, Bernhard P. Wrobel