This dataset contains images of five 3D models that can be used to evaluate pipelines for 3D reconstruction from images. Each model is placed in a reference scene and is rendered under different lighting and camera conditions. For each of the five models, 8 scenes are created and for each scene 100 images are taken from different points of view.
We present a MATLAB function to compute the subdivision matrices of semi-regular univariate interpolatory RBF-based binary subdivision schemes. The construction is the adaptation of the one presented in "Stationary binary subdivision schemes using radial basis function interpolation", B.-G. Lee, Y. J. Lee, J. Yoon (Adv. Comput. Math, 2006) and "Analysis of stationary subdivision schemes for curve design based on radial basis function interpolation", Y. J. Lee, J. Yoon (Appl. Math. Comput., 2010), to the semi-regular case, i.e. when the starting mesh is formed by two different uniform mesh that meet eachother at 0.
The main function, RBFs_semi.m, given the stepsizes of the two uniform mesh, the family of radial basis function, the number of points used for the local computation, the required polynomial reproduction and, eventually, further parameters, determines the subdivision matrix of the scheme in the form of the regular mask on the left, the regular mask on the right and the irregular part of the matrix around 0. The supported families of RBFs are (inverse) multi-quadric, Gaussian, Wendland's functions, Wu's functions, Buhmann's functions, polyharmonic functions and Euclid's hat functions (see e.g. "Meshfree approximation methods with MATLAB", G. E. Fasshauer). For further information about how to choose the parameters for each family see the files in the Aux folder.
We present filters for the irregular framelets of semi-regular Dubuc-Deslauriers 2n-point wavelet tight frames with mesh parameters h_\ell = 1 and h_r > 0 for the cases:
n = 2, h_r = 1.5, 2, 2.5, 3
n = 3, h_r = 1.5, 2, 2.25, 2.5
n = 4, h_r = 1.5, 2, 2.15, 2.3
n = 5, h_r = 1.5, 2, 2.1, 2.2
These filters have been computed using the method described in "Semi-regular Dubuc-Deslaurier wavelet tight frames" submitted to Journal of Computational and Applied Mathematics Special Issue for SMART 2017.
The filters are the columns of the matrix Q_irr where R_irr = Q_irr * transpose(Q_irr). To avoid numerical fluctuations Q_irr is computed via singular value decomposition, with threshold on the singular values set to 10^-8.
The filters depend only on the ratio h_\ell over h_r and, when this ratio is inverted, it is sufficient to flip the filters. Therefore there is no loss of generality in considering h_\ell = 1 and h_r greater than or equal to 1 only.
Moreover, for any fixed natural number n and h_\ell = 1, there is an interval of availability for h_r of the form ( 1/c, c ), where h_r = 1 reduces to the regular case. For n = 2, the exact value of c is 3.5 while for the other values of n the approximated values of c are 2.6225, 2.3591 and 2.2346 respectively for n = 3, 4 and 5. For the examples presented we choose two common values of h_r working for all n=2,...,5 and two values specifically chosen for each n spreaded out between 2 and c.
Contributors:Sara Silva, Leonardo Vanneschi, Maria J. Vasconcelos, Ana I.R. Cabral, Pedro C. Silva
Every year, large areas of savannas and woodlands burn due to natural conditions and land management
practices. Given the relevant level of greenhouse gas emissions produced by biomass burning in tropical regions, it is becoming even more important to clearly define historic fire regimes so that prospective emission reduction management strategies can be well informed, and their results Measured, Reported, and Verified (MRV). Thus, developing tools for accurately, and periodically mapping burned areas, based on cost advantageous, expedite, and repeatable rigorous approaches, is important. The main objective of this study is to investigate the potential of novel Genetic Programming (GP) methodologies for classifying burned areas in satellite imagery over savannas and tropical woodlands and to assess if they can improve over the popular and currently applied methods of Maximum Likelihood classification and Classification and Regression Tree analysis. The tests are performed using three Landsat images from Brazil (South America), Guinea-Bissau (West Africa) and the Democratic Republic of Congo (Central Africa). Burned areas were digitized on-screen to produce mapped information serving as surrogate ground-truth. Validation results show that all methods provide an overestimation of burned area, but GP achieves higher accuracy values in two of the three cases. GP is the most versatile machine learning method available today, but still largely underused in remote sensing. This study shows that standard GP can produce better results than two classical methods, and illustrates its versatility and potential in becoming a mainstream method for more difficult tasks involving the large amounts of newly available data.