9 research outputs found
Efficient Spatially Adaptive Convolution and Correlation
Fast methods for convolution and correlation underlie a variety of
applications in computer vision and graphics, including efficient filtering,
analysis, and simulation. However, standard convolution and correlation are
inherently limited to fixed filters: spatial adaptation is impossible without
sacrificing efficient computation. In early work, Freeman and Adelson have
shown how steerable filters can address this limitation, providing a way for
rotating the filter as it is passed over the signal. In this work, we provide a
general, representation-theoretic, framework that allows for spatially varying
linear transformations to be applied to the filter. This framework allows for
efficient implementation of extended convolution and correlation for
transformation groups such as rotation (in 2D and 3D) and scale, and provides a
new interpretation for previous methods including steerable filters and the
generalized Hough transform. We present applications to pattern matching, image
feature description, vector field visualization, and adaptive image filtering
Adaptive Fourier-Based Surface Reconstruction
In this paper, we combine Kazhdan's FFT-based approach to surface reconstruction from oriented points with adaptive subdivision and partition of unity blending techniques. The advantages of our surface reconstruction method include a more robust surface restoration in regions where the surface bends close to itself and a lower memory consumption. The latter allows us to achieve a higher reconstruction accuracy than the original global approach. Furthermore, our reconstruction process is guided by a global error control achieved by computing the Hausdorff distance of selected input samples to intermediate reconstructions
Adaptive Fourier-Based Surface Reconstruction
In this paper, we combine Kazhdan's FFT-based approach to surface reconstruction from oriented points with adaptive subdivision and partition of unity blending techniques. The advantages of our surface reconstruction method include a more robust surface restoration in regions where the surface bends close to itself and a lower memory consumption. The latter allows us to achieve a higher reconstruction accuracy than the original global approach. Furthermore, our reconstruction process is guided by a global error control achieved by computing the Hausdorff distance of selected input samples to intermediate reconstructions
Error-Guided Adaptive Fourier-based Surface Reconstruction
In this paper, we propose to combine Kazhdan's FFT-based approach to surface reconstruction from oriented points with adaptive subdivision and partition of unity blending techniques. This removes the main drawback of the FFT-based approach which is a high memory consumption for geometrically complex datasets. This allows us to achieve a higher reconstruction accuracy compared with the original global approach. Furthermore, our reconstruction process is guided by a global error control accomplished by computing the Hausdorff distance of selected input samples to intermediate reconstructions. The advantages of our surface reconstruction method include also a more robust surface restoration in regions where the surface folds back to itself