A new low-pass edge-aware filter that is invariant to scale and translation/
Colunche, Juan Carlos Rojas
A new low-pass edge-aware filter that is invariant to scale and translation/ Um novo filtro passa-baixa sensível a arestas, invariante por escala e por translação Juan Carlos Rojas Colunche. - Rio de Janeiro: IMPA, 2020. - video online
Defesa de Tese Banca: Diego Nehab - Orientador - IMPA Luiz Henrique de Figueiredo - IMPA Benar Fux Svaiter - IMPA Ralph Teixeira - UFF Eduardo Gastal - UFRGS Leonardo Koller Sacht - Suplente - UFSC.
Resumo: Removing high frequencies using low-pass linear and translation-invariant (LTI) filters is the most prevalent method to avoid aliasing. However, LTI filters couple sharpness to an oscillatory nature, which forces the choice between ringing or excessive smoothing. In this work, we discuss nonlinear filters which remove detail but preserve edges. Nonlinear filters can be sharp without introducing oscillations. However, they are more difficult to use and are not well understood. To solve this problem, we propose nonlinear filters that preserve the properties of LTI filters as much as possible. In particular, we start from the analysis of the recent Rolling Guidance Filter (RGF), including its behavior under translation and domain and range scaling, and obtain the conditions under which they converge uniformly. We also make an empirical analysis based on test images, identifying different problems. Among them, issues on the approximation of smooth regions, oversharpening, inconsistent edge preservation with the number of iterations or local contrast variations, and the need for an input-dependent parameter calibration. We then propose a new nonlinear filter, the Adaptive Regularized Rolling Guidance Filter (ARRGF), that does not suffer from these issues. In particular, it is range-scaling invariant and preserves smooth regions without excessive edge oversharpening. This way, it preserves edges throughout the image, independently of local contrast levels. We also make an empirical analysis based on test images, finding a single set of parameters that work well for a wide range of input images. Finally, we identify some of its limitations and propose topics for future work .
Matematica.
A new low-pass edge-aware filter that is invariant to scale and translation/ Um novo filtro passa-baixa sensível a arestas, invariante por escala e por translação Juan Carlos Rojas Colunche. - Rio de Janeiro: IMPA, 2020. - video online
Defesa de Tese Banca: Diego Nehab - Orientador - IMPA Luiz Henrique de Figueiredo - IMPA Benar Fux Svaiter - IMPA Ralph Teixeira - UFF Eduardo Gastal - UFRGS Leonardo Koller Sacht - Suplente - UFSC.
Resumo: Removing high frequencies using low-pass linear and translation-invariant (LTI) filters is the most prevalent method to avoid aliasing. However, LTI filters couple sharpness to an oscillatory nature, which forces the choice between ringing or excessive smoothing. In this work, we discuss nonlinear filters which remove detail but preserve edges. Nonlinear filters can be sharp without introducing oscillations. However, they are more difficult to use and are not well understood. To solve this problem, we propose nonlinear filters that preserve the properties of LTI filters as much as possible. In particular, we start from the analysis of the recent Rolling Guidance Filter (RGF), including its behavior under translation and domain and range scaling, and obtain the conditions under which they converge uniformly. We also make an empirical analysis based on test images, identifying different problems. Among them, issues on the approximation of smooth regions, oversharpening, inconsistent edge preservation with the number of iterations or local contrast variations, and the need for an input-dependent parameter calibration. We then propose a new nonlinear filter, the Adaptive Regularized Rolling Guidance Filter (ARRGF), that does not suffer from these issues. In particular, it is range-scaling invariant and preserves smooth regions without excessive edge oversharpening. This way, it preserves edges throughout the image, independently of local contrast levels. We also make an empirical analysis based on test images, finding a single set of parameters that work well for a wide range of input images. Finally, we identify some of its limitations and propose topics for future work .
Matematica.