Publication

Non-Euclidean Pyramids

Michaël Unser, Thierry Blu
2000
Conference Papers

Abstract

We propose to design the reduction operator of an image pyramid so as to minimize the approximation error in the $l _{ p }$ sense (not restricted to the usual p = 2), where p can take non-integer values. The underlying image model is specified using arbitrary shift-invariant basis functions such as splines. The solution is determined by an iterative optimization algorithm, based on digital filtering. Its convergence is accelerated by the use of first and second derivatives. For p = 1, our modified pyramid is robust to outliers; edges are preserved better than in the standard case where p = 2. For 1 < p < 2, the pyramid decomposition combines the qualities of $l _{ 1 }$ and $l _{ 2 }$ approximations. The method is applied to edge detection and its improved performance over the standard formulation is determined.

Official source

https://infoscience.epfl.ch/entities/publication/844d72d3-1cd5-4099-af7d-f212ecc94d97

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Michaël Unser, Thierry Blu
2000
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/844d72d3-1cd5-4099-af7d-f212ecc94d97

About this result

Related concepts (32)

Digital filter

In signal processing, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is typically an electronic circuit operating on continuous-time analog signals. A digital filter system usually consists of an analog-to-digital converter (ADC) to sample the input signal, followed by a microprocessor and some peripheral components such as memory to store data and filter coefficients etc.

Edge detection

Edge detection includes a variety of mathematical methods that aim at identifying edges, curves in a at which the image brightness changes sharply or, more formally, has discontinuities. The same problem of finding discontinuities in one-dimensional signals is known as step detection and the problem of finding signal discontinuities over time is known as change detection. Edge detection is a fundamental tool in , machine vision and computer vision, particularly in the areas of feature detection and feature extraction.

Filter (signal processing)

In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of many other targets for filtering exist.