## Noise Reduction With Multiscale Edge Representation And Perceptual Criteria (1992)

Venue: | in Proceedings of IEEE-SP International Symposium on Time-Frequency and TimeScale Analysis |

Citations: | 8 - 1 self |

### BibTeX

@INPROCEEDINGS{Lu92noisereduction,

author = {Jian Lu and John B. Weaver and Dennis M. Healy and Yansun Xu},

title = {Noise Reduction With Multiscale Edge Representation And Perceptual Criteria},

booktitle = {in Proceedings of IEEE-SP International Symposium on Time-Frequency and TimeScale Analysis},

year = {1992},

pages = {555--558}

}

### OpenURL

### Abstract

The wavelet multiscale edge representation of signals developed by Mallat and Zhong provides a new tool for signal and image processing. We built up a tree structure of wavelet-transform(WT) maxima and developed metrics for analyzing the WT maxima tree. These metrics fall into two classes corresponding to two perceptual criteria, scaling and spatial stabilities, for discriminating features from background noise. Identified noisy branches are trimmed off the WT maxima tree. This technique of noise reduction preserves edges well while suppressing noise. We present experimental results of processing simulated and medical images with this technique. 1. INTRODUCTION It has been well-known that the human visual system (HVS) performs "multichannel decompositions"[1] on input visual signals. This is done with retinal receptive fields of different sizes. There is physiological evidence that these receptive fields act like edge detectors of different sizes and with different spatial tunings. The...

### Citations

554 |
Characterization of signals from multiscale edges
- Mallat, Zhong
- 1992
(Show Context)
Citation Context ...cale edge representation of visual information might be complete. Recently, with the development of wavelet multiscale representations, there have been a number of investigations on this subject[4][5]=-=[6]-=-[7]. Results from these investigations show that a multiscale edge representation is precise and stable in terms of the quality of reconstruction[6], though it is not complete in general[7]. Such a re... |

437 | Singularity detection and processing with wavelets
- Mallat, HwangW
(Show Context)
Citation Context ...ough it is not complete in general[7]. Such a representation is suitable for practical signal and image processing. Its applications have already been shown in compact coding[8] and noise reduction[9]=-=[10]-=-. The multiscale edge representation resembles the functions of the HVS. Therefore, we were encouraged to study certain processing techniques that are believed to be functioning in the HVS. In this pa... |

268 |
Multifrequency Channel Decompositions of Images and Wavelet Models
- Mallat
- 1989
(Show Context)
Citation Context ...multiscale edge representation of visual information might be complete. Recently, with the development of wavelet multiscale representations, there have been a number of investigations on this subject=-=[4]-=-[5][6][7]. Results from these investigations show that a multiscale edge representation is precise and stable in terms of the quality of reconstruction[6], though it is not complete in general[7]. Suc... |

155 |
Scale space filtering
- Witkin
- 1983
(Show Context)
Citation Context ...presents a WT maximum point at a scale. A branch on the tree connects certain nodes according to the split/merge relations between WT maxima. The tree can be constructed by the coarse-to-fine tracking=-=[12]-=- of the WT maxima. If a continuous WT is used, the evolution of WT maxima can be traced precisely by slowly varying the scale parameter[13]. Uncertainties exist in the tree construction from the discr... |

115 |
Edge focusing
- Bergholm
- 1987
(Show Context)
Citation Context ...a. The tree can be constructed by the coarse-to-fine tracking[12] of the WT maxima. If a continuous WT is used, the evolution of WT maxima can be traced precisely by slowly varying the scale parameter=-=[13]-=-. Uncertainties exist in the tree construction from the discrete WT maxima. Starting at the coarsest scale, we track the WT maxima from one scale to another inside a window determined by the size of t... |

112 |
Zero-crossings of a wavelet transform
- Mallat
- 1991
(Show Context)
Citation Context ...tiscale edge representation of visual information might be complete. Recently, with the development of wavelet multiscale representations, there have been a number of investigations on this subject[4]=-=[5]-=-[6][7]. Results from these investigations show that a multiscale edge representation is precise and stable in terms of the quality of reconstruction[6], though it is not complete in general[7]. Such a... |

42 |
Principles of perceptual organization
- Wertheimer
- 1958
(Show Context)
Citation Context ...osure of the maxima contour. These three metrics represent another perceptual criterion called spatial stability. In contouring WT maxima, we have used two important principles of perceptual groupings=-=[17]-=- known as proximity and (amplitude) similarity. A large group often indicates spatially stable features that catch our eyes. Indeed, noisy maxima contours are often short, of small average amplitude a... |

16 |
Bandpass channels, zero-crossings, and early visual information processing
- Marr, Ullman, et al.
- 1979
(Show Context)
Citation Context ... receptive fields of different sizes. There is physiological evidence that these receptive fields act like edge detectors of different sizes and with different spatial tunings. These findings led Marr=-=[2]-=-[3] to conjecture that a multiscale edge representation of visual information might be complete. Recently, with the development of wavelet multiscale representations, there have been a number of inves... |

12 |
T.: Parsing scale-space and spatial stability analysis
- Bischof, Caelli
- 1988
(Show Context)
Citation Context ...Later, Bischof and Caelli justified the use of such a measure by showing that the measure is a function of cross-scale correlation and will have a weak and randomly distributed response to white noise=-=[15]-=-. Our first metric is similar to Witkin's in the Gaussian scale-space. The second is important in discriminating isolated noise in smooth regions that may survive over a fairly large range of scales b... |

8 |
Edge representation from wavelet transform maxima
- Zhong
- 1991
(Show Context)
Citation Context ...g[6] is a set containing the local maxima of the wavelet transform modulus. Mallat and Zhong constructed a family of spline wavelets; the low order ones, quadratic and cubic, are most commonly used[6]=-=[11]-=-. These wavelets are similar to the derivative of a Gaussian and the associated wavelet transform acts like an edge detector at multiple scales. Therefore, a collection of module local maxima of the W... |

7 |
Some Useful Properties of Pyramids
- Rosenfeld
- 1984
(Show Context)
Citation Context ...ur going through these two positions at the immediate coarser scale. This algorithm reflects the idea of using features at the coarse scale as context for fine scales, which was suggested by Rosenfeld=-=[14]-=- nearly a decade ago. Once WT maxima are contoured at each scale, the generalized WT maxima tree is constructed by assigning each maxima contour to a node in a tree and following a procedure similar t... |

3 |
Eklundh, "On the computation of a scale-space primal sketch
- Lindeberg, O
- 1991
(Show Context)
Citation Context ...an scale-space. The second is important in discriminating isolated noise in smooth regions that may survive over a fairly large range of scales but are of relatively small maxima amplitudes in average=-=[16]-=-. The third delineates different types of edges. Mallat and Hwang have shown that upon appropriate scaling of WT maxima amplitudes, the third measure is an estimate of the Lipschitz regularity of sing... |

2 |
Un contre-example a la conjecture de Marr et a celle de
- Meyer
- 1991
(Show Context)
Citation Context ...e edge representation of visual information might be complete. Recently, with the development of wavelet multiscale representations, there have been a number of investigations on this subject[4][5][6]=-=[7]-=-. Results from these investigations show that a multiscale edge representation is precise and stable in terms of the quality of reconstruction[6], though it is not complete in general[7]. Such a repre... |

2 |
Noise reduction by constrained reconstructions in the wavelet-transform domain
- Lu, Xu, et al.
- 1992
(Show Context)
Citation Context ... though it is not complete in general[7]. Such a representation is suitable for practical signal and image processing. Its applications have already been shown in compact coding[8] and noise reduction=-=[9]-=-[10]. The multiscale edge representation resembles the functions of the HVS. Therefore, we were encouraged to study certain processing techniques that are believed to be functioning in the HVS. In thi... |

1 |
Compact image coding from edges
- Mallat, Zhong
- 1991
(Show Context)
Citation Context ...y of reconstruction[6], though it is not complete in general[7]. Such a representation is suitable for practical signal and image processing. Its applications have already been shown in compact coding=-=[8]-=- and noise reduction[9][10]. The multiscale edge representation resembles the functions of the HVS. Therefore, we were encouraged to study certain processing techniques that are believed to be functio... |