In this paper, we analyse two well-known objective image quality metrics, the peak-signal-to-noise ratio (PSNR) as well as the structural similarity index measure (SSIM), and we derive a simple mathematical relationship between them which works for various kinds of image degradations such as Gaussian blur, additive Gaussian white noise, jpeg and jpeg2000 compression. A series of tests realized on images extracted from the Kodak database gives a better understanding of the similarity and difference between the SSIM and the PSNR.

Image Quality Metrics: PSNR vs. SSIM

Vision in general and images in particular have always played an important and essential role in human life. Today, image processing is a very active research area with many applications. In order to cope with the wide variety of image processing problems, several techniques have been introduced and developed, quite often with great success. Among the different techniques that are currently in use, we also encounter fuzzy techniques. The use of fuzzy techniques in image processing is one of the main topics of the Fuzziness and Uncertainty Modelling Research Group of Prof. Kerre. In this paper, we briefly summarize some achievements of the past years.

https://www.springer.com/productFlyer_978-3-7908-1304-3.pdf?SGWID=0-0-1297-2086775-0

Fuzzy techniques in image processing

Removing or reducing impulse noise is a very active research area in image processing. In this paper we describe a new algorithm that is especially developed for reducing all kinds of impulse noise: fuzzy impulse noise detection and reduction method (FIDRM). It can also be applied to images having a mixture of impulse noise and other types of noise. The result is an image quasi without (or with very little) impulse noise so that other filters can be used afterwards. This nonlinear filtering technique contains two separated steps: an impulse noise detection step and a reduction step that preserves edge sharpness. Based on the concept of fuzzy gradient values, our detection method constructs a fuzzy set impulse noise. This fuzzy set is represented by a membership function that will be used by the filtering method, which is a fuzzy averaging of neighboring pixels. Experimental results show that FIDRM provides a significant improvement on other existing filters. FIDRM is not only very fast, but also very effective for reducing little as well as very high impulse noise.

A fuzzy impulse noise detection and reduction method

This paper proposes an image statistic for detecting random-valued impulse noise. By this statistic, we can identify most of the noisy pixels in the corrupted images. Combining it with an edge-preserving regularization, we obtain a powerful two-stage method for denoising random-valued impulse noise, even for noise levels as high as 60%. Simulation results show that our method is significantly better than a number of existing techniques in terms of image restoration and noise detection

/pdf/a-detection-statistic-for-random-valued-impulse-noise-4icj4d1ffh.pdf

A Detection Statistic for Random-Valued Impulse Noise

Interval-valued fuzzy sets constructed from matrices: Application to edge detection

A new fuzzy filter is presented for the noise reduction of images corrupted with additive noise. The filter consists of two stages. The first stage computes a fuzzy derivative for eight different directions. The second stage uses these fuzzy derivatives to perform fuzzy smoothing by weighting the contributions of neighboring pixel values. Both stages are based on fuzzy rules which make use of membership functions. The filter can be applied iteratively to effectively reduce heavy noise. In particular, the shape of the membership functions is adapted according to the remaining noise level after each iteration, making use of the distribution of the homogeneity in the image. A statistical model for the noise distribution can be incorporated to relate the homogeneity to the adaptation scheme of the membership functions. Experimental results are obtained to show the feasibility of the proposed approach. These results are also compared to other filters by numerical measures and visual inspection.

/pdf/noise-reduction-by-fuzzy-image-filtering-12cmmuf7qz.pdf

Noise reduction by fuzzy image filtering

A new framework for reducing impulse noise from digital color images is presented, in which a fuzzy detection phase is followed by an iterative fuzzy filtering technique. We call this filter the fuzzy two-step color filter. The fuzzy detection method is mainly based on the calculation of fuzzy gradient values and on fuzzy reasoning. This phase determines three separate membership functions that are passed to the filtering step. These membership functions will be used as a representation of the fuzzy set impulse noise (one function for each color component). Our proposed new fuzzy method is especially developed for reducing impulse noise from color images while preserving details and texture. Experiments show that the proposed filter can be used for efficient removal of impulse noise from color images without distorting the useful information in the image

Fuzzy Two-Step Filter for Impulse Noise Reduction From Color Images

1. Fuzzy Filters for Noise Removal.- 2. Fuzzy Filters for Noise Reduction in Images.- 3. Real-time Image Noise Cancellation Based on Fuzzy Similarity.- 4. Fuzzy Rule-Based Color Filtering Using Statistical Indices.- 5. Fuzzy Based Image Segmentation.- 6. Fuzzy Thresholding and Histogram Analysis.- 7. Color Image Segmentation by Analysis of 3D Histogram with Fuzzy Morphological Filters.- 8. Fast and Robust Fuzzy Edge Detection.- 9. Fuzzy Data Fusion for Multiple Cue Image and Video Segmentation.- 10. Fuzzy Image Enhancement in the Framework of Logarithmic Models.- 11. Observer-Dependent Image Enhancement.- 12. Fuzzy Techniques in Digital Image Processing and Shape Analysis.- 13. Adaptive Fuzzy Filters and Their Application to Online Maneuvering Target Tracking.- 14. Lossy Image Compression and Reconstruction Based on Fuzzy Relational Equation.- 15. Avoidance of Highlights through ILFOs in Automated Visual Inspection.- Appendix Color Images.

Fuzzy Filters for Image Processing

Noise reduction is a well-known problem in image processing The reduction of noise in an image sometimes is as a goal itself, and sometimes is considered as a pre-processing step Besides the classical filters for noise reduction, quite a lot of fuzzy inspired filters have been proposed during the past years However, it is very difficult to judge the quality of this wide variety of filters For which noise types are they designed? How do they perform for those noise types? How do they perform compared to each other? Can we select filters that clearly outperform the others? Is there a difference between numerical and visual results? In this paper, we answer these questions for images that are corrupted with Gaussian noise

D. Van der Weken

Papers

Noise reduction by fuzzy image filtering

A fuzzy impulse noise detection and reduction method

Fuzzy Two-Step Filter for Impulse Noise Reduction From Color Images

Fuzzy Filters for Image Processing

Fuzzy Filters for Noise Reduction: The Case of Gaussian Noise