Ferdinando Di Martino

An image coding/decoding method based on direct and inverse fuzzy transforms

With some modifications, we adopt the coding/decoding method of image processing based on the direct and inverse fuzzy transforms defined in previous papers. By normalizing the values of its pixels, any image can be considered as a fuzzy matrix (relation) which is subdivided in submatrices (possibly square) called blocks. Each block is compressed with the formula of the discrete fuzzy transform of a function in two variables and successively it is decompressed via the related inverse fuzzy transform. The decompressed blocks are recomposed for the reconstruction of the image, whose quality is evaluated by calculating the PSNR (Peak Signal to Noise Ratio) with respect to the original image. A comparison with the coding/decoding method of image processing based on the fuzzy relation equations with the Lukasiewicz triangular norm and the DCT method are also presented. By using the same compression rate in the three methods, the results show that the PSNR obtained with the usage of direct and inverse fuzzy transforms is higher than the PSNR determined either with fuzzy relation equations method or in the DCT one and it is close to the PSNR determined in JPEG method for small values of the compression rate.

Fuzzy transforms method in prediction data analysis

We present a prediction method based on Fuzzy transforms for forecasting problems and we compare it with the well known Wang-Mendels one. Another comparison is made on the Local Linear Wavelet Neural Network method via forecasting time series. We apply these concepts to a Mackey-Glass chaotic time series and to the monthly NAO climatic index time series.

Fragile watermarking tamper detection with images compressed by fuzzy transform

An original image is divided in smaller images called blocks, compressed with a fuzzy transform to images of sizes 2x2 for which we apply a fragile watermarking process as introduced by Chen and Wang (Expert Systems with Applications 36 (2009) 1300-1307). A pre-processing phase is considered to determine the best compression rate for the coding process. We test this scheme in tamper detection analysis on a sample of images by simulating various types of computer attack. The obtained results are good in terms of accuracy for tamper detection with compressed images and of dimensionality of the image dataset to store the original images.

A segmentation method for images compressed by fuzzy transforms

In this paper we describe a segmentation method applied to images which are compressed by using Fuzzy Transforms. The segmentation of the images is realized via the FGFCM (Fast Generalized Fuzzy C-Means) clustering algorithm, which is robust to noise and outliers. The optimal number of clusters is determined via the PCAES (Partition Coefficient And Exponential Separation) validity index. We use a similarity measure defined via Lukasiewicz t-norm for comparison between the original image and the reconstructed images. The best results are obtained if this similarity measure overcomes a threshold value, experimentally determined from the analysis of the trend of it with respect to the PSNR (Peak Signal to Noise Ratio).

Fuzzy transforms for compression and decompression of color videos

We use fuzzy transforms for coding/decoding color frames of videos and we compare the results with the same frames reconstructed with the standard JPEG method. We classify all the frames in intra-frames and predictive frames by adopting a similarity measure based on the Lukasiewicz t-norm and a pre-processing phase which determines the best similarity threshold value. The compression is made on particular frames, called @D-frames, obtained from a suitable difference defined on the values of the pixels of an intra-frame and a predictive frame. Under high compression rates, we see that the Peak Signal to Noise Ratio of the frames obtained with the fuzzy transforms is averagely close to the PSNR obtained with the JPEG method. We use the videos at URL sampl.eng.ohiostate.edu/~sampl/database.htm.

The extended fuzzy C-means algorithm for hotspots in spatio-temporal GIS

In spatial analysis buffer impact areas are called hotspots and are determined by means of density clustering methods. In a previous work, we found these hotspots in the context of a Geographic Information System (GIS) by using the extended fuzzy C-means (EFCM). Here we show how the spatial distribution of the hotspots can evolve temporally and like applicational example, we present the spatial-temporal evolution in the period 2000-2006 of the fire point-events data of the Santa Fe district (NM) (downloaded from URL: www.fs.fed.us/r3/gis/sfe_gis.shtml).

A method for coding/decoding images by using fuzzy relation equations

By using some well known fuzzy relation equations and the theory of the continuous triangular norms, we get lossy compression and decompression of images, here interpreted as two-argument fuzzy matrices.

A color image reduction based on fuzzy transforms

We present a new method for color image reduction based on the concept of fuzzy transform. Any image in a single band can be considered as a fuzzy matrix which is subdivided into submatrices called blocks. Each block is compressed with various_compression rates by means of a fuzzy transform in two variables. We compare our method with recent three algorithms due to G. Beliakov, H. Bustince and D. Paternain based on the minimizing penalty functions defined over a discrete lattice. The quality of the reduced image is measured by the Mean Square Error (MSE) and Penalty function (PEN) obtained by comparing both magnified and original images. We also point out a threshold of the compression rate beyond which the MSE follows a linear trend and the corresponding loss of information is still acceptable.

Image reduction method based on the F-transform

We present a new method of (color) image reduction based on the F-transform technique with a generalized fuzzy partition. This technique successfully combines approximation (when reduction is performed) and interpolation (when reconstruction is produced). The efficiency of the proposed method is theoretically justified by its linear complexity and by comparison with interpolation, and aggregation-based reductions. We also analyze the measures (