Partitioned Iterated Function Systems Research Articles

CNN-based classification of phonocardiograms using fractal techniques

Deep Learning based heart sound classification is of significant interest in reducing the burden of manual auscultation through the automated detection of signals, including abnormal heartbeats. This work presents a method for classifying phonocardiogram (PCG) signals as normal or abnormal by applying a deep Convolutional Neural Network (CNN) after transforming the signals into 2D color images. In particular, a new methodology based on fractal theory, which exploits Partitioned Iterated Function Systems (PIFS) to generate 2D color images from 1D signals is presented. PIFS have been extensively investigated in the context of image coding and indexing on account of their ability to interpolate and identify self-similar features in an image. Our classification approach has shown a high potential in terms of noise robustness and does not require any pre-processing steps or an initial segmentation of the signal, as instead happens in most of the approaches proposed in the literature. In this preliminary work, we have carried out several experiments on the database released for the 2016 Physionet Challenge, both in terms of different classification networks and different inputs to the networks, thus also evaluating the data quality. Among all experiments, we have obtained the best result of 0.85 in terms of modified Accuracy (MAcc).

FASHE: A FrActal Based Strategy for Head Pose Estimation.

Head pose estimation (HPE) represents a topic central to many relevant research fields and characterized by a wide application range. In particular, HPE performed using a singular RGB frame is particular suitable to be applied at best-frame-selection problems. This explains a growing interest witnessed by a large number of contributions, most of which exploit deep learning architectures and require extensive training sessions to achieve accuracy and robustness in estimating head rotations on three axes. However, methods alternative to machine learning approaches could be capable of similar if not better performance. To this regard, we present FASHE, an approach based on partitioned iterated function systems (PIFS) to represent auto-similarities within face image through a contractive affine function transforming the domain blocks extracted only once by a single frontal reference image, in a good approximation of the range blocks which the target image has been partitioned into. Pose estimation is achieved by finding the closest match between fractal code of target image and a reference array by means of Hamming distance. The results of experiments conducted exceed the state of the art on both Biwi and Ponting'04 datasets as well as approaching those of the best performing methods on the challenging AFLW2000 database. In addition, the applications to GOTCHA Video Dataset demonstrate that FASHE successfully operates in-the-wild.

Optimizing Infrared Camera Resolution for Small Object Detection using Subpixel Rendering and PIFS in Multiresolution Image Analysis.

Background: Breast cancer screening techniques have been developing rapidly in the field of imaging systems. One of these techniques is thermography, which is an alternative modality for mammography to detect breast lesions. Thermography utilization has been progressively developing as various models and methods of object processing improvement. Currently, the Fluke TIS20 infrared camera, with a resolution of 320 × 240, has not been used to measure precisely small objects such as early breast cancer lesions. Retrieval and processing of single images lead into imprecise object measurements and false positive results.Objective: Problems have been arisen due to the limitations of the camera resolution, object retrieval techniques and suboptimal image processing. The aim of this study was to detect accurately breast cancer lesions in rats, which were induced by carcinogenic compounds.Material and Methods: In this experimental study, development of models was conducted based on increasing image by optimizing the ability of low-resolution infrared (IR) cameras to identify s mall objects precisely. Image pixel density increased by adjusting the distance of the objects from the camera and multiple images of objects gradually shifting were used to measure object dimensions precisely.Results: The results showed that cancerous lesions as small as 1.27 mm could be detected. This method of lesion detection had a sensitivity and specificity of 93% and 77 % respectively.Conclusion: Small objects (cancerous lesions) were measured by increasing image resolution through splitting pixels into subpixels and combining several images using Partitioned Iterated Function Systems (PIFS).

Image contrast enhancement through regional application of partitioned iterated function systems

A new technique is presented for enhancing the contrast in digital images, combining the theory of partitioned iterated function system (PIFS) and image segmentation. The image is first segmented through the region growing segmentation technique, and the PIFS enhancement algorithm is applied separately to each image segment. The defined PIFS of each section is modeled by a contractive transformation, which consists of an affine spatial transform, as well as the linear transform of the graylevels of image segment pixels. The transformation of the graylevels is determined by two parameters that adjust the brightness and contrast of the transformed image segment. After the PIFS algorithm is applied to each extracted image segment, a lowpass version of the original image is created. The contrast-enhanced image is obtained by suitably combining the original image with its lowpass version. The proposed regional PIFS approach was applied to numerous test images, ranging from medical data of various modalities to standard images. The obtained quantitative and qualitative results showed superior performance on behalf of the proposed method when compared with three other widely used contrast enhancement methods, namely, contrast stretching, unsharp masking, and contrast-limited adaptive histogram equalization.

Randomized Algorithm for Scaling Factors in Fractal Image Compression

fractal compression methods are based on iterative function systems (IFS), which was developed by Barnsley (1) and Jacquin (2). During compression, the algorithm partitions the image into a set of square blocks (domain blocks). After this a new partition is made into smaller range blocks (2). The domain blocks are generally double the size of range blocks. For every range block the nearest domain block is identified among all domain blocks after applying a set of transformations on the domain blocks. Smaller sized images are obtained by storing the information about these transformations alone. The transforms store the domain number, scaling constant, offset etc. This method of compression is called the partitioned iteration function system (PIFS). This paper explores the use of variable scaling factors for the transformation from domain to the range blocks. This variable factor has been generated using a pseudo-random number generator. The results show comparable ratios of compression and RMS error with PIFS (Partitioned iterated function systems) based fractal compression.

A Compression Algorithm for Vibration Signal of Rotating Machinery Based on Partitioned Iterated Function Systems

The partitioned iterated function systems (PIFS) were introduced into the compression of vibration signal. The actual vibration data of ZLH600-2 pump were adopted to verify the performance of PIFS. Also the compression ratios and the computation time were good, but the spectrum and amplitude, as important performances, were deformed after compression. If the concerned frequency of users was significantly lower than the sampling frequency and the required compression ratios was not more than 2, the compression using PIFS in vibration signal of rotating machinery was comfortable. Otherwise, the information loss in the compression could not be ignored. The decoded signals with the different compression parameters were listed in the paper and it was a meaningful exploration of the IFS on diagnosis and laid the foundation for further research.

FARO: FAce Recognition Against Occlusions and Expression Variations

Face recognition is widely considered as one of the most promising biometric techniques, allowing high recognition rates without being too intrusive. Many approaches have been presented to solve this special pattern recognition problem, also addressing the challenging cases of face changes, mainly occurring in expression, illumination, or pose. On the other hand, less work can be found in literature that deals with partial occlusions (i.e., sunglasses and scarves). This paper presents face recognition against occlusions and expression variations (FARO) as a new method based on partitioned iterated function systems (PIFSs), which is quite robust with respect to expression changes and partial occlusions. In general, algorithms based on PIFSs compute a map of self-similarities inside the whole input image, searching for correspondences among small square regions. However, traditional algorithms of this kind suffer from local distortions such as occlusions. To overcome such limitation, information extracted by PIFS is made local by working independently on each face component (eyes, nose, and mouth). Distortions introduced by likely occlusions or expression changes are further reduced by means of an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ad hoc</i> distance measure. In order to experimentally confirm the robustness of the proposed method to both lighting and expression variations, as well as to occlusions, FARO has been tested using AR-faces database, one of the main benchmarks for the scientific community in this context. A further validation of FARO performances is provided by the experimental results produced on Face Recognition Grand Challenge database.

Contrast enhancement of images using Partitioned Iterated Function Systems

A new algorithm for the contrast enhancement of images, based on the theory of Partitioned Iterated Function System (PIFS), is presented. A PIFS consists of contractive transformations, such that the original image is the fixed point of the union of these transformations. Each transformation involves the contractive affine spatial transform of a square block, as well as the linear transform of the gray levels of its pixels. The transformation of the gray levels is determined by two parameters which adjust the brightness and the contrast of the transformed block. The PIFS is used in order to create a lowpass version of the original image. The contrast-enhanced image is obtained by adding the difference of the original image with its lowpass version, to the original image itself. The proposed algorithm uses a predefined constant value for the contrast parameter, whereas, the parameters of the affine spatial transform, as well as the parameter adjusting the brightness, are calculated using k-dimensional trees. The lowpass version of the original image is obtained applying the PIFS on the original image repeatedly while using a value for the contrast parameter that is lower than the predefined one. Quantitative and qualitative results stress the superior performance of the proposed contrast enhancement algorithm against four other widely used contrast enhancement methods; namely, linear and nonlinear unsharp masking, Contrast Limited Adaptive Histogram Equalization and Local Range Modification.

Applications of Partitioned Iterated Function Systems in Image and Video Compression

Iterated function systems (IFS) have been used to compress image data. Because of difficulty in finding IFS in natural images, a technique based on partitioned IFS (PIFS) has been proposed for image compression. In this technique, an image to be compressed is divided into nonoverlapping blocks. For each block an affine transformation is found in the image. This set of affine transformations (called PIFS) corresponds to a unique image. In the simplest case, images are partitioned into fixed size blocks. In this paper, we investigate image and video compression techniques using variable block sizes based on the quadtree partition. One property of images generated using PIFS is scalability: they have fine detail in any scale. We exploit this property to reduce required compression time and improve compression performance. There are large amounts of temporal redundancy between fames of a video sequence. We describe a method to remove temporal redundancies effectively using a quadtree partitioning technique. We have implemented the above schemes to compress image and video sequences and will report our experimental results.