Partitioned Iterated Function System Research Articles

A characterization method for the physical features of honed texture surface of engine cylinder liner

A machine vision method is proposed to characterize the physical features of the honed surface texture on the cylinder liner of internal combustion engines. According to the gray image information of the surface texture of the cylinder liner, the curvelet transform method is employed to extract the physical features of the multi-scale anisotropic surface topography image of the cylinder liner, and the partitioned iterated function system (PIFS) is constructed to calculate fractal dimension to describe the physical features of the surface texture of the cylinder liner. The proposed PIFS-based method is applied to the honed surface and dimple-textured surface of the cylinder liner, the effectiveness and the accuracy are verified by comparing with the other two methods.

Digital Video Compression Using DCT-Based Iterated Function System (IFS)

Large video files processing involves a huge volume of data. The codec, storage systems and network needs resource utilization, so it becomes important to minimize the used memory space and time to distribute these videos over the Internet using compression techniques. Fractal image and video compression falls under the category of lossy compression. It gives best results when used for natural images.
 This paper presents an efficient method to compress an AVI (Audio Video Interleaved) file with fractal video compression(FVC). The video first is separated into a sequence of frames that are a color bitmap images, then images are transformed from RGB color space to Luminance/Chrominance components (YIQ) color space; each of these components is compressed alone with Enhanced Partition Iterated Function System (EPIFS), then fractal codes are saved.
 The classical IFS suffers from a very long encoding time that needed to find the best matching for each range block when compared with the domain image blocks. In this work, the (FVC) is enhanced by enhancing the IFS of the fractal image compression using a classification scheme based on the Discrete Cosine Transform (DCT). Experimentation is performed by considering different block sizes and jump steps to reduce number of the tested domain blocks. Results shows a significant reduction in the encoding time with good quality and high compression ratio for different video files.

Robust face recognition after plastic surgery using region-based approaches

This paper advances the use of region-based strategies for addressing the problem of face recognition after plastic surgery. The proposed methods implement the region-based approach in several ways. FARO (FAce Recognition against Occlusions and Expression Variations) divides the face into relevant regions (left eye, right eye, nose and mouth) and then codes them independently using Partitioned Iterated Function System (PIFS) processing. FACE (Face Analysis for Commercial Entities) applies a localized version of image correlation index. Finally, the Split Face Architecture (SFA), adaptive and integrative in nature, can leverage any known recognition method, from PCA to most recent ones (including FARO and FACE), provided that it is possible to divide the face into regions. Experimental results, compared with those available from recent experiments reported in literature, show that our methods yield much better performance than state-of-the art algorithms, both holistic and region based.

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.

Difference based Non-linear Fractal Image Compression

Good fractal compression methods rely on iterative function systems (IFS), which have been designed by Barnsley [1] and Jacquin [2]. The main principle is that an image can be built by combining parts which are similar to the other parts. When encoding an image, the image is partitioned into possibly overlapping square blocks called domain blocks. Subsequently a new partition is made into smaller range blocks [2]. For each range block the closest domain block is searched among all domain blocks by applying a set of transformations on the domain blocks. Compression is obtained by storing only the information about these transformations. The information stored includes domain number, scaling constant, offset etc. This method of compressing images is called Partitioned Iterated Function System (PIFS). This paper explores the use of difference between range and domain elements to find the scaling constants and offset. This paper also explores the implications of mapping IFS blocks on a non-linear basis between range and domain blocks. Further, difference based non-linear mapping is also looked upon. The results show comparable ratios of compression and RMS error with PIFS based fractal compression

Using Triangular Function To Improve Size Of Population In Quantum Evolution Algorithm For Fractal Image Compression

Fractal Image Compression is a well-known problem which is in the class of NP-Hard problems. Quantum Evolutionary Algorithm is a novel optimization algorithm which uses a probabilistic representation for solutions and is highly suitable for combinatorial problems like Knapsack problem. Genetic algorithms are widely used for fractal image compression problems, but QEA is not used for this kind of problems yet. This paper improves QEA whit change population size and used it in fractal image compression. Utilizing the self-similarity property of a natural image, the partitioned iterated function system (PIFS) will be found to encode an image through Quantum Evolutionary Algorithm (QEA) method Experimental results show that our method has a better performance than GA and conventional fractal image compression algorithms.

Effects of information loss in texture details due to the PIFS encoding on load and friction in hydrodynamic bearings

Textured surfaces can significantly improve the performance of hydrodynamic bearings. However, there is no generally accepted method for their accurate and automated 3D characterization. A promising solution to this problem is partition iterated function system (PIFS) model, which encapsulates information about 3D topography of textured surfaces. However, some loss in surface details can occur. Therefore, before PIFS could be used, effects of this information loss on load and friction need to be investigated. In this study, this issue was addressed using a textured hydrodynamic pad bearing. The results obtained showed that PIFS models might become useful in characterization of textured surfaces.

Web Enabled Based Face Recognition using Partitioned Iterated function system

Many conventional methods of face recognition depend solely on appearance and model based. However there is inbuilt degree of self-similarity in the image of faces, which can be efficiently utilized through representation exploiting self-transformations, known as Iterated Function System (IFS). Interestingly, virtually all images of natural or man-made objects, show region wise self similarity although they may not be globally self similar. Such objects can be represented by Partitioned Iterated Function System (PIFS) very compactly. Hence, we propose is to carry out the face recognition using Partitioned Iterated Function System. This approach has been tested upon the 106 images of 27 persons using FERET database. The results obtained under the variance, rotation and scaling are outperforming. In this approach we carried out face recognition based on PIFS representation and matching carried out in the PIFS code domain, which is more efficient than correlation in the image domain. The recognition method is efficient in terms of time complexity as the PIFS code of reference faces are built off-line and recognition of query object involves only comparison of its PIFS code with those in the database online.

Web Enabled Based Face Recognition using Partitioned Iterated Function System

Web Enabled Based Face Recognition using Partitioned Iterated Function System

Fractal image compression based on spatial correlation and hybrid genetic algorithm

In order to solve the high complexity of the conventional encoding scheme for fractal image compression, a spatial correlation hybrid genetic algorithm based on the characteristics of fractal and partitioned iterated function system (PIFS) is proposed in this paper. There are two stages for the algorithm: (1) Make use of spatial correlation in images for both range and domain pool to exploit local optima. (2) Adopt simulated annealing genetic algorithm (SAGA) to explore the global optima if the local optima are not satisfied. In order to avoid premature convergence, the algorithm adopt dyadic mutation operator to take place of the traditional one. Experiment results show that the algorithm convergent rapidly. At the premise of good quality of the reconstructed image, the algorithm saved the encoding time and obtained high compression ratio.

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.

Schema genetic algorithm for fractal image compression

In this paper, fractal image compression using schema genetic algorithm (SGA) is proposed. Utilizing the self-similarity property of a natural image, the partitioned iterated function system (PIFS) will be found to encode an image through genetic algorithm (GA) method. In SGA, the genetic operators are adapted according to the schema theorem in the evolutionary process performed on the range blocks. Such a method can speed up the encoder and also preserve the image quality. Simulations show that the encoding time of our method is over 100 times faster than that of the full search method, while the retrieved image quality is still acceptable. The proposed method is also compared to another GA method proposed by Vences and Rudomin. Simulations also show that our method is superior to their method in both the speedup ratio and retrieved quality. Finally, a comparison of the proposed SGA to the traditional GA is presented to demonstrate that when the schema theorem is embedded, the performance of GA has significant improvement.

Spatial correlation genetic algorithm for fractal image compression

Abstract Fractal image compression explores the self-similarity property of a natural image and utilizes the partitioned iterated function system (PIFS) to encode it. This technique is of great interest both in theory and application. However, it is time-consuming in the encoding process and such drawback renders it impractical for real time applications. The time is mainly spent on the search for the best-match block in a large domain pool. In this paper, a spatial correlation genetic algorithm (SC-GA) is proposed to speed up the encoder. There are two stages for the SC-GA method. The first stage makes use of spatial correlations in images for both the domain pool and the range pool to exploit local optima. The second stage is operated on the whole image to explore more adequate similarities if the local optima are not satisfied. With the aid of spatial correlation in images, the encoding time is 1.5 times faster than that of traditional genetic algorithm method, while the quality of the retrieved image is almost the same. Moreover, about half of the matched blocks come from the correlated space, so fewer bits are required to represent the fractal transform and therefore the compression ratio is also improved.

Similarity-based image retrieval system using partitioned iterated function system codes

We propose a new image retrieval system using partitioned iterated function system (PIFS) codes. In PIFS encoding, a compression code contains mapping information between similar regions in the same image. This mapping information can be treated as vectors, and representative vectors can be generated using them. Representative vectors describe the features of the image. Hence, the similarity between images is directly calculable from representative vectors. This similarity is applicable to image retrieval. In this article, we explain this scheme and demonstrate its efficiency experimentally.

Classification of tribological surfaces

The reliable and accurate 3-D characterization and classification of tribological surfaces is still a challenging problem. Many tribological surfaces exhibit topographical features over a wide range of scales; ranging from nano-scales (atomic or molecular scales) to micro-scales (up to hundred micrometer scales). There are several surface topography characterization methods that exist today. However, due to the non-stationary and multi-scale nature of tribological surfaces even for the moderately complicated topography of a tribological surface, these methods provide a limited description. Recently a new method, based on fractal modelling, has been developed and applied to the characterization of tribological surfaces. The method involves construction of a mathematical model, called a partition iterated function system (PIFS), for surface data. This model encapsulates complete information about the surface 3-D data. Iterative application of this model into any initial image results in a sequence of images converging to the original surface image. Based on this method a pattern recognition system has been developed and applied to the classification of tribological surfaces. Recently, the work has been conducted on the improvement of the PIFS method. An attempt was made to apply both fractals and wavelets to analyze surface topography data. It was thought that since the fractal method allows the characterization of surface topography over the widest achievable range of scales and the wavelet method provides the characterization of surface topography at individual scales a combination of these two methods could provide the most accurate results. The hybrid fractal-wavelet method has recently been developed and applied to the characterization of tribological surfaces. In this paper it is demonstrated that it is possible to both characterize and classify tribological surfaces without the need for any surface parameters, with unique precision and accuracy. Also a short overview of recent advances and developments in the characterization and classification of tribological surfaces is presented.

Hybrid Fractal-Wavelet Method for Characterization of Tribological Surfaces—A Preliminary Study

Many types of tribological surfaces have been observed to exhibit a multiscale nature, i.e. topographical features over different scales ranging from nanometers to hundreds of micrometers. Consequently, recent developments in the characterization of tribological surfaces have concentrated on wavelet transformation and fractal-based methods. The wavelet methods are used due to their ability to decompose surface data into different scale components and to characterize surface data at each individual scale. On the other hand, fractal methods are used due to their ability to characterize surface data in a scale-invariant manner. It has been shown that these two capabilities of (i) decomposition of surface data and (ii) scale-invariant analysis are essential in the characterization of 3-D surface topography. Thus, it is apparent that a characterization method which exhibits both of these capabilities would yield the best results. Developing such a method is not an easy task. This problem in the characterization of tribological surfaces is addressed in our paper. A new method, called a hybrid fractal-wavelet method, is proposed. This method is a combination of a partition iterated function system (PIFS) and a symmetric wavelet transform (SWT). The PIFS is used to scale-invariantly characterize the surface topography over a wide range of different scales, while the SWT is used to characterize the surface topography at each individual scale. This multiscale characterization ability of the newly developed method is demonstrated on a tribological surface example.

Characterization and classification of wear particles and surfaces

Wear particles and surfaces are three-dimensional (3-D) objects and their numerical characterization and classification is still largely an unresolved problem. Usually a set of various parameters is employed to describe the surface topography. These parameters are of limited use, especially when dealing with anisotropic surfaces. To solve this problem a modified Hurst orientation transform (HOT) method has been developed and applied to characterize the surface anisotropy. However, despite the apparent success this method does not yet provide a full description of the surface topography. It is known that complex structures observed in nature can be described and modeled by a combination of simple mathematical rules. It is therefore reasonable to assume that, in principle, it should also be possible to describe any surface by a set of such rules. The problem is in finding those rules. For this purpose, a modified partitioned iterated function system (PIFS) was developed and applied to encode the 3-D surface topography information, i.e. to obtain full description of surface topography of wear particles and surfaces. Importantly, PIFS information gained from individual wear particles or surfaces allows to classify them in groups which are characteristic to a particular failure type. This, in turn, allows to ascribe an ‘unclassified’ particle or surface to a particular group/category which is characteristic to a specific failure type or wear mechanism. This forms the basis of a system, which when fully developed, would allow an automated recognition of particles and surface morphologies without the need for experts. The system then can be developed further to include diagnosis of the type of failure. In this paper an overview of recent advances and developments in the characterization, classification and recognition of wear particles and surfaces is presented.

Scale-invariant analysis of wear particle surface morphology I: Theoretical background, computer implementation and technique testing

Reliable numerical characterization of wear particle surface morphology is an important and still unresolved engineering problem. Since the shape and surface topography of wear particles often exhibits a fractal nature, fractal methods are frequently employed in their characterization. However, the fractal methods used in the particle analysis ignore the fundamental property that fractal objects can be described by a small set of mathematical rules. Finding those rules that describe a particular fractal image is a difficult problem and no general solution exists to date. In this paper, a new method for the characterization of wear particle morphology is proposed and described. The method is based on a partitioned iterated function system (PIFS) which is a collection of contractive affine transformations. Each affine transformation converts one part of a wear particle image onto another part of the same image. PIFSs were constructed for both computer-generated and scanning electron microscope images of wear particles. Results obtained in this study clearly demonstrate that the morphology of wear particles can be effectively characterized by the PIFS method.

Scale-invariant analysis of wear particle surface morphology: III: Pattern recognition

A new scale-invariant pattern recognition method has been developed for the characterization of wear particle surface morphology. The method is based on a partition-iterated function system (PIFS) constructed for a wear particle image. A database containing PIFSs constructed for different classes of wear particles was built. Each class is a set of wear particles exhibiting a similar morphology. The objective of pattern recognition is to assign a new wear particle, which is not yet classified, into one of these particle classes. For the classification, PIFSs taken from the database are decoded with the unclassified particle image used as an initial image. Decoded images obtained from PIFSs are then individually compared with the new particle image. If the difference calculated between these images is less than a threshold value, the new particle is assigned to a class. Problems associated with the use of the pattern recognition method, such as rotational- and translation-invariance, comparison between two images and computer implementation, are addressed in this paper. The effects of image resolution, tilt angle, noise, gain variations and defocusing were also investigated. Results obtained for computer-generated images of fractal surfaces and microscopic images of wear particles are demonstrated.

Scale-invariant analysis of wear particle surface morphology: II. Fractal dimension

Fractal dimension is the most popular parameter used to scale-invariantly characterize the roughness of wear particle surfaces. However, methods used to calculate the fractal dimension can be ineffective when applied to data-limited, low-resolution wear particle images or when wear particle surfaces do not conform to a fractional Brownian motion model. In this paper, a new fractal method, which is called a fractal dimension by partition iterated function system (FD-PIFS), was developed and used to estimate the fractal dimension from wear particle surfaces. The newly developed method is based on a PIFS constructed for an image of a wear particle surface. The PIFS is a set of contractive affine transformations that describe scale-invariantly and uniquely the surface topography of a wear particle. The effectiveness of the FD-PIFS method was evaluated. The fractal dimension was first calculated for computer generated images of isotropic fractal surfaces and then calculated for scanning electron microscope images of wear particles found in artificial implants and synovial joints. The effects of measurement conditions such as noise, resolution, gain variations and focusing on fractal dimension calculated were also investigated.