Fractal Dimension Features Research Articles

SU‐FF‐I‐138: Computer‐Aided Image Texture Analysis as An Indicator of Image Quality: A Feasibility Study in FFDM

Purpose: Image quality is often quantified using signal‐to‐noise‐ratio (SNR). We hypothesize that clinical image texture features are also reflective of image quality. To test feasibility, we investigated the relationship between quantitative image texture features and SNR as a function of acquisition parameters for a full‐field digital mammography (FFDM) system. Method and Materials: An anthropomorphic breast phantom (Model 169, Gammex RMI, Madison, WI) was imaged with a Senographe 2000D (General Electric Medical Systems, Chalfont St. Giles, UK). Images were acquired with various target/filter, kV (25 – 32 kV) and mAs combinations. The mAs was varied from 10 to 300% of that required for a standard phototimed exposure yielding an average glandular dose (AGD) of 1.8 mGy. SNR was computed in a 2.5cm2 retroareolar region of interest (ROI) segmented from linear images after flat‐field and offset correction. Signal intensity was computed as the average pixel value in the ROI. Noise was computed as the RMS difference of two images acquired using the same acquisition parameters. Image texture features of skewness, coarseness, contrast, energy, homogeneity, and fractal dimension were computed in the corresponding ROI from the Premium View™ processed FFDM images. Results: Homogeneity decreases continuously as a function of mAs. Skewness, coarseness, and fractal dimension increase, while contrast and energy decrease, until all reach a threshold. The threshold occurs between 40–100% of the phototimed AGD, beyond which no further change is seen. Linear regressions with mAs were strong after logrithmic transformation, having R2 ⩾ 0.84, p < 0.001 for coarseness, energy, and homogeneity. Conclusions: Clinical texture features are indicative of image quality. While homogeneity correlates closely with SNR, other texture features reach a threshold, seeming to indicate optimal dose settings. Further work is underway to fully investigate the potential use of image texture as an indicator of clinically acceptable FFDM image quality.

Analysis and classification of commercial ham slice images using directional fractal dimension features

This paper presents a novel and non-destructive approach to the appearance characterization and classification of commercial pork, turkey and chicken ham slices. Ham slice images were modelled using directional fractal ( DF 0 ° ; 45 ° ; 90 ° ; 135 ° ) dimensions and a minimum distance classifier was adopted to perform the classification task. Also, the role of different colour spaces and the resolution level of the images on DF analysis were investigated. This approach was applied to 480 wafer thin ham slices from four types of hams (120 slices per type): i.e., pork (cooked and smoked), turkey (smoked) and chicken (roasted). DF features were extracted from digitalized intensity images in greyscale, and R, G, B, L ∗, a ∗, b ∗, H, S, and V colour components for three image resolution levels (100%, 50%, and 25%). Simulation results show that in spite of the complexity and high variability in colour and texture appearance, the modelling of ham slice images with DF dimensions allows the capture of differentiating textural features between the four commercial ham types. Independent DF features entail better discrimination than that using the average of four directions. However, DF dimensions reveal a high sensitivity to colour channel, orientation and image resolution for the fractal analysis. The classification accuracy using six DF dimension features ( a 90 ° ∗ , a 135 ° ∗ , H 0 ° , H 45 ° , S 0 ° , H 90 ° ) was 93.9% for training data and 82.2% for testing data.

Application of Image Texture Analysis for Online Determination of Curd Moisture and Whey Solids in a Laboratory‐Scale Stirred Cheese Vat

A noninvasive technology, which could be employed online to monitor syneresis, would facilitate the production of higher quality and more consistent cheese products. Computer vision techniques such as image texture analysis have been successfully established as rapid, consistent, and nondestructive tools for determining the quality of food products. In this study, the potential of image texture analysis to monitor syneresis of cheese curd in a stirred vat was studied. A fully randomized 2-factor (milk pH and stirring speed), 2-level factorial design was carried out in triplicate. During syneresis, images of the surface of the stirred curd-whey mixture were captured using a computer vision system. The images were subjected to 5 image texture analysis methods by which 109 image texture features were extracted. Significant correlations were observed between a number of image texture features and curd moisture and whey solids. Multiscale analysis techniques of fractal dimension and wavelet transform were demonstrated to be the most useful for predicting syneresis indices. Fractal dimension features predicted curd moisture and whey solids during syneresis with standard errors of prediction of 1.03% (w/w) and 0.58 g/kg, respectively. It was concluded that syneresis indices were most closely related to the image texture features of multiscale representation. The results of this study indicate that image texture analysis has potential for monitoring syneresis.

SU‐GG‐I‐50: Breast Tissue Classification in Digital Breast Tomosynthesis Images Using Texture Features

Purpose: Breast density is a known breast cancer risk factor. Digital breast tomosynthesis (DBT) is a tomographic x‐ray breast imaging modality with superior breast tissue visualization in comparison to mammography. The goal of our on‐going study is to evaluate the performance of DBT texture features in distinguishing between dense and fatty breast tissue regions. Our hypothesis is that DBT texture analysis could result in more discriminative features to characterize breast density in comparison to mammography, and ultimately yield more accurate measures of risk. Method and Materials: DBT images and digital mammograms (DM) from 39 women were analyzed. DBT and DM acquisition was performed with a GE Senographe 2000D FFDM system modified to allow positioning of the x‐ray tube at 9 locations by varying the angle from −25° to +25° in increments of 6.25°. Filtered‐backprojection was used to reconstruct DBT tomographic planes in 1 mm increments. The dense tissue area was delineated within each breast image using a widely validated thresholding technique (Cumulus Ver. 4.0, University of Toronto). Two regions of interest (ROIs) were manually selected in each breast image: one within the dense tissue region and another within the fatty region. Texture features of skewness, coarseness, contrast, fractal dimension, energy and homogeneity were computed from all available ROIs. Two‐tailed paired Student's t‐test was applied to compare the means of the texture feature distributions from the dense versus the fatty ROIs. Results: Coarseness, contrast, energy and homogeneity were statistically significantly different (p⩽0.001) between dense and fatty ROIs. Dense ROIs have lower coarseness, higher contrast, higher energy and lower homogeneity. Conclusion: X‐ray image texture differs between dense and fatty breast tissue regions. Further work is underway to fully compare the relative performance of texture features in classifying dense versus fatty tissue regions using DM, DBT source projections, and reconstructed DBT images.

An image recognition method by rough classification for a scene image

We have recognized the regions of scene images for image recognition. First, the proposed segmentation method classifies images into several segments without using the Euclidian distance. We need several features to recognize regions. However, they are different for chromatic and achromatic colors. The regions are divided into three categories (black, achromatic, and chromatic). In this article, we focus on the achromatic category. The averages of the intensity and the fractal dimension features of the regions in the achromatic category are calculated. We recognize the achromatic region by using a neural network with suitable features. In order to show the effectiveness of the proposed method, we have recognized the regions.

Liver fibrosis identification based on ultrasound images captured under varied imaging protocols

Diagnostic ultrasound is a useful and noninvasive method in clinical medicine. Although due to its qualitative, subjective and experience-based nature, ultrasound image interpretation can be influenced by image conditions such as scanning frequency and machine settings. In this paper, a novel method is proposed to extract the liver features using the joint features of fractal dimension and the entropies of texture edge co-occurrence matrix based on ultrasound images, which is not sensitive to changes in emission frequency and gain. Then, Fisher linear classifier and support vector machine are employed to test a group of 99 in-vivo liver fibrosis images from 18 patients, as well as other 273 liver images from 18 normal human volunteers.

Texture classification with combined rotation and scale invariant wavelet features

In this work, a new rotational and scale invariant feature set for textural image classification, combined invariant feature (CIF) set has been introduced. It is an integration of the crude wavelets like Gaussian, Mexican Hat and orthogonal wavelets like Daubechies to achieve a high quality rotational and scale invariant feature set. Also it is added with features obtained using the newly proposed weighted smoothening Gaussian filter masks to improve the classification results. To reduce the effect of overlapping features, the variations among the feature set are analyzed and the eigenfeatures are extracted to produce good classification result. The rotational invariance is achieved by using these two wavelets with their directional properties and the scale invariance is achieved by a method, which is an extension to fractal dimension (FD) features. The first- and second-order statistical parameter and entropy characterize the quality of the features extracted. Furthermore, a comparison that shows the higher recognition rate achieved with the newly proposed method for the set of 6720 samples collected from 105 different textures of Brodatz, Vistek, Indezine databases and some additional images collected from other resources of indexed and true color images is shown.

Rock unit discrimination on Landsat TM, SIR-C and Radarsat images using spectral and textural information

The paper presents results for spectral and textural analysis of the rock units in Landsat Thematic Mapper (TM) images, dual-band (L and C) and dual-polarization (HH and HV) Shuttle Imaging Radar (SIR)-C images, and C-band HH polarization Standard Beam 4 and Extended High Incidence Beam 3 Radarsat images from a study area between California and Arizona, USA. Fractal dimension, lacunarity and grey-level co-occurrence matrix (GLCM) textural feature images were created from the SIR-C and Radarsat images. Fractal dimensions were calculated using a differential box counting method and lacunarity measures were obtained using a new grey-scale lacunarity estimation method for 36 sample images extracted from the SIR-C and Radarsat images. The fractal dimension and lacunarity curves and class signature separability analysis show that, for rock unit discrimination using image textural features in the study area, the SIR-C L-HH image is more suitable than other SIR-C images and Radarsat images, and that co-polarization (HH) generally provides more textural information than cross-polarization (HV) in the study area. The study also shows that lacunarity measures can reveal the scaling properties of radar image textures for rock units. The combination of spectral information from Landsat TM images and textural information from radar images improves the image classification accuracy of rock units in the study area.

Wavelet-based rotational invariant roughness features for texture classification and segmentation

In this paper, we introduce a rotational invariant feature set for texture segmentation and classification, based on an extension of fractal dimension (FD) features. The FD extracts roughness information from images considering all available scales at once. In this work, a single scale is considered at a time so that textures with scale-dependent properties are satisfactorily characterized. Single-scale features are combined with multiple-scale features for a more complete textural representation. Wavelets are employed for the computation of single- and multiple-scale roughness features because of their ability to extract information at different resolutions. Features are extracted in multiple directions using directional wavelets, and the feature vector is finally transformed to a rotational invariant feature vector that retains the texture directional information. An iterative K-means scheme is used for segmentation, and a simplified form of a Bayesian classifier is used for classification. The use of the roughness feature set results in high-quality segmentation performance. Furthermore, it is shown that the roughness feature set exhibits a higher classification rate than other feature vectors presented in this work. The feature set retains the important properties of FD-based features, namely insensitivity to absolute illumination and contrast.

Fractal analysis in the detection of colonic cancer images.

The aim of this study was to investigate the value of fractal dimension in separating normal and cancerous images, and to examine the relationship between fractal dimension and traditional texture analysis features. Forty-four normal images and 58 cancer images from sections of the colon were analyzed. A "leave-one-out" analysis approach was used to classify the samples into each group. With fractal analysis there was a highly significant difference between groups (p < 0.0001). Correlation and entropy features showed greater differences between the groups (p < 0.0001). Nevertheless, the addition of fractal analysis to the feature analysis improved the sensitivity from 90% to 95% and specificity from 86% to 93%.

Texture Segmentation using Fractal Signature

Fractal dimension is a powerful tool to characterize roughness in an image. This paper presents fractal geometry based approach for texture segmentation. Five fractal dimension features are calculated from the original image, the high-gray image, the low-gray level image, the horizontally and vertically smoothed image. Supervised texture segmentation is achieved using minimum distance and fuzzy classifier for different window sizes. The fuzzy classifier with smaller window size gives better performance.

Dynamical Features of the Local Fractal Dimension of Brain Waves and Its Applicability for Diagnosis of Senile Dementia

We have studied local irregularity of brain waves using “local fractal dimensions (LFDs)” for two groups of elderly people, one healthy and the other affected by senile dementia. It is determined that (a) the probability distribution of the LFDs for both groups is subject to the universal law of the beta distribution; (b) the stochastic processes of LFDs of the two groups show a marked difference. We have demonstrated the applicability of the present statistical method based on the LFD for estimating the degree of progression of dementia.

Fractal dimension based features are useful descriptors of leaf complexity and shape

An application of fractal dimensions as measures of leaf complexity to morphometric studies and automated plant identification is presented. Detailed algorithms for the calculation of compass dimension and averaged mass dimension together with a simple method of grasping the scale range related variability are given. An analysis of complexity of more than 300 leaves from 10 tree species is reported. Several classical biometric descriptors as well as 16 fractal dimension features were computed on digitized leaf silhouettes. It is demonstrated that properly defined fractal dimension based features may be used to discriminate between species with more than 90% accuracy, especially when used together with other measures. It seems, therefore, that they can be utilized in computer identification systems and for purely taxonomical purposes.

Discrimination of MR images of breast masses with fractal-interpolation function models

The authors evaluated the feasibility of using statistical fractal-dimension features to improve discrimination between benign and malignant breast masses at magnetic resonance (MR) imaging. The study evaluated MR images of 32 malignant and 20 benign breast masses from archived data at the University of Pennsylvania Medical Center. The test set included four cases that were difficult to evaluate on the basis of border characteristics. All diagnoses had been confirmed at excisional biopsy. The fractal-dimension feature was computed as the mean of a sample space of fractal-dimension estimates derived from fractal interpolation function models. To evaluate the performance of the fractal-dimension feature, the classification effectiveness of five expert-observer architectural features was compared with that of the fractal dimension combined with four expert-observer features. Feature sets were evaluated with receiver operating characteristic analysis. Discrimination analysis used artificial neural networks and logistic regression. Robustness of the fractal-dimension feature was evaluated by determining changes in discrimination when the algorithm parameters were perturbed. The combination of fractal-dimension and expert-observer features provided a statistically significant improvement in discrimination over that achieved with expert-observer features alone. Perturbing selected parameters in the fractal-dimension algorithm had little effect on discrimination. A statistical fractal-dimension feature appears to be useful in distinguishing MR images of benign and malignant breast masses in cases where expert radiologists may have difficulty. The statistical approach to estimating the fractal dimension appears to be more robust than other fractal measurements on data-limited medical images.

The use of fractal features from the periphery of cell nuclei as a classification tool.

A polygonization‐based method is used to estimate the fractal dimension and several new scalar lacunarity features from digitized transmission electron micrographs (TEM) of mouse liver cell nuclei. The fractal features have been estimated in different segments of 1D curves obtained by scanning the 2D cell nuclei in a spiral‐like fashion called “peel‐off scanning”. This is a venue to separate estimates of fractal features in the center and periphery of a cell nucleus. Our aim was to see if a small set of fractal features could discriminate between samples from normal liver, hyperplastic nodules and hepatocellular carcinomas. The Bhattacharyya distance was used to evaluate the features. Bayesian classification with pooled covariance matrix and equal prior probabilities was used as the rule for classification. Several single fractal features estimated from the periphery of the cell nuclei discriminated samples from the hyperplastic nodules and hepatocellular carcinomas from normal ones. The outer 25–30% of the cell nuclei contained important texture information about the differences between the classes. The polygonization‐based method was also used as an analysis tool to relate the differences between the classes to differences in the chromatin structure.

Optical wave propagation of fractal fields

The evolution of the complex amplitude of a fractal optical field during propagation through free space (Fresnel transform) and through a quadratic refractive index medium (fractional Fourier transform) is discussed. To that end, the two above transforms have been introduced within the framework of the generalized Fresnel transform (GFT) and their scaling properties formulated. These scaling properties are shown to be suitable to reveal the self-similarity behaviour of the fractal field. A general method to determine the fractal dimension and other fractal features from the diffraction patterns is proposed. As an application of the method, a numerical experiment has been carried out for the diffraction of a triadic Cantor set in free space and in a quadratic index medium. The determination of the fractal dimension is illustrated in the two cases.

Features of fractal dimension anomaly of radon content in underground water in North China before and after the 1976 Tangshan earthquake

Based on the fractal theory, proceeding from the observed data of the random content of underground water, the fractal dimension of the sequence of sudden changes of the radon content of 27 wells (springs) in North China before and after the Tangshan earthquake has been calculated using a month-by-month sliding method. The variation of fractal dimensions anomalies before and after the main shock in time and space was studied. The following phenomena were discovered: The fractal dimension of the radon content changed distinctly before the earthquake; the stations where the fractal dimension anomalies of the radon content appeared are within 300 km from the epicenter; the increase and decrease areas of the fractal dimensions of the radon content appeared clearly; just before the earthquake, the increase area filled the whole of North China except the epicentral area, where the fractal dimensions are decreasing.

Texture segmentation using fractal dimension

This paper deals with the problem of recognizing and segmenting textures in images. For this purpose the authors employ a technique based on the fractal dimension (FD) and the multi-fractal concept. Six FD features are based on the original image, the above average/high gray level image, the below average/low gray level image, the horizontally smoothed image, the vertically smoothed image, and the multi-fractal dimension of order two. A modified box-counting approach is proposed to estimate the FD, in combination with feature smoothing in order to reduce spurious regions. To segment a scene into the desired number of classes, an unsupervised K-means like clustering approach is used. Mosaics of various natural textures from the Brodatz album as well as microphotographs of thin sections of natural rocks are considered, and the segmentation results to show the efficiency of the technique. Supervised techniques such as minimum-distance and k-nearest neighbor classification are also considered. The results are compared with other techniques. >

Fractal interpolation of radar signatures for detecting stationary targets in ground clutter

The fundamentals of fractal geometry are reviewed, and its application to the millimeter-wave radar detection of stationary targets in a clutter background is described. First, high-range-resolution (HRR) profiles are used to determine the fractal interpolation functions needed to create fractal signatures. The fractal dimension is then determined for these signatures. On the basis of the value of the fractal dimension, the signature is declared to represent either a target of interest or clutter. The results of a CFAR (constant false alarm rate) simulation are presented to illustrate the performance of the method. They indicate that the fractal dimension feature used seems to be independent of amplitude. Thus, the fractal dimension information combined with traditional amplitude processing techniques will improve probabilities of detection.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>