OBJECTIVE: The goal of this study was to develop a novel pupil and iris segmentation algorithm. We evaluated segmentation performance based on a fractal model. Two methods were compared: Daugman's and our new proposed method. METHODS: We received 200 anterior segment images with 3,872x2,592 pixels. Here we present an active contour model that accurately detects pupil boundaries in order to improve the performance of segmentation systems. We propose a method that uses iris segmentation based on a fractal model. We compared the performance of Daugman's method and the proposed new method and statistically analyzed the results. RESULTS: We manually compared segmentation with the Daugman's method and the new proposed method. The findings showed that the proposed segmentation accuracy was about 2.5 percent higher than Daugman's method. There was a significant difference (p<0.05) between the under and over data between the two methods. CONCLUSION: The results of this study show that the new proposed method was more accurate than the conventional method for the measurement of segmentation of the eye by CAD (Computer-aided Diagnosis).
Eye ; Fractals ; Iris ; Pupil

Strange attractor can be constructed from time series data such as heart sound. In the areas of the recognition and diagnosis of abnormal heart sounds, signal presentation method is very useful because good features can be detected from good presentation. This paper examines efficiency in diagnosing abnormal heart sounds of the two different methods for constructing attractor. Nine different heart sounds from typical clinical conditions were used for this study. The first method was constructing attractors using original heart sounds, and the second was modifying the original sounds by autocorrelation and they were then applied to the orignal sounds as to cross correlation checks. Attractors could be constructed using signals generated by these methods, and values of fractal dimensions would then be calculated which has been a well known method to measure characteristics of attractors. The results showed that the second method appeared to provide more efficient way to correctly classify abnormal heart sounds.
Diagnosis ; Fractals* ; Heart Sounds* ; Heart*

Fractal, a mathematics concept, is used to describe an image of self-similarity and scale invariance. Some organisms have been discovered with the fractal characteristics, such as cerebral cortex surface, retinal vessel structure, cardiovascular network, and trabecular bone, etc. It has been preliminarily confirmed that the three-dimensional structure of cells cultured in vitro could be significantly enhanced by bionic fractal surface. Moreover, fractal theory in clinical research will help early diagnosis and treatment of diseases, reducing the patient's pain and suffering. The development process of diseases in the human body can be expressed by the fractal theories parameter. It is of considerable significance to retrospectively review the preparation and application of fractal surface and its diagnostic value in medicine. This paper gives an application of fractal and its theories in the medical science, based on the research achievements in our laboratory.
Biomedical Research ; Bionics ; Fractals ; Humans

PURPOSE: This study was done to know the usefulness of fractal analysis when evaluating the radiologic changes after decompression on jaw bone cystic lesions using fractal analysis. MATERIALS AND METHODS: 30cases of cystic lesions were followed up after decompression. Panoramic image was used to observe radiologic changes around the cystic lesion. The part of the panoramic image which showed radiologic change was defined as region of interest(ROI); The fractal dimension of the ROI was calculated using box-counting method. RESULTS: Using sign-rank test, there was a statistically significant difference in fractal dimensions after decompression therapy(P<;0.0001). The fractal dimensions statistically increased after decompression(the median of D:0.12). CONCLUSIONS: The ROI after decompression showed higher fractal dimensions which offer the objective proof of the bone healing around cystic lesions after decompression treatment.
Bone Cysts* ; Decompression* ; Fractals* ; Jaw*

The purpose of this study was to investigate wether a radiographic estimate of osseous fractal dimension is useful in the characterization of structural changes in bone. Ten specimens of bone were progressively decalcified in fresh 50ml solutions of 0.1N hydrochloric acid solution at cummulative timed periods of 5, 10, 20, 30, 60 and 90 minutes, and radiographed from 0 degree projection angle controlled by intraoral parelleling device. The test set of 70 radiographs was digitally filtered to reduce film-grain noise. I performed one-dimensional variance and fractal analysis of bony profiles or scan lines, Correlation analysis quantified the relationship between variance and fractal dimension. The obtained results were as follow ; 1. After the first stage of decalcification variance and fractal dimension of scan line pixel intensities generally decreased with a range of 57.94 to 12.64 and 1.59 to 1.36. 2. Correlation coefficient(r) relating variance to fractal dimension was consistantly excellent(range r=0.90 to 0.98). 3. Variance and fractal dimension were much alike in ability to discriminate, at leat on a group basis, between contrl and decalcified specimens.
Fractals* ; Hydrochloric Acid ; Noise ; Osteoporosis*

PURPOSE: To evaluate the relationship between morphometric analysis of bone microstructure from digital radiographic image and trabecular bone strength. MATERIALS AND METHODS: One hundred eleven bone specimens with 5 mm thickness were obtained from the mandibles of 5 pigs. Digital images of specimens were taken using a direct digital intraoral radiographic system. After selection of ROI (100x100 pixel) within the trabecular bone, mean gray level and standard deviation were obtained. Fractal dimension and the variants of morphometric analysis (trabecular area, periphery, length of skeletonized trabeculae, number of terminal point, number of branch point) were obtained from ROI. Punch sheer strength analysis was performed using Instron (model 4465, Instron Corp., USA). The loading force (loading speed 1 mm/min) was applied to ROI of bone specimen by a 2 mm diameter punch. Stress-deformation curve was obtained from the punch sheer strength analysis and maximum stress, yield stress, Young's modulus were measured. RESULTS: Maximum stress had a negative linear correlation with mean gray level and fractal dimension significantly (p< 0.05). Yield stress had a negative linear correlation with mean gray level, periphery, fractal dimension and the length of skeletonized trabeculae significantly (p< 0.05). Young's modulus had a negative linear correlation with mean gray level and fractal dimension significantly (p< 0.05). CONCLUSIONS: The strength of cancellous bone exhibited a significantly linear relationship between mean gray level, fractal dimension and morphometric analysis. The methods described above can be easily used to evaluate bone quality clinically.
Elastic Modulus ; Fractals ; Mandible ; Radiography ; Skeleton ; Swine

PURPOSE: The purpose of this study was to evaluate the effect of the kV on fractal dimension of trabecular bone in digital radiographs. MATERIALS AND METHODS: 16 bone cores were obtained from patients who had taken partial resection of tibia due to accidents. Each bone core along with an aluminum step wedge was radiographed with an occlusal film at 0.08 sec and with the constant film-focus distance (32 cm). All radiographs were acquired at 60, 75, and 90 kV. A rectangular ROI was drawn at medial part, distal part, and the bone defect area of each bone core image according to each kV. The directional fractal dimension was measured using Fourier Transform spectrum, and the anisotropy was obtained using directional fractal dimension. The values were compared by the repeated measures ANOVA. RESULTS: The fractal dimensions increased along with kV increase (p<0.05). The anisotropy measurements did not show statistically significant difference according to kV change. The fractal dimensions of the bone defect areas of the bone cores have low values contrast to the non-defect areas of the bone cores. The anisotropy measurements of the bone defect areas were lower than those of the non-defect areas of the bone cores, but not statistically significant. CONCLUSION: Fractal analysis can notice a difference of a change of voltage of x-ray tube and bone defect or not. And anisotropy of a trabecular bone is coherent even with change of the voltage of x-ray tube or defecting off a part of bone.
Aluminum ; Anisotropy* ; Fourier Analysis ; Fractals* ; Humans ; Tibia

The purpose of this study was to investigate whether a radiographic estimate of osseous fractal dimension and power spectrum of 2D discrete Fourier transform is useful in the characterization of structural changes in bone. Ten specimens of bone were decalcified in fresh 50 ml solutions of 0.1 N hydrochloric acid solution at cummulative timed periods of 0 and 90 minutes, and radiographed from 0 degree projection angle controlled by intraoral parelleling device. I performed one-dimensional variance, fractal analysis of bony profiles and 2D discrete Fourier transform. The results of this study indicate that variance and fractal dimension of scan line pixel intensities decreased significantly in decalcified groups but Fourier spectral analysis didn't discriminate well between control and decalcified specimens.
Fourier Analysis* ; Fractals* ; Hydrochloric Acid ; Osteoporosis

PURPOSE: This study was performed to evaluate possible variations in maxillary and mandibular bone texture of normal population using the fractal analysis, particles count, and area fraction in intraoral radiographs. MATERIALS AND METHODS: Periapical radiographs of patients who had full mouth intraoral radiographs were collected. Regions of interest (100x100 pixels) were located between the teeth of the maxillary anterior, premolar, and molar area, as well as the mandibular anterior, premolar, and molar areas. The fractal dimension (FD) was calculated by using the box counting method. The particle count (PC) and area fraction (AF) analyses were also performed. RESULTS: There was no significant difference in the FD values among the different groups of age, gender, upper, and lower jaws. The mean FD value was 1.49+/-0.01. The mean PC ranged from 44 to 54, and the mean AF ranged from 10.92 to 11.85. The values of FD, PC, and AF were significantly correlated with each other except for the upper molar area. CONCLUSION: According to the results, patients with normal trabecular pattern showed a FD of approximately 1.5. Based on these results, further investigation would be recommended if the FD value of patient significantly differenct from this number, since the alteration of this value indicates microstructural modification of trabecular pattern of the jaws. Additionally, with periapical radiographs, simple and cost-effective, PC and AF could be used to assess the deviation from the normal.
Bicuspid ; Fractals ; Humans ; Jaw ; Molar ; Mouth ; Tooth

The linear analysis for heart rate variability (HRV), including time domain method, frequency domain method and time-frequency analysis, has reached a lot of consensus. The non-linear analysis has also been widely applied in biomedical and clinical researches. However, for non-linear HRV analysis, especially for short-term non-linear HRV analysis, controversy still exists, and a unified standard and conclusion has not been formed. This paper reviews and discusses three short-term non-linear HRV analysis methods (fractal dimension, entropy and complexity) and their principles, progresses and problems in clinical application in detail, in order to provide a reference for accurate application in clinical medicine.
Electrocardiography ; Entropy ; Fractals ; Heart Rate ; Humans