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

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*

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*

PURPOSE: To evaluate the radiographic change of operation sites after orthognathic surgery using the digital image processing and fractal analysis. MATERIALS AND METHODS: A series of panoramic radiographs of thirty-five randomly selected patients who had undergone mandibular orthognathic surgery (bilateral sagittal split ramus osteotomy) without clinical complication for osseous healing, were taken. The panoramic radiographs of each selected patient were taken at pre-operation (stage 0), 1 or 2 days after operation (stage 1), 1 month after operation (stage 2), 6 months after operation (stage 3), and 12 months after operation (stage 4). The radiographs were digitized at 600 dpi, 8 bit, and 256 gray levels. The region of interest, centered on the bony gap area of the operation site, was selected and the fractal dimension was calculated by using the tile-counting method. The mean values and standard deviations of fractal dimension for each stage were calculated and the differences among stage 0, 1, 2, 3, and 4 were evaluated through repeated measures of the ANOVA and paired t-test. RESULTS: The mean values and standard deviations of the fractal dimensions obtained from stage 0, 1, 2, 3, and 4 were 1.658 +/-0.048, 1.580 +/-0.050, 1.607 +/-0.046, 1.624 +/-0.049, and 1.641 +/-0.061, respectively. The fractal dimensions from stage 1 to stage 4 were shown to have a tendency to increase (p<0.05). CONCLUSION: The tendency of the fractal dimesion to increase relative to healing time may be a useful means of evaluating post-operative bony healing of the osteotomy site.
Fractals* ; Humans ; Orthognathic Surgery* ; Osteotomy ; Wound Healing

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

PURPOSE: The purpose of this study is to examine the effects of X-ray beam angulation on the fractal dimension of trabecular bone structure of human dry mandible using the tile counting method. MATERIALS AND METHODS: We divided 5 human dry mandibles into an angle and a molar groups depending on the regions and deciding the region of interest (ROI). When contrasted with the ROI, the inferior cortex was appointed to be low and the lines perpendicular to the buccal cortex were appointed to be the standard angle. Direct digital intraoral radiographs were obtained from 9 different projection angles. We analyzed statistically the fractal dimension using the tile counting method. RESULTS: There was a statistically significant difference in the fractal dimension of the regions and the mandibles, but there was no statistically significant difference in the fractal dimension according to the X-ray beam angulation. CONCLUSION: There is no statistically significant effect of the angle of the projection on the fractal dimension of trabecular bone structure of a human dry mandible according to the tile counting method.
Fractals* ; Humans* ; Mandible* ; Molar ; Radiography, Dental, Digital

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