Extended principal component analysis and its applications to image analysis

The objectives of this research are to analyze and develop a modified Principal Component Analysis (PCA) and to develop a two-dimensional PCA with applications in image processing. PCA is a classical multivariate technique where its mathematical treatment is purely based on the eigensystem of positive-definite symmetric matrices. Its main function is to statistically transform a set of correlated variables to a new set of uncorrelated variables over $\IR\sp{n}$ by retaining most of the variations present in the original variables.^ The variances of the Principal Components (PCs) obtained from the modified PCA form a correlation matrix of the original variables. The decomposition of this correlation matrix into a diagonal matrix produces a set of orthonormal basis that can be used to linearly transform the given PCs. It is this linear transformation that reproduces the original variables. The two-dimensional PCA can be devised as a two successive of one-dimensional PCA. It can be shown that, for an $m\times n$ matrix, the PCs obtained from the two-dimensional PCA are the singular values of that matrix.^ In this research, several applications for image analysis based on PCA are developed, i.e., edge detection, feature extraction, and multi-resolution PCA decomposition and reconstruction. ^

The effect of the use of computer assisted instruction (CAI) on attitudes and computational scores of developmental mathematics students at two inner city schools with predominantly Black enrollment

This study examined the effects of computer assisted instruction (CAI) 1 hour per week for 18 weeks on changes in computational scores and attitudes of developmental mathematics students at schools with predominantly Black enrollment. Comparisons were made between students using CAI with differing software--PLATO, CSR or both together--and students using traditional instruction (TI) only.^ This study was conducted in the Dade County Public School System from February through June 1991, at two senior high schools. The dependent variables, the State Student Assessment Test (SSAT), and the School Subjects Attitude Scales (SSAS), measured students' computational scores and attitudes toward mathematics in 3 categories: interest, usefulness, and difficulty, respectively.^ Univariate analyses of variance were performed on the least squares mean differences from pretest to posttest for testing main effects and interactions. A t-test measured significant main effects and interactions. Results were interpreted at the.01 level of significance.^ Null hypotheses 1, 2, and 3 compared versions of CAI with the control group, for changes in mathematical computation scores measured with the SSAT. It could not be concluded that changes in standardized mathematics test scores of students using CAI with differing software 1 hour per week for 18 class hours combined with TI were significantly higher than changes in test scores for students receiving TI only.^ Null hypotheses 4, 5, and 6 tested the effects of CAI for attitudes toward mathematics for experimental groups against control groups measured with the SSAS. Changes in attitudes toward mathematics of students using CAI with differing software 1 hour per week for 18 class hours combined with TI were not significantly higher than attitude changes for students receiving TI only.^ Teacher effect on students' computational scores was a more influential variable than CAI. No interaction was found between gender and learning method on standardized mathematics test scores (null hypothesis 7). ^

The Effect of Active Student Responding in Computer-Assisted Instruction on Social-Studies Learning by Students with Learning Disabilities: A Brief Report

An alternating treatment design was used to compare the effects of three student response conditions (Clicking, Repeating, and Listening) during computer-assisted instruction on social-studies facts learning and maintenance. Results showed that all students learned and maintained more social-studies facts taught in the Repeating condition followed by the Clicking condition.

Achievement of generic baccalaureate student nurses using computer -assisted instruction simulations during a nursing review course

The use of computer assisted instruction (CAI) simulations as an instructional strategy provides nursing students with a critical thinking approach for evaluating risks and benefits and choosing correct alternatives in "safe" patient care situations. It was hypothesized that using CAI simulations during an upper level nursing review course would have a positive effect on the students' posttest scores. Subjects (n = 36) were senior nursing students enrolled in a nursing review course in an undergraduate baccalaureate program. A limitation of the study was the small sample size. The study employed a modified group experimental design using the t test for independent samples. The group who received the CAI simulations during the physiological system review demonstrated a significant increase (p $<$.01) in the posttest score mean when compared to the lecture-discussion group score mean. There was no significant difference between high and low clinical grade point average (GPA) students in the CAI and lecture-discussion groups and their score means on the posttest. However, score mean differences of the low clinical GPA students showed a greater increase for the CAI group than the lecture-discussion group. There was no significant difference between the groups in their system content subscore means on the exit examination completed three weeks later. It was concluded that CAI simulations are as effective as lecture-discussion in assisting upper level students to process information for clinical decision making. CAI simulations can be considered as an instructional strategy to supplement or replace lecture content during a review course, allowing more efficient use of faculty time. It is recommended that the study be repeated using a larger sample size. Further investigations are recommended in comparing the effectiveness of computer software formats and various instructional strategies for other learning situations and student populations. ^

Fractal analysis of flocs formed in edible oil -water emulsions by image analysis techniques

Edible oil is an important contaminant in water and wastewater. Oil droplets smaller than 40 μm may remain in effluent as an emulsion and combine with other contaminants in water. Coagulation/flocculation processes are used to remove oil droplets from water and wastewater. By adding a polymer at proper dose, small oil droplets can be flocculated and separated from water. The purpose of this study was to characterize and analyze the morphology of flocs and floc formation in edible oil-water emulsions by using microscopic image analysis techniques. The fractal dimension, concentration of polymer, effect of pH and temperature are investigated and analyzed to develop a fractal model of the flocs. Three types of edible oil (corn, olive, and sunflower oil) at concentrations of 600 ppm (by volume) were used to determine the optimum polymer dosage and effect of pH and temperature. To find the optimum polymer dose, polymer was added to the oil-water emulsions at concentration of 0.5, 1.0, 1.5, 2.0, 3.0 and 3.5 ppm (by volume). The clearest supernatants obtained from flocculation of corn, olive, and sunflower oil were achieved at polymer dosage of 3.0 ppm producing turbidities of 4.52, 12.90, and 13.10 NTU, respectively. This concentration of polymer was subsequently used to study the effect of pH and temperature on flocculation. The effect of pH was studied at pH 5, 7, 9, and 11 at 30°C. Microscopic image analysis was used to investigate the morphology of flocs in terms of fractal dimension, radius of oil droplets trapped in floc, floc size, and histograms of oil droplet distribution. Fractal dimension indicates the density of oil droplets captured in flocs. By comparison of fractal dimensions, pH was found to be one of the most important factors controlling droplet flocculation. Neutral pH or pH 7 showed the highest degree of flocculation, while acidic (pH 5) and basic pH (pH 9 and pH 11) showed low efficiency of flocculation. The fractal dimensions achieved from flocculation of corn, olive, and sunflower oil at pH 7 and temperature 30°C were 1.2763, 1.3592, and 1.4413, respectively. The effect of temperature was explored at temperatures 20°, 30°, and 40°C and pH 7. The results of flocculation of oil at pH 7 and different temperatures revealed that temperature significantly affected flocculation. The fractal dimension of flocs formed in corn, olive and sunflower oil emulsion at pH 7 and temperature 20°, 30°, and 40°C were 1.82, 1.28, 1.29, 1.62, 1.36, 1.42, 1.36, 1.44, and 1.28, respectively. After comparison of fractal dimension, radius of oil droplets captured, and floc length in each oil type, the optimal flocculation temperature was determined to be 30°C. ^

The effect of active student responding in computer -assisted instruction on social -studies learning by students with learning disabilities

The purpose of this study was to compare the effects of three student response conditions during computer-assisted instruction on the acquisition and maintenance of social-studies facts. Two of the conditions required active student responding (ASR), whereas the other required an on-task (OT) response. Participants were five fifth-grade students, with learning disabilities enrolled in a private school. An alternating treatments design with a best treatments phase was used to compare the effects of the response procedures on three major dependent measures: same-day tests, next-day tests, and maintenance tests. ^ Each week for six weeks, participants were provided daily one-to-one instruction on sets of 21 unknown social-studies facts using a hypermedia computer program, with a new set of facts being practiced each week. Each set of 21 facts was divided randomly into three conditions: Clicking-ASR, Repeating-ASR, and Listening-OT. Hypermedia lesson began weekly with the concept introduction lesson, followed by practice and testing. Practice and testing occurred four days per week, per set. During Clicking-ASR, student practice involved the selection of a social-studies response by clicking on an item with the mouse on the hypermedia card. Repeating-ASR instruction required students to orally repeat the social-studies facts when prompted by the computer. During Listening-OT, students listened to the social-studies facts being read by the computer. During weeks seven and eight, instruction occurred with seven unknown facts using only the best treatment. ^ Test results show that all for all 5 students, the Repeating-ASR practice procedure resulted in more social-studies facts stated correctly on same-day tests, next-day tests, and one-and two-week maintenance tests. Clicking-ASR was the next most effective procedure. During the seventh and eighth week of instruction when only the best practice condition was implemented, Repeating-ASR produced higher scores than all conditions (including Repeating-ASR) during the first six weeks of the study. ^ The results lend further support to the growing body of literature that demonstrates the positive relation between ASR and student achievement. Much of the ASR literature has focused on the effects of increased ASR during teacher-led or peer-mediated instruction. This study adds a dimension to that research in that it demonstrated the importance of ASR during computer-assisted instruction and further suggests that the type of ASR used during computer-assisted instruction may influence learning. Future research is needed to investigate the effectiveness of other types of ASR during computer-assisted instruction and to identify other fundamental characteristics of an effective computer-assisted instruction. ^

Motion correction algorithm of lung tumors for respiratory gated PET images

Respiratory gating in lung PET imaging to compensate for respiratory motion artifacts is a current research issue with broad potential impact on quantitation, diagnosis and clinical management of lung tumors. However, PET images collected at discrete bins can be significantly affected by noise as there are lower activity counts in each gated bin unless the total PET acquisition time is prolonged, so that gating methods should be combined with imaging-based motion correction and registration methods. The aim of this study was to develop and validate a fast and practical solution to the problem of respiratory motion for the detection and accurate quantitation of lung tumors in PET images. This included: (1) developing a computer-assisted algorithm for PET/CT images that automatically segments lung regions in CT images, identifies and localizes lung tumors of PET images; (2) developing and comparing different registration algorithms which processes all the information within the entire respiratory cycle and integrate all the tumor in different gated bins into a single reference bin. Four registration/integration algorithms: Centroid Based, Intensity Based, Rigid Body and Optical Flow registration were compared as well as two registration schemes: Direct Scheme and Successive Scheme. Validation was demonstrated by conducting experiments with the computerized 4D NCAT phantom and with a dynamic lung-chest phantom imaged using a GE PET/CT System. Iterations were conducted on different size simulated tumors and different noise levels. Static tumors without respiratory motion were used as gold standard; quantitative results were compared with respect to tumor activity concentration, cross-correlation coefficient, relative noise level and computation time. Comparing the results of the tumors before and after correction, the tumor activity values and tumor volumes were closer to the static tumors (gold standard). Higher correlation values and lower noise were also achieved after applying the correction algorithms. With this method the compromise between short PET scan time and reduced image noise can be achieved, while quantification and clinical analysis become fast and precise.

The efficacy of an interactive computer system for teaching developmental mathematics to college students

Many students are entering colleges and universities in the United States underprepared in mathematics. National statistics indicate that only approximately one-third of students in developmental mathematics courses pass. When underprepared students repeatedly enroll in courses that do not count toward their degree, it costs them money and delays graduation. This study investigated a possible solution to this problem: Whether using a particular computer assisted learning strategy combined with using mastery learning techniques improved the overall performance of students in a developmental mathematics course. Participants received one of three teaching strategies: (a) group A was taught using traditional instruction with mastery learning supplemented with computer assisted instruction, (b) group B was taught using traditional instruction supplemented with computer assisted instruction in the absence of mastery learning and, (c) group C was taught using traditional instruction without mastery learning or computer assisted instruction. Participants were students in MAT1033, a developmental mathematics course at a large public 4-year college. An analysis of covariance using participants' pretest scores as the covariate tested the null hypothesis that there was no significant difference in the adjusted mean final examination scores among the three groups. Group A participants had significantly higher adjusted mean posttest score than did group C participants. A chi-square test tested the null hypothesis that there were no significant differences in the proportions of students who passed MAT1033 among the treatment groups. It was found that there was a significant difference in the proportion of students who passed among all three groups, with those in group A having the highest pass rate and those in group C the lowest. A discriminant factor analysis revealed that time on task correctly predicted the passing status of 89% of the participants. ^ It was concluded that the most efficacious strategy for teaching developmental mathematics was through the use of mastery learning supplemented by computer-assisted instruction. In addition, it was noted that time on task was a strong predictor of academic success over and above the predictive ability of a measure of previous knowledge of mathematics.^

Motion Correction Algorithm of Lung Tumors for Respiratory Gated PET Images

Respiratory gating in lung PET imaging to compensate for respiratory motion artifacts is a current research issue with broad potential impact on quantitation, diagnosis and clinical management of lung tumors. However, PET images collected at discrete bins can be significantly affected by noise as there are lower activity counts in each gated bin unless the total PET acquisition time is prolonged, so that gating methods should be combined with imaging-based motion correction and registration methods. The aim of this study was to develop and validate a fast and practical solution to the problem of respiratory motion for the detection and accurate quantitation of lung tumors in PET images. This included: (1) developing a computer-assisted algorithm for PET/CT images that automatically segments lung regions in CT images, identifies and localizes lung tumors of PET images; (2) developing and comparing different registration algorithms which processes all the information within the entire respiratory cycle and integrate all the tumor in different gated bins into a single reference bin. Four registration/integration algorithms: Centroid Based, Intensity Based, Rigid Body and Optical Flow registration were compared as well as two registration schemes: Direct Scheme and Successive Scheme. Validation was demonstrated by conducting experiments with the computerized 4D NCAT phantom and with a dynamic lung-chest phantom imaged using a GE PET/CT System. Iterations were conducted on different size simulated tumors and different noise levels. Static tumors without respiratory motion were used as gold standard; quantitative results were compared with respect to tumor activity concentration, cross-correlation coefficient, relative noise level and computation time. Comparing the results of the tumors before and after correction, the tumor activity values and tumor volumes were closer to the static tumors (gold standard). Higher correlation values and lower noise were also achieved after applying the correction algorithms. With this method the compromise between short PET scan time and reduced image noise can be achieved, while quantification and clinical analysis become fast and precise.