Windows into Elementary Mathematics:Alternate public images of mathematics and mathematicians

Research on students’ (and teachers’) images of mathematics and mathematicians reveals a number of stereotypical images, most of which are negative. In this paper we present an overview of some these images and stereotypes and consider the questions: (1) how might the image of mathematics and mathematicians be a problem in mathematics education, and (2) what can be done to remedy the situation? Also, we consider an outreach project called Windows into Elementary Mathematics. In this project mathematicians are interviewed about their perspectives on elementary mathematics topics and their interviews are videotaped and are posted online, along with supporting images and interactive content. In this context we consider the questions: (3) what is the Windows project about, and (4) how might it offer an alternate (and perhaps better) image of mathematics and mathematicians? Lastly, we share an example where activities from the project were used in a math-for-teachers course.

Automatic classification of prostate stromal tissue in histological images using Haralick descriptors and Local Binary Patterns

In this paper we presente a classification system that uses a combination of texture features from stromal regions: Haralick features and Local Binary Patterns (LBP) in wavelet domain. The system has five steps for classification of the tissues. First, the stromal regions were detected and extracted using segmentation techniques based on thresholding and RGB colour space. Second, the Wavelet decomposition was applied in the extracted regions to obtain the Wavelet coefficients. Third, the Haralick and LBP features were extracted from the coefficients. Fourth, relevant features were selected using the ANOVA statistical method. The classication (fifth step) was performed with Radial Basis Function (RBF) networks. The system was tested in 105 prostate images, which were divided into three groups of 35 images: normal, hyperplastic and cancerous. The system performance was evaluated using the area under the ROC curve and resulted in 0.98 for normal versus cancer, 0.95 for hyperplasia versus cancer and 0.96 for normal versus hyperplasia. Our results suggest that texture features can be used as discriminators for stromal tissues prostate images. Furthermore, the system was effective to classify prostate images, specially the hyperplastic class which is the most difficult type in diagnosis and prognosis.

Effect of digitization parameters on periapical radiographic image quality with regard to anatomic landmarks

The aim of this study was to evaluate the influence of digitization parameters on periapical radiographic image quality, with regard to anatomic landmarks. Digitized images (n = 160) were obtained using a flatbed scanner with resolutions of 300, 600 and 2400 dpi. The radiographs of 2400 dpi were decreased to 300 and 600 dpi before storage. Digitizations were performed with and without black masking using 8-bit and 16-bit grayscale and saved in TIFF format. Four anatomic landmarks were classified by two observers (very good, good, moderate, regular, poor), in two random sessions. Intraobserver and interobserver agreements were evaluated by Kappa statistics. Inter and intraobserver agreements ranged according to the anatomic landmarks and resolution used. The results obtained demonstrated that the cement enamel junction was the anatomic landmark that presented the poorest concordance. The use of black masking provided better results in the digitized image. The use of a mask to cover radiographs during digitization is necessary. Therefore, the concordance ranged from regular to moderate for the intraobserver evaluation and concordance ranged from regular to poor for interobserver evaluation.

Fluorescence Level of Composites Assessed by Computer Processing of Digital Images - ScanWhite

The human dentition is naturally translucent, opalescent and fluorescent. Differences between the level of fluorescence of tooth structure and restorative materials may result in distinct metameric properties and consequently perceptible disparate esthetic behavior, which impairs the esthetic result of the restorations, frustrating both patients and staff. In this study, we evaluated the level of fluorescence of different composites (Durafill in tones A2 (Du), Charisma in tones A2 (Ch), Venus in tone A2 (Ve), Opallis enamel and dentin in tones A2 (OPD and OPE), Point 4 in tones A2 (P4), Z100 in tones A2 ( Z1), Z250 in tones A2 (Z2), Te-Econom in tones A2 (TE), Tetric Ceram in tones A2 (TC), Tetric Ceram N in tones A1, A2, A4 (TN1, TN2, TN4), Four seasons enamel and dentin in tones A2 (and 4SD 4SE), Empress Direct enamel and dentin in tones A2 (EDE and EDD) and Brilliant in tones A2 (Br)). Cylindrical specimens were prepared, coded and photographed in a standardized manner with a Canon EOS digital camera (400 ISO, 2.8 aperture and 1/ 30 speed), in a dark environment under the action of UV light (25 W). The images were analyzed with the software ScanWhite©-DMC/Darwin systems. The results showed statistical differences between the groups (p < 0.05), and between these same groups and the average fluorescence of the dentition of young (18 to 25 years) and adults (40 to 45 years) taken as control. It can be concluded that: Composites Z100, Z250 (3M ESPE) and Point 4 (Kerr) do not match with the fluorescence of human dentition and the fluorescence of the materials was found to be affected by their own tone.

Fractal descriptors for discrimination of microscopy images of plant leaves

This study proposes the application of fractal descriptors method to the discrimination of microscopy images of plant leaves. Fractal descriptors have demonstrated to be a powerful discriminative method in image analysis, mainly for the discrimination of natural objects. In fact, these descriptors express the spatial arrangement of pixels inside the texture under different scales and such arrangements are directly related to physical properties inherent to the material depicted in the image. Here, we employ the Bouligand-Minkowski descriptors. These are obtained by the dilation of a surface mapping the gray-level texture. The classification of the microscopy images is performed by the well-known Support Vector Machine (SVM) method and we compare the success rate with other literature texture analysis methods. The proposed method achieved a correctness rate of 89%, while the second best solution, the Co-occurrence descriptors, yielded only 78%. This clear advantage of fractal descriptors demonstrates the potential of such approach in the analysis of the plant microscopy images.

Applying enhancement filters in the pre-processing of images of lymphoma

Lymphoma is a type of cancer that affects the immune system, and is classified as Hodgkin or non-Hodgkin. It is one of the ten types of cancer that are the most common on earth. Among all malignant neoplasms diagnosed in the world, lymphoma ranges from three to four percent of them. Our work presents a study of some filters devoted to enhancing images of lymphoma at the pre-processing step. Here the enhancement is useful for removing noise from the digital images. We have analysed the noise caused by different sources like room vibration, scraps and defocusing, and in the following classes of lymphoma: follicular, mantle cell and B-cell chronic lymphocytic leukemia. The filters Gaussian, Median and Mean-Shift were applied to different colour models (RGB, Lab and HSV). Afterwards, we performed a quantitative analysis of the images by means of the Structural Similarity Index. This was done in order to evaluate the similarity between the images. In all cases we have obtained a certainty of at least 75%, which rises to 99% if one considers only HSV. Namely, we have concluded that HSV is an important choice of colour model at pre-processing histological images of lymphoma, because in this case the resulting image will get the best enhancement.

Automatic method to classify images based on multiscale fractal descriptors and paraconsistent logic

In this study is presented an automatic method to classify images from fractal descriptors as decision rules, such as multiscale fractal dimension and lacunarity. The proposed methodology was divided in three steps: quantification of the regions of interest with fractal dimension and lacunarity, techniques under a multiscale approach; definition of reference patterns, which are the limits of each studied group; and, classification of each group, considering the combination of the reference patterns with signals maximization (an approach commonly considered in paraconsistent logic). The proposed method was used to classify histological prostatic images, aiming the diagnostic of prostate cancer. The accuracy levels were important, overcoming those obtained with Support Vector Machine (SVM) and Bestfirst Decicion Tree (BFTree) classifiers. The proposed approach allows recognize and classify patterns, offering the advantage of giving comprehensive results to the specialists.

Classification of histological images based on the stationary wavelet transform

Non-Hodgkin lymphomas are of many distinct types, and different classification systems make it difficult to diagnose them correctly. Many of these systems classify lymphomas only based on what they look like under a microscope. In 2008 the World Health Organisation (WHO) introduced the most recent system, which also considers the chromosome features of the lymphoma cells and the presence of certain proteins on their surface. The WHO system is the one that we apply in this work. Herewith we present an automatic method to classify histological images of three types of non-Hodgkin lymphoma. Our method is based on the Stationary Wavelet Transform (SWT), and it consists of three steps: 1) extracting sub-bands from the histological image through SWT, 2) applying Analysis of Variance (ANOVA) to clean noise and select the most relevant information, 3) classifying it by the Support Vector Machine (SVM) algorithm. The kernel types Linear, RBF and Polynomial were evaluated with our method applied to 210 images of lymphoma from the National Institute on Aging. We concluded that the following combination led to the most relevant results: detail sub-band, ANOVA and SVM with Linear and RBF kernels.

Development of a simple method for determination of NO2 in air using digital scanner images

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Locating control points in aerial images with a multi-scale approach based on terrestrial image patches

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Plant identification based on leaf midrib cross-section images using fractal descriptors

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Statistical analysis of texture in trunk images for biometric identification of tree species

The identification of tree species is a key step for sustainable management plans of forest resources, as well as for several other applications that are based on such surveys. However, the present available techniques are dependent on the presence of tree structures, such as flowers, fruits, and leaves, limiting the identification process to certain periods of the year Therefore, this article introduces a study on the application of statistical parameters for texture classification of tree trunk images. For that, 540 samples from five Brazilian native deciduous species were acquired and measures of entropy, uniformity, smoothness, asymmetry (third moment), mean, and standard deviation were obtained from the presented textures. Using a decision tree, a biometric species identification system was constructed and resulted to a 0.84 average precision rate for species classification with 0.83accuracy and 0.79 agreement. Thus, it can be considered that the use of texture presented in trunk images can represent an important advance in tree identification, since the limitations of the current techniques can be overcome.

Output only based modal analysis of a reduced scale building using digital camera images

The article discusses a proposal of displacement measurement using a unique digital camera aiming at to exploit its feasibility for Modal Analysis applications. The proposal discusses a non-contact measuring approach able to measure multiple points simultaneously by using a unique digital camera. A modal analysis of a reduced scale lab building structure based only at the responses of the structure measured with the camera is presented. It focuses at the feasibility of using a simple ordinary camera for performing the output only modal analysis of structures and its advantage. The modal parameters of the structure are estimated from the camera data and also by using ordinary experimental modal analysis based on the Frequency Response Function (FRF) obtained by using the usual sensors like accelerometer and force cell. The comparison of the both analysis showed that the technique is promising noncontact measuring tool relatively simple and effective to be used in structural modal analysis

Comparison of linear measurements and analyses taken from plaster models and three-dimensional images

Digital models are an alternative for carrying out analyses and devising treatment plans in orthodontics. The objective of this study was to evaluate the accuracy and the reproducibility of measurements of tooth sizes, interdental distances and analyses of occlusion using plaster models and their digital images. Thirty pairs of plaster models were chosen at random, and the digital images of each plaster model were obtained using a laser scanner (3Shape R-700, 3Shape A/S). With the plaster models, the measurements were taken using a caliper (Mitutoyo Digimatic(®), Mitutoyo (UK) Ltd) and the MicroScribe (MS) 3DX (Immersion, San Jose, Calif). For the digital images, the measurement tools used were those from the O3d software (Widialabs, Brazil). The data obtained were compared statistically using the Dahlberg formula, analysis of variance and the Tukey test (p < 0.05). The majority of the measurements, obtained using the caliper and O3d were identical, and both were significantly different from those obtained using the MS. Intra-examiner agreement was lowest when using the MS. The results demonstrated that the accuracy and reproducibility of the tooth measurements and analyses from the plaster models using the caliper and from the digital models using O3d software were identical.

Estimation of chlorophyll-a concentration and the trophic state of the Barra Bonita hydroelectric reservoir using oli/landsat-8 images

Reservoirs are artificial environments built by humans, and the impacts of these environments are not completely known. Retention time and high nutrient availability in the water increases the eutrophic level. Eutrophication is directly correlated to primary productivity by phytoplankton. These organisms have an important role in the environment. However, high concentrations of determined species can lead to public health problems. Species of cyanobacteria produce toxins that in determined concentrations can cause serious diseases in the liver and nervous system, which could lead to death. Phytoplankton has photoactive pigments that can be used to identify these toxins. Thus, remote sensing data is a viable alternative for mapping these pigments, and consequently, the trophic. Chlorophyll-a (Chl-a) is present in all phytoplankton species. Therefore, the aim of this work was to evaluate the performance of images of the sensor Operational Land Imager (OLI) onboard the Landsat-8 satellite in determining Chl-a concentrations and estimating the trophic level in a tropical reservoir. Empirical models were fitted using data from two field surveys conducted in May and October 2014 (Austral Autumn and Austral Spring, respectively). Models were applied in a temporal series of OLI images from May 2013 to October 2014. The estimated Chl-a concentration was used to classify the trophic level from a trophic state index that adopted the concentration of this pigment-like parameter. The models of Chl-a concentration showed reasonable results, but their performance was likely impaired by the atmospheric correction. Consequently, the trophic level classification also did not obtain better results.