Continuous images of Cantor's ternary set

The Hausdorff-Alexandroff Theorem states that any compact metric space is the continuous image of Cantor's ternary set $C$. It is well known that there are compact Hausdorff spaces of cardinality equal to that of $C$ that are not continuous images of Cantor's ternary set. On the other hand, every compact countably infinite Hausdorff space is a continuous image of $C$. Here we present a compact countably infinite non-Hausdorff space which is not the continuous image of Cantor's ternary set

On the segmentation of astronomical images via level-set methods

Astronomical images are of crucial importance for astronomers since they contain a lot of information about celestial bodies that can not be directly accessible. Most of the information available for the analysis of these objects starts with sky explorations via telescopes and satellites. Unfortunately, the quality of astronomical images is usually very low with respect to other real images and this is due to technical and physical features related to their acquisition process. This increases the percentage of noise and makes more difficult to use directly standard segmentation methods on the original image. In this work we will describe how to process astronomical images in two steps: in the first step we improve the image quality by a rescaling of light intensity whereas in the second step we apply level-set methods to identify the objects. Several experiments will show the effectiveness of this procedure and the results obtained via various discretization techniques for level-set equations.Comment: 24 pages, 59 figures, paper submitte

Representativeness and Diversity in Photos via Crowd-Sourced Media Analysis

In this paper we present a hybrid three steps mechanism for automated-human media analysis employed for selecting a small number of representative and diverse images in the context of a noisy set of images. The first step consists in the automatic retrieval from web of a large database of candidate images. In the second step, a proposed image analysis method is employed with the goal of diminishing the time, pay and cognitive load and implicitly people’s work. This is done by automatically selecting a set of potentially relevant and diverse images. Considering the semantic gap between low-level features and high-level semantics in images, the last step is necessary and consists in images being annotated and assessed by the crowd. The aim is to evaluate the level of representativeness and diversity of the selected set of images and providing images of highest quality. The method was validated in the context of the retrieval of images with monuments and using more than 30,000 images retrieved from various social image search platforms

Simple coarse graining and sampling strategies for image recognition

A conceptually simple way to classify images is to directly compare test-set data and training-set data. The accuracy of this approach is limited by the method of comparison used, and by the extent to which the training-set data cover configuration space. Here we show that this coverage can be substantially increased using simple strategies of coarse graining (replacing groups of images by their centroids) and stochastic sampling (using distinct sets of centroids in combination). We use the MNIST and Fashion-MNIST data sets to show that coarse graining can be used to convert a subset of training images into many fewer image centroids, with no loss of accuracy of classification of test-set images by direct (nearest-neighbor) classification. Distinct batches of centroids can be used in combination as a means of stochastically sampling configuration space, and can classify test-set data more accurately than can the unaltered training set. The approach works most naturally with multiple processors in parallel

High-Throughput Classification of Radiographs Using Deep Convolutional Neural Networks.

The study aimed to determine if computer vision techniques rooted in deep learning can use a small set of radiographs to perform clinically relevant image classification with high fidelity. One thousand eight hundred eighty-five chest radiographs on 909 patients obtained between January 2013 and July 2015 at our institution were retrieved and anonymized. The source images were manually annotated as frontal or lateral and randomly divided into training, validation, and test sets. Training and validation sets were augmented to over 150,000 images using standard image manipulations. We then pre-trained a series of deep convolutional networks based on the open-source GoogLeNet with various transformations of the open-source ImageNet (non-radiology) images. These trained networks were then fine-tuned using the original and augmented radiology images. The model with highest validation accuracy was applied to our institutional test set and a publicly available set. Accuracy was assessed by using the Youden Index to set a binary cutoff for frontal or lateral classification. This retrospective study was IRB approved prior to initiation. A network pre-trained on 1.2 million greyscale ImageNet images and fine-tuned on augmented radiographs was chosen. The binary classification method correctly classified 100 % (95 % CI 99.73-100 %) of both our test set and the publicly available images. Classification was rapid, at 38 images per second. A deep convolutional neural network created using non-radiological images, and an augmented set of radiographs is effective in highly accurate classification of chest radiograph view type and is a feasible, rapid method for high-throughput annotation