Mutual information is one of the mostly used measures for evaluating image similarity. In this paper, we investigate the application of three different Tsallis-based generalizations of mutual information to analyze the similarity between scanned documents. These three generalizations derive from the Kullback–Leibler distance, the difference between entropy and conditional entropy, and the Jensen–Tsallis divergence, respectively. In addition, the ratio between these measures and the Tsallis joint entropy is analyzed. The performance of all these measures is studied for different entropic indexes in the context of document classification and registration.

Shannon entropy has been commonly used to quantify the image informativeness. The main drawback of this measure is that it does not take into account the spatial distribution of pixels. In this paper, we analyze four information-theoretic measures that overcome this limitation. Three of them (entropy rate, excess entropy, and erasure entropy) consider the image as a stationary stochastic process, while the fourth (partitional information) is based on an information channel between image regions and histogram bins. Experimental results, applied to natural and synthetic images, show the performance of these measures to characterize several informativeness aspects of an image. We also analyze their behavior under some image effects such as blurring, contrast change, and noise.

Frequency histograms are ubiquitous, being practically used in any field of science. In this paper, we present a partial order for frequency histograms and, to our knowledge, no order of this kind has been yet defined. This order is based on the stochastic order of discrete probability distributions and it has invariance properties that make it unique. First, we model a frequency histogram as a sequence of bins associated with a discrete probability (or relative frequency) distribution. Then, we consider that two histograms are ordered if they are defined on the same sequence of bins and their respective frequency distributions are stochastically ordered. The ordering can be easily spotted because the respective cumulative distribution functions of the frequencies of two ordered histograms do not cross each other. Finally, with each bin we can associate a representative value of the bin, and for two ordered histograms it holds that all quasi-arithmetic means (such as arithmetic, harmonic, and geometric mean) of the representative values weighted by the frequencies are ordered in the same direction than the histograms are. Our theoretical study is supported by three experiments in the fields of image processing, traffic flow, and income distribution.

“Wasan” is the collective name given to a set of mathematical texts written in Japan in the Edo period (1603–1867). These documents represent a unique type of mathematics and amalgamate the mathematical knowledge of a time and place where major advances where reached. Due to these facts, Wasan documents are considered to be of great historical and cultural significance. This paper presents a fully automatic algorithmic process to first detect the kanji characters in Wasan documents and subsequently classify them using deep learning networks. We pay special attention to the results concerning one particular kanji character, the “ima” kanji, as it is of special importance for the interpretation of Wasan documents. As our database is made up of manual scans of real historical documents, it presents scanning artifacts in the form of image noise and page misalignment. First, we use two preprocessing steps to ameliorate these artifacts. Then we use three different blob detector algorithms to determine what parts of each image belong to kanji Characters. Finally, we use five deep learning networks to classify the detected kanji. All the steps of the pipeline are thoroughly evaluated, and several options are compared for the kanji detection and classification steps. As ancient kanji database are rare and often include relatively few images, we explore the possibility of using modern kanji databases for kanji classification. Experiments are run on a dataset containing 100 Wasan book pages. We compare the performance of three blob detector algorithms for kanji detection obtaining 79.60% success rate with 7.88% false positive detections. Furthermore, we study the performance of five well-known deep learning networks and obtain 99.75% classification accuracy for modern kanji and 90.4% for classical kanji. Finally, our full pipeline obtains 95% correct detection and classification of the “ima” kanji with 3% False positives.

Tissue establishments are responsible for processing, testing, preserving, storing, and distributing allografts from donors to be transplanted into recipients. In some situations, a matching process is required to determine the allograft that best fits the recipient. Allograft morphology is a key consideration for the matching process. The manual procedures applied to obtain these parameters make the process error-prone. A new system to manage bone allograft-recipient matching for tissue establishments is proposed. The system requires bone allografts to be digitalized and the resulting images to be stored in a DICOM file. The system provides functionalities to: (i) manage DICOM files (registered in the PACs) from both allografts and recipients; (ii) reconstruct 3D models from DICOM images; (iii) explore 3D models using 2D, 3D, and multiplanar reconstructions; (iv) take allograft and recipient measurements; and (v) visualize and interact with recipient and allograft data simultaneously. The system has been installed in the Barcelona Tissue Bank (Banc de Sang i Teixits), which has digitalized the bone allografts to test the system. A use case with a femur is presented to test all the viewer functionalities. In addition, the recipient-allograft workflow is evaluated to show the steps of the procedure where the viewer can be used. The bone allograft-recipient matching procedure can be optimized using software tools with functionalities to visualize, interact, and take measurements.