Conventional radiography is the widely used imaging technology in diagnosing, monitoring, and prognosticating musculoskeletal (MSK) diseases because of its easy availability, versatility, and cost-effectiveness. Bone overlaps are prevalent in conventional radiographs, and can impede the accurate assessment of bone characteristics by radiologists or algorithms, posing significant challenges to conventional clinical diagnosis and computer-aided diagnosis. This work initiated the study of a challenging scenario - bone layer separation in conventional radiographs, in which separate overlapped bone regions enable the independent assessment of the bone characteristics of each bone layer and lay the groundwork for MSK disease diagnosis and its automation. This work proposed a Bone Layer Separation GAN (BLS-GAN) framework that can produce high-quality bone layer images with reasonable bone characteristics and texture. This framework introduced a reconstructor based on conventional radiography imaging principles, which achieved efficient reconstruction and mitigates the recurrent calculations and training instability issues caused by soft tissue in the overlapped regions. Additionally, pre-training with synthetic images was implemented to enhance the stability of both the training process and the results. The generated images passed the visual Turing test, and improved performance in downstream tasks. This work affirms the feasibility of extracting bone layer images from conventional radiographs, which holds promise for leveraging layer separation technology to facilitate more comprehensive analytical research in MSK diagnosis, monitoring, and prognosis.

Rheumatoid arthritis (RA) is a chronic autoimmune disease characterized by joint inflammation and progressive structural damage. Joint space width (JSW) is a critical indicator in conventional radiography (CR) for evaluating disease progression, which has become a prominent research topic in computer-aided diagnostic (CAD) systems. However, deep learning-based radiological CAD systems for JSW analysis face significant challenges in data quality, including data imbalance, limited variety, and annotation difficulties. This work introduced a challenging image synthesis scenario and proposed Layer Separation Networks (LSN) to accurately separate the soft tissue layer, the upper bone layer, and the lower bone layer in conventional radiographs of finger joints. Using these layers, the adjustable JSW images can be synthesized to address data quality challenges and achieve ground truth (GT) generation. Experimental results demonstrated that LSN-based synthetic images closely resemble real radiographs, and significantly enhanced the performance in downstream tasks. The code and dataset are available at: https://github.com/pokeblow/LSN.

We developed an automatic ensemble training method for fusing massive-training artificial neural network (MTANN) deep-learning modules in classification between polyps and non-polyps in CT colonography. We started from an initial MTANN module that had been trained with an initial set of polyps and non-polyps. We applied the trained initial module to polyps and non-polyps to analyze the weakness of the initial module. We arranged the output scores of the initial module to form a score scale in receiver-operating-characteristic (ROC) space, representing the “degree of difficulty” in distinction between polyps and non-polyps by the initial module. Based on the score-space, several sets of training polyps and non-polyps with different degrees of difficulties were determined. We trained several MTANN modules with the several sets of training samples so that each module became an expert at a certain level of difficulty. We then combined expert modules with a mixing module to form a “mixture of expert” MTANNs. Our database consisted of CT colonography datasets acquired from 100 patients, including 26 polyps. The mixture of expert MTANNs with the ensemble training method distinguished all polyps correctly from more than 50% of the non-polyps. We compared the effectiveness of the ensemble training with that of training with manually selected cases. The performance of the mixture of expert MTANNs with ensemble training method was superior to that of the “reference-standard” MTANNs trained with manually selected cases, which could reduce the cost of the manual selection.

Automated radiology report generation aims to generate paragraphs that describe fine-grained visual differences among cases, especially those between the normal and the diseased. Existing methods seldom consider the cross-modal alignment between textual and visual features and tend to ignore disease tags as an auxiliary for report generation. To bridge the gap between textual and visual information, in this study, we propose a “Jointly learning framework for automated disease Prediction and radiology report Generation (JPG)” to improve the quality of reports through the interaction between the main task (report generation) and two auxiliary tasks (feature alignment and disease prediction). The feature alignment and disease prediction help the model learn text-correlated visual features and record diseases as keywords so that it can output high-quality reports. Besides, the improved reports in turn provide additional harder samples for feature alignment and disease prediction to learn more precise visual and textual representations and improve prediction accuracy. All components are jointly trained in a manner that helps improve them iteratively and progressively. Experimental results demonstrate the effectiveness of JPG on the most commonly used IU X-RAY dataset, showing its superior performance over multiple state-of-the-art image captioning and medical report generation methods with regard to BLEU, METEOR, and ROUGE metrics.

Federated Learning (FL) enables multiple institutes to train models collaboratively without sharing private data. Most of the current FL research focuses on perspectives such as communication efficiency, privacy protection, and personalization. Almost all work assumed that the data of FL are already ideally collected. However, in medical image analysis scenarios, data annotation demands both expertise and tedious labor, which means it is a critical problem that cannot be neglected in FL. In this study, we proposed a federated active learning (FedAL) framework that can decrease the annotation workload while maintaining the performance of FL. To the best of our knowledge, this is the first federated active learning framework working on medical images. Using only up to 50% of samples, our FedAL was able to achieve state-of-the-art performance on the real-world dermoscopic task. Our FedAL outperformed active learning methods under FL and achieved the performance comparable to full data FL.

The aim of this article is to develop a methodology for measuring thedegree of unpredictabilityin dynamical systems with memory, i.e., systems with responses dependent on a history of past states. The proposed model is generic, and can be employed in a variety of settings, although its applicability here is examined in the particular context of an industrial environment: gas turbine engines. The given approach consists in approximating the probability distribution of the outputs of a system with a deep recurrent neural network; such networks are capable of exploiting the memory in the system for enhanced forecasting capability. Once the probability distribution is retrieved, theentropyormissing informationabout the underlying process is computed, which is interpreted as the uncertainty with respect to the system's behavior. Hence, the model identifies how far the system dynamics are from its typical response, in order to evaluate the system reliability and to predict system faults and/ornormal accidents. The validity of the model is verified with sensor data recorded from commissioning gas turbines, belonging to normal and faulty conditions.

In this paper, a methodology for assessing the unpredictability of systems with memory was developed. The proposed approach consists in approximating the probability distribution exhibited by the response of a system, understood as a stochastic process, with a deep recurrent neural network; such networks offer increased forecasting capability by exploiting an accumulative register of previous system states. Once the probability distribution is computed, the uncertainty or entropy of the underlying process is measured. This measure determines the degree of regularity in the system, and identifies how atypical the system dynamics are. The proposed model was validated by identifying industrial gas turbine engine faults from recorded sensor data.

Lung nodules that overlap with ribs and clavicles in chest radiographs can be difficult to be detected by radiologists as well as by computer-aided detection systems. Removing bony structures would result in better visualization of undetectable lesions. Our purpose in this study was to develop a deep-learning scheme to separate ribs and clavicles from soft tissue in chest radiographs. To achieve this, we developed a mixture of anatomy-specific, orientation-frequency-specific (ASOFS) deep neural network convolution (NNC) experts. Anatomy-specific (AS) architecture was designed to separate bony structures from soft tissue in different lung segments. The orientation-frequency-specific (OFS) was designed to decompose bone and soft-tissue structures into specific orientation-frequency components of different scales using a multi-resolution decomposition technique. For evaluation, we used a database of 118 chest radiographs with pulmonary nodules. Quantitative and qualitative evaluation showed that our ASOFS NNC was superior to a state-of-the-art bone-suppression technique. Particularly, our NNC scheme separated ribs and clavicles from soft tissue, while it was better able to maintain the conspicuity of lung nodules and vessels, comparing to the reference technique. Therefore, our deep-learning scheme can be useful for radiologists as well as CAD systems in detection of lung nodules in chest radiographs.

Deep learning has recently proven extremely successful in many low-level image-processing tasks including natural image denoising. However, with regards to designing deep models for practical image processing, there are numerous essential viewpoints that one ought to consider. In this work, we first aimed to reply to probably the most critical design questions through theoretical analysis and extensive experiments: How deep and wide a deep denoiser should and can be? Does denoising performance get improved by using residual learning? Can and should we switch from the region-based to image-based models? And second, based on our analysis, we designed a deep neural network for natural image denoising which was hundred-layer deep, exploited both internal and external residual learning, and was trained in an image-based fashion. Our deep denoiser achieved the state-of-the-art results quantitatively and qualitatively on multiple datasets including one with more than 10,000 images.

Half of the polyps surgically removed during conventional colonoscopy are benign with no malignant potential. Our purpose was to develop a CADx system for distinction between neoplastic and non-neoplastic lesions in CTC to reduce "unnecessary" colonoscopic polypectomy. Although computer aided detection (CADe) systems have been developed, less attention was given to the development of CADx systems. Our CADx system consists of shape-index-based coarse segmentation of lesions, 3D volume growing and sub-voxel refinement for fine segmentation of lesions, morphologic and texture feature analysis, Wilks' lambda-based stepwise feature selection, linear discriminant analysis for providing an integrated imaging biomarker for diagnosis of neoplastic lesions. Our database contained biopsy-confirmed 54 neoplastic lesions in 29 patients and 14 non-neoplastic lesions in 10 patients. Our CADx system integrating the selected features was able to determine an accurate likelihood of being a neoplasm and distinguish 87% (47/54) neoplastic lesions from 57% (8/14) non-neoplastic lesions correctly only using computed tomography (CT) images, achieving an area under the receiver operating characteristic curve (AUC) of 0.82. This study showed the potential of the use of CTC as a diagnostic tool beyond already accepted detection, thus, CTC with CADx would be potentially useful for reducing "unnecessary" polypectomy.

This paper proposes a new approach to label-equivalence-based two-scan connected-component labeling. We use two strategies to reduce repeated checking-pixel work for labeling. The first is that instead of scanning image lines one by one and processing pixels one by one as in most conventional two-scan labeling algorithms, we scan image lines alternate lines, and process pixels two by two. The second is that by considering the transition of the configuration of pixels in the mask, we utilize the information detected in processing the last two pixels as much as possible for processing the current two pixels. With our method, any pixel checked in the mask when processing the current two pixels will not be checked again when the next two pixels are processed; thus, the efficiency of labeling can be improved. Experimental results demonstrated that our method was more efficient than all conventional labeling algorithms.

We propose a feature selection method based on a sequential forward floating selection (SFFS) procedure to improve the performance of a classifier in computerized detection of polyps in CT colonography (CTC). The feature selection method is coupled with a nonlinear support vector machine (SVM) classifier. Unlike the conventional linear method based on Wilks' lambda, the proposed method selected the most relevant features that would maximize the area under the receiver operating characteristic curve (AUC), which directly maximizes classification performance, evaluated based on AUC value, in the computer-aided detection (CADe) scheme. We presented two variants of the proposed method with different stopping criteria used in the SFFS procedure. The first variant searched all feature combinations allowed in the SFFS procedure and selected the subsets that maximize the AUC values. The second variant performed a statistical test at each step during the SFFS procedure, and it was terminated if the increase in the AUC value was not statistically significant. The advantage of the second variant is its lower computational cost. To test the performance of the proposed method, we compared it against the popular stepwise feature selection method based on Wilks' lambda for a colonic-polyp database (25 polyps and 2624 nonpolyps). We extracted 75 morphologic, gray-level-based, and texture features from the segmented lesion candidate regions. The two variants of the proposed feature selection method chose 29 and 7 features, respectively. Two SVM classifiers trained with these selected features yielded a 96% by-polyp sensitivity at false-positive (FP) rates of 4.1 and 6.5 per patient, respectively. Experiments showed a significant improvement in the performance of the classifier with the proposed feature selection method over that with the popular stepwise feature selection based on Wilks' lambda that yielded 18.0 FPs per patient at the same sensitivity level.

Most lung nodules that are missed by radiologists as well as computer-aided detection (CADe) schemes overlap with ribs or clavicles in chest radiographs (CXRs). The purpose of this study was to separate bony structures such as ribs and clavicles from soft tissue in CXRs. To achieve this, we developed anatomically specific multiple massive-training artificial neural networks (MTANNs) combined with total variation (TV) minimization smoothing and a histogram-matching-based consistency improvement method. The anatomically specific multiple MTANNs were designed to separate bones from soft tissue in different anatomic segments of the lungs. Each of the MTANNs was trained with the corresponding anatomic segment in the teaching bone images. The output segmental images from the multiple MTANNs were merged to produce an entire bone image. TV minimization smoothing was applied to the bone image for reduction of noise while preserving edges. This bone image was then subtracted from the original CXR to produce a soft-tissue image where bones were separated out. This new method was compared with conventional MTANNs with a database of 110 CXRs with nodules. Our new anatomically specific MTANNs separated rib edges, ribs close to the lung wall, and the clavicles from soft tissue in CXRs to a substantially higher level than did the conventional MTANNs, while the conspicuity of lung nodules and vessels was maintained. Thus, our technique for bone-soft-tissue separation by means of our new MTANNs would be potentially useful for radiologists as well as CADe schemes in detection of lung nodules on CXRs.

Whenever one wants to distinguish, recognize, and/or measure objects (connected components) in binary images, labeling is required. This paper presents two efficient label-equivalence-based connected-component labeling algorithms for 3-D binary images. One is voxel based and the other is run based. For the voxel-based one, we present an efficient method of deciding the order for checking voxels in the mask. For the run-based one, instead of assigning each foreground voxel, we assign each run a provisional label. Moreover, we use run data to label foreground voxels without scanning any background voxel in the second scan. Experimental results have demonstrated that our voxel-based algorithm is efficient for 3-D binary images with complicated connected components, that our run-based one is efficient for those with simple connected components, and that both are much more efficient than conventional 3-D labeling algorithms.

This paper presents a run- and label-equivalence-based one-and-a-half-scan algorithm for labeling connected components in a binary image. Major differences between our algorithm and conventional label-equivalence-based algorithms are: (1) all conventional label-equivalence-based algorithms scan all pixels in the given image at least twice, whereas our algorithm scans background pixels once and object pixels twice; (2) all conventional label-equivalence-based algorithms assign a provisional label to each object pixel in the first scan and relabel the pixel in the later scan(s), whereas our algorithm assigns a provisional label to each run in the first scan, and after resolving label equivalences between runs, by using the recorded run data, it assigns each object pixel a final label directly. That is, in our algorithm, relabeling of object pixels is not necessary any more. Experimental results demonstrated that our algorithm is highly efficient on images with many long runs and/or a small number of object pixels. Moreover, our algorithm is directly applicable to run-length-encoded images, and we can obtain contours of connected components efficiently.

A major challenge in the current computer-aided detection (CAD) of polyps in CT colonography (CTC) is to reduce the number of false-positive (FP) detections while maintaining a high sensitivity level. A pattern-recognition technique based on the use of an artificial neural network (ANN) as a filter, which is called a massive-training ANN (MTANN), has been developed recently for this purpose. The MTANN is trained with a massive number of subvolumes extracted from input volumes together with the teaching volumes containing the distribution for the "likelihood of being a polyp;" hence the term "massive training." Because of the large number of subvolumes and the high dimensionality of voxels in each input subvolume, the training of an MTANN is time-consuming. In order to solve this time issue and make an MTANN work more efficiently, we propose here a dimension reduction method for an MTANN by using Laplacian eigenfunctions (LAPs), denoted as LAP-MTANN. Instead of input voxels, the LAP-MTANN uses the dependence structures of input voxels to compute the selected LAPs of the input voxels from each input subvolume and thus reduces the dimensions of the input vector to the MTANN. Our database consisted of 246 CTC datasets obtained from 123 patients, each of whom was scanned in both supine and prone positions. Seventeen patients had 29 polyps, 15 of which were 5-9 mm and 14 were 10-25 mm in size. We divided our database into a training set and a test set. The training set included 10 polyps in 10 patients and 20 negative patients. The test set had 93 patients including 19 polyps in seven patients and 86 negative patients. To investigate the basic properties of a LAP-MTANN, we trained the LAP-MTANN with actual polyps and a single source of FPs, which were rectal tubes. We applied the trained LAP-MTANN to simulated polyps and rectal tubes. The results showed that the performance of LAP-MTANNs with 20 LAPs was advantageous over that of the original MTANN with 171 inputs. To test the feasibility of the LAP-MTANN, we compared the LAP-MTANN with the original MTANN in the distinction between actual polyps and various types of FPs. The original MTANN yielded a 95% (18/19) by-polyp sensitivity at an FP rate of 3.6 (338/93) per patient, whereas the LAP-MTANN achieved a comparable performance, i.e., an FP rate of 3.9 (367/93) per patient at the same sensitivity level. With the use of the dimension reduction architecture, the time required for training was reduced from 38 h to 4 h. The classification performance in terms of the area under the receiver-operating-characteristic curve of the LAP-MTANN (0.84) was slightly higher than that of the original MTANN (0.82) with no statistically significant difference (p-value =0.48).

Segmentation of lesions plays an important role in computer-aided diagnostic (CAD) schemes, because the accuracy of segmentation affects the accuracy of the feature extraction and analysis based on segmented lesions, and therefore, the final accuracy of classification. Accurate segmentation is difficult especially for complicated patterns such as lesions overlapping or touching normal structures, low-contrast lesions, and subtle opacities. With standard segmentation methods, normal structures overlapping or touching lesions are often erroneously included in segmented regions. In addition, normal structures are often segmented erroneously as lesions. Thus, improving the specificity of segmentation methods is very important in the development of a CAD scheme. Our purpose in this study was to develop a supervised lesion segmentation method based on a massive-training artificial neural network (MTANN) filter in a CAD scheme for detection of lung nodules in CT. The MTANN filter was trained with actual nodules in CT images to segment nodules with improved specificity. With the MTANN-based segmentation method, the specificity of the segmentation was improved; thus, the overall performance of our CAD scheme was improved substantially.

Computer-aided diagnostic (CAD) schemes often employ a filter for enhancement of lesions as a preprocessing step for improving sensitivity and specificity. The filter enhances objects similar to a model employed in the filter; e.g., a blob enhancement filter based on the Hessian matrix enhances sphere-like objects. Actual lesions, however, often differ from a simple model, e.g., a lung nodule is generally modeled as a solid sphere, but there are nodules of various shapes and with inhomogeneities inside such as a spiculated one and a ground-glass opacity. Thus, conventional filters often fail to enhance actual lesions. Our purpose in this study was to develop a supervised filter for enhancement of lesions by use of a massive-training artificial neural network (MTANN) in a computer-aided diagnostic (CAD) scheme for detection of lung nodules in CT. The MTANN filter was trained with actual nodules in CT images to enhance actual patterns of nodules. By use of the MTANN filter, the sensitivity and specificity of our CAD scheme were improved substantially. With the database with 69 lung cancers, our CAD scheme with the MTANN filter achieve a 97% sensitivity with 6.7 false positives (FPs) per section, whereas a conventional CAD scheme with a difference-image technique achieved a 96% sensitivity with 19.3 FPs per section.

We present an efficient run-based two-scan algorithm for labeling connected components in a binary image. Unlike conventional label-equivalence-based algorithms, which resolve label equivalences between provisional labels, our algorithm resolves label equivalences between provisional label sets. At any time, all provisional labels that are assigned to a connected component are combined in a set, and the smallest label is used as the representative label. The corresponding relation of a provisional label and its representative label is recorded in a table. Whenever different connected components are found to be connected, all provisional label sets concerned with these connected components are merged together, and the smallest provisional label is taken as the representative label. When the first scan is finished, all provisional labels that were assigned to each connected component in the given image will have a unique representative label. During the second scan, we need only to replace each provisional label by its representative label. Experimental results on various types of images demonstrate that our algorithm outperforms all conventional labeling algorithms.

This paper presents a fast linear-time two-scan algorithm for labeling connected components in binary images. In the first scan, provisional labels are assigned to object pixels in the same way as do most conventional labeling algorithms. To improve efficiency, we use corresponding equivalent label sets and a representative label table for resolving label equivalences. When the first scan is finished, all provisional labels belonging to each connected component in a given image are combined in the corresponding equivalent label set, and they are assigned a unique representative label with the representative label table. During the second scan, by use of the completed representative label table, all provisional labels belonging to each connected component are replaced by their representative label. Our algorithm is very simple in principle, and is easy to implement. Experimental results demonstrated that the efficiency of our algorithm is superior to that of other labeling algorithms.

When lung nodules overlap with ribs or clavicles in chest radiographs, it can be difficult for radiologists as well as computer-aided diagnostic (CAD) schemes to detect these nodules. In this paper, we developed an image-processing technique for suppressing the contrast of ribs and clavicles in chest radiographs by means of a multiresolution massive training artificial neural network (MTANN). An MTANN is a highly nonlinear filter that can be trained by use of input chest radiographs and the corresponding "teaching" images. We employed "bone" images obtained by use of a dual-energy subtraction technique as the teaching images. For effective suppression of ribs having various spatial frequencies, we developed a multiresolution MTANN consisting of multiresolution decomposition/composition techniques and three MTANNs for three different-resolution images. After training with input chest radiographs and the corresponding dual-energy bone images, the multiresolution MTANN was able to provide "bone-image-like" images which were similar to the teaching bone images. By subtracting the bone-image-like images from the corresponding chest radiographs, we were able to produce "soft-tissue-image-like" images where ribs and clavicles were substantially suppressed. We used a validation test database consisting of 118 chest radiographs with pulmonary nodules and an independent test database consisting of 136 digitized screen-film chest radiographs with 136 solitary pulmonary nodules collected from 14 medical institutions in this study. When our technique was applied to nontraining chest radiographs, ribs and clavicles in the chest radiographs were suppressed substantially, while the visibility of nodules and lung vessels was maintained. Thus, our image-processing technique for rib suppression by means of a multiresolution MTANN would be potentially useful for radiologists as well as for CAD schemes in detection of lung nodules on chest radiographs.

Low-dose helical computed tomography (LDCT) is being applied as a modality for lung cancer screening. It may be difficult, however, for radiologists to distinguish malignant from benign nodules in LDCT. Our purpose in this study was to develop a computer-aided diagnostic (CAD) scheme for distinction between benign and malignant nodules in LDCT scans by use of a massive training artificial neural network (MTANN). The MTANN is a trainable, highly nonlinear filter based on an artificial neural network. To distinguish malignant nodules from six different types of benign nodules, we developed multiple MTANNs (multi-MTANN) consisting of six expert MTANNs that are arranged in parallel. Each of the MTANNs was trained by use of input CT images and teaching images containing the estimate of the distribution for the "likelihood of being a malignant nodule," i.e., the teaching image for a malignant nodule contains a two-dimensional Gaussian distribution and that for a benign nodule contains zero. Each MTANN was trained independently with ten typical malignant nodules and ten benign nodules from each of the six types. The outputs of the six MTANNs were combined by use of an integration ANN such that the six types of benign nodules could be distinguished from malignant nodules. After training of the integration ANN, our scheme provided a value related to the "likelihood of malignancy" of a nodule, i.e., a higher value indicates a malignant nodule, and a lower value indicates a benign nodule. Our database consisted of 76 primary lung cancers in 73 patients and 413 benign nodules in 342 patients, which were obtained from a lung cancer screening program on 7847 screenees with LDCT for three years in Nagano, Japan. The performance of our scheme for distinction between benign and malignant nodules was evaluated by use of receiver operating characteristic (ROC) analysis. Our scheme achieved an Az (area under the ROC curve) value of 0.882 in a round-robin test. Our scheme correctly identified 100% (76/76) of malignant nodules as malignant, whereas 48% (200/413) of benign nodules were identified correctly as benign. Therefore, our scheme may be useful in assisting radiologists in the diagnosis of lung nodules in LDCT.

We propose a method for extracting the left ventricular (LV) contours from left ventriculograms by means of a neural edge detector (NED) in order to extract the contours which accord with those traced by a cardiologist. The NED is a supervised edge detector based on a modified multilayer neural network, and is trained by use of a modified back-propagation algorithm. The NED can acquire the function of a desired edge detector through training with a set of input images and the desired edges obtained from the contours traced by a cardiologist. The proposed contour-extraction method consists of 1) detection of "subjective edges" by use of the NED; 2) extraction of rough contours by use of low-pass filtering and edge enhancement; and 3) a contour-tracing method based on the contour candidates synthesized from the edges detected by the NED and the rough contours. Through experiments, it was shown that the proposed method was able to extract the contours in agreement with those traced by an experienced cardiologist, i.e., we achieved an average contour error of 6.2% for left ventriculograms at end-diastole and an average difference between the ejection fractions obtained from the manually traced contours and those obtained from the computer-extracted contours of 4.1%.

We propose a new edge enhancer based on a modified multilayer neural network, which is called a neural edge enhancer (NEE), for enhancing the desired edges clearly from noisy images. The NEE is a supervised edge enhancer: Through training with a set of input noisy images and teaching edges, the NEE acquires the function of a desired edge enhancer. The input images are synthesized from noiseless images by addition of noise. The teaching edges are made from the noiseless images by performing the desired edge enhancer. To investigate the performance, we carried out experiments to enhance edges from noisy artificial and natural images. By comparison with conventional edge enhancers, the following was demonstrated: The NEE was robust against noise, was able to enhance continuous edges from noisy images, and was superior to the conventional edge enhancers in similarity to the desired edges. To gain insight into the nonlinear kernel of the NEE, we performed analyses on the trained NEE. The results suggested that the trained NEE acquired directional gradient operators with smoothing. Furthermore, we propose a method for edge localization for the NEE. We compared the NEE, together with the proposed edge localization method, with a leading edge detector. The NEE was proven to be useful for enhancing edges from noisy images.

Presents a fast algorithm for labeling connected components in binary images based on sequential local operations. A one-dimensional table, which memorizes label equivalences, is used for uniting equivalent labels successively during the operations in forward and backward raster directions. The proposed algorithm has a desirable characteristic: the execution time is directly proportional to the number of pixels in connected components in an image. By comparative evaluations, it has been shown that the efficiency of the proposed algorithm is superior to those of the conventional algorithms.