Abstract-Over the past few decades, a large family of algorithms-supervised or unsupervised; stemming from statistics or geometry theory-has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algorithm called Marginal Fisher Analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. We show that MFA effectively overcomes the limitations of the traditional Linear Discriminant Analysis algorithm due to data distribution assumptions and available projection directions. Real face recognition experiments show the superiority of our proposed MFA in comparison to LDA, also for corresponding kernel and tensor extensions.

We demonstrate trans-rectal optical tomography of the prostate using an endo-rectal near-infrared (NIR) applicator integrated with a transrectal ultrasound (TRUS) probe. The endo-rectal NIR applicator incorporated a design presented in our previously reported work. A continuous-wave NIR optical tomography system is combined with a commercial US scanner to form the dual-modality imager. Sagittal transrectal imaging is performed concurrently by endo-rectal NIR and TRUS. The TRUS ensures accurate positioning of the NIR applicator as well as guides NIR image reconstruction using the spatial prior of the target. The use of a condom, which is standard for TRUS, is found to have minimal effect on trans-rectal NIR imaging. Tests on avian tissues validates that NIR imaging can recover the absorption contrast of a target, and its accuracy is improved when the TRUS spatial prior is incorporated. Trans-rectal NIR/US imaging of a healthy canine prostate in situ is reported.

Deep convolutional neural networks have promoted significant progress in building extraction from high-resolution remote sensing imagery. Although most of such work focuses on modifying existing image segmentation networks in computer vision, we propose a new network in this paper, Deep Encoding Network (DE-Net), that is designed for the very problem based on many lately introduced techniques in image segmentation. Four modules are used to construct DE-Net: the inceptionstyle downsampling modules combining a striding convolution layer and a max-pooling layer, the encoding modules comprising six linear residual blocks with a scaled exponential linear unit (SELU) activation function, the compressing modules reducing the feature channels, and a densely upsampling module that enables the network to encode spatial information inside feature maps. Thus, DE-Net achieves stateoftheart performance on the WHU Building Dataset in recall, F1-Score, and intersection over union (IoU) metrics without pretraining. It also outperformed several segmentation networks in our self-built Suzhou Satellite Building Dataset. The experimental results validate the effectiveness of DE-Net on building extraction from aerial imagery and satellite imagery. It also suggests that given enough training data, designing and training a network from scratch may excel fine-tuning models pre-trained on datasets unrelated to building extraction.

We investigate the feasibility of trans-rectal optical tomography of the prostate using an endo-rectal near-infrared (NIR) applicator that is to be integrated with a trans-rectal ultrasound (TRUS) probe. Integration with TRUS ensures accurate endo-rectal positioning of the NIR applicator and the utility of using TRUS spatial prior information to guide NIR image reconstruction. The prostate NIR image reconstruction is challenging even with the use of spatial prior owing to the anatomic complexity of the imaging domain. A hierarchical reconstruction algorithm is developed that implements cascaded initial-guesses for nested domains. This hierarchical image reconstruction method is then applied to evaluating a number of NIR applicator designs for integration with a sagittal TRUS transducer. A NIR applicator configuration feasible for instrumentation development is proposed that contains one linear array of optodes on each lateral side of the sagittal TRUS transducer. The performance of this NIR applicator is characterized for the recovery of single tumor mimicking lesion as well as dual targets in the prostate. The results suggest a strong feasibility of transrectal prostate imaging by use of the endo-rectal NIR/US probe.

The subject of this work is to establish a mathematical framework that provides the basis and tool for automated reasoning and uncertainty reasoning based on linguistic information. This paper focuses on a flexible and realistic approach, i.e., the use of linguistic terms, specially, the symbolic approach acts by direct computation on linguistic terms. An algebra model with linguistic terms, which is based on a logical algebraic structure, i.e., lattice implication algebra, is constructed and applied to represent imprecise information and deal with both comparable and incomparable linguistic terms (i.e., non-ordered linguistic terms). Some properties and its substructures of this algebraic model are discussed.

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This is Part II of the work that examines photon diffusion in a homogenous medium enclosed by a concave circular cylindrical applicator or enclosing a convex circular cylindrical applicator. Part I of this work [J. Opt. Soc. Am. A 27, 648 (2010)] analytically examined the steady-state photon diffusion between a source and a detector for two specific cases: (1) the detector is placed only azimuthally with respect to the source, and (2) the detector is placed only longitudinally with respect to the source, in the infinitely long concave and convex applicator geometries. For the first case, it was predicted that the decay rate of photon fluence would become smaller in the concave geometry and greater in the convex geometry than that in the semi-infinite geometry for the same source-detector distance. For the second case, it was projected that the decay rate of photon fluence would be greater in the concave geometry and smaller in the convex geometry than that in the semi-infinite geometry for the same source-detector distance. This Part II of the work quantitatively examines these predictions from Part I through several approaches, including (a) the finite-element method, (b) the Monte Carlo simulation, and (c) experimental measurement. Despite that the quantitative examinations have to be conducted for finite cylinder applicators with large length-to-radius ratio to approximate the infinite-length condition modeled in Part I, the results obtained by these quantitative methods for two concave and three convex applicator dimensions validated the qualitative trend predicted by Part I and verified the quantitative accuracy of the analytic treatment of Part I in the diffusion regime of the measurement, at a given set of absorption and reduced scattering coefficients of the medium.

In vivo trans-rectal near-infrared (NIR) optical tomography was performed concurrently with, albeit reconstructed without spatial a prior of, trans-rectal ultrasound (US) on transmissible venereal tumor (TVT) developed as a model in the canine pelvic canal. Studies were taken longitudinally at prior to, 14 days after, and 35 days after the TVT injection. As the tumor grew, the nodules became increasingly hyperabsorptive and moderately hyperscattering on NIR. The regions of strong NIR contrast, especially on absorption images, correlated well with those of US hypoechoic masses indicative of tumors. Combining the information of trans-rectal NIR and US detected the tumor more accurately than did the US alone at 14 days postinjection.