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.
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