Color Image and Multispectral Image Denoising Using Block Diagonal Representation

Filtering images of more than one channel is challenging in terms of both efficiency and effectiveness. By grouping similar patches to utilize the self-similarity and sparse linear approximation of natural images, recent nonlocal and transform-domain methods have been widely used in color and multispectral image (MSI) denoising. Many related methods focus on the modeling of group level correlation to enhance sparsity, which often resorts to a recursive strategy with a large number of similar patches. The importance of the patch level representation is understated. In this paper, we mainly investigate the influence and potential of representation at patch level by considering a general formulation with block diagonal matrix. We further show that by training a proper global patch basis, along with a local principal component analysis transform in the grouping dimension, a simple transform-threshold-inverse method could produce very competitive results. Fast implementation is also developed to reduce computational complexity. Extensive experiments on both simulated and real datasets demonstrate its robustness, effectiveness and efficiency

The thickness of amalgamations of graphs

The thickness $\theta(G)$ of a graph $G$ is the minimum number of planar spanning subgraphs into which the graph $G$ can be decomposed. As a topological invariant of a graph, it is a measurement of the closeness to planarity of a graph, and it also has important applications to VLSI design. In this paper, the thickness of graphs that are obtained by vertex-amalgamation and bar-amalgamation of any two graphs whose thicknesses are known are obtained, respectively. And the lower and upper bounds for the thickness of graphs that are obtained by edge-amalgamation and 2-vertex-amalgamation of any two graphs whose thicknesses are known are also derived, respectively.Comment: 5 page

Collaborative Receptive Field Learning

The challenge of object categorization in images is largely due to arbitrary translations and scales of the foreground objects. To attack this difficulty, we propose a new approach called collaborative receptive field learning to extract specific receptive fields (RF's) or regions from multiple images, and the selected RF's are supposed to focus on the foreground objects of a common category. To this end, we solve the problem by maximizing a submodular function over a similarity graph constructed by a pool of RF candidates. However, measuring pairwise distance of RF's for building the similarity graph is a nontrivial problem. Hence, we introduce a similarity metric called pyramid-error distance (PED) to measure their pairwise distances through summing up pyramid-like matching errors over a set of low-level features. Besides, in consistent with the proposed PED, we construct a simple nonparametric classifier for classification. Experimental results show that our method effectively discovers the foreground objects in images, and improves classification performance.Comment: 16 pages, 8 figure

Sharp Moser-Trudinger inequalities on Riemannian manifolds with Negative curvature

Let $M$ be a complete, simply connected Riemannian manifold with negative curvature. We obtain some Moser-Trudinger inequalities with sharp constants on $M$.Comment: 13 page

Learning Mid-Level Features and Modeling Neuron Selectivity for Image Classification

We now know that mid-level features can greatly enhance the performance of image learning, but how to automatically learn the image features efficiently and in an unsupervised manner is still an open question. In this paper, we present a very efficient mid-level feature learning approach (MidFea), which only involves simple operations such as $k$-means clustering, convolution, pooling, vector quantization and random projection. We explain why this simple method generates the desired features, and argue that there is no need to spend much time in learning low-level feature extractors. Furthermore, to boost the performance, we propose to model the neuron selectivity (NS) principle by building an additional layer over the mid-level features before feeding the features into the classifier. We show that the NS-layer learns category-specific neurons with both bottom-up inference and top-down analysis, and thus supports fast inference for a query image. We run extensive experiments on several public databases to demonstrate that our approach can achieve state-of-the-art performances for face recognition, gender classification, age estimation and object categorization. In particular, we demonstrate that our approach is more than an order of magnitude faster than some recently proposed sparse coding based methods.Comment: 19 pages, 14 figure

Incorporating Sememes into Chinese Definition Modeling

Chinese definition modeling is a challenging task that generates a dictionary definition in Chinese for a given Chinese word. To accomplish this task, we construct the Chinese Definition Modeling Corpus (CDM), which contains triples of word, sememes and the corresponding definition. We present two novel models to improve Chinese definition modeling: the Adaptive-Attention model (AAM) and the Self- and Adaptive-Attention Model (SAAM). AAM successfully incorporates sememes for generating the definition with an adaptive attention mechanism. It has the capability to decide which sememes to focus on and when to pay attention to sememes. SAAM further replaces recurrent connections in AAM with self-attention and relies entirely on the attention mechanism, reducing the path length between word, sememes and definition. Experiments on CDM demonstrate that by incorporating sememes, our best proposed model can outperform the state-of-the-art method by +6.0 BLEU

Morphology and structure of extremely red objects at z∼1z\sim1 in the CANDELS-COSMOS field

Using high-resolution HST/Wide Field Camera 3 F125W imaging from the CANDELS-COSMOS field, we report the the structural and morphological properties of Extremely Red Objects (EROs) at $z\sim1$. Based on the UVJ color criteria, we separate EROs into two types: old passive galaxies (OGs) and dusty star-forming galaxies (DGs). For a given stellar mass, we find that the mean size of OGs (DGs) is smaller by a factor of $\sim2$ (1.5) than that of present-day early-type (late-type) galaxies at rest-frame optical wavelength. We derive the average effective radii of OGs and DGs, corresponding to $2.09\pm1.13$ kpc and $3.27\pm1.14$ kpc, respectively. Generally, The DGs are heterogeneous, with mixed features including bulges, disks, and irregular structures, with relatively high $M_{\rm 20}$, small size and low $G$, while OGs are elliptical-like compact morphologies with lower $M_{\rm 20}$, larger size and higher $G$, indicating the more concentrated and symmetric spatial extent of stellar population distribution in OGs than DGs. The findings imply that OGs and DGs have different evolutionary processes, and the minor merger scenario is the most likely mechanism for the structural properties of OGs. However, the size evolution of DGs is possibly due to the secular evolution of galaxies

Predicting the outcomes of fuel drop impact on heated surfaces using SPH simulation

The impact of liquid drops on a heated solid surface is of great importance in many engineering applications. This paper describes the simulation of the drop-wall interaction using the smoothed particle hydrodynamics (SPH) method. The SPH method is a Lagrangian mesh-free method that can be used to solve the fluid equations. A vaporization model based on the SPH formulation was also developed and implemented. A parametric study was conducted to characterize the effects of impact velocity and wall temperature on the impact outcome. The present numerical method was able to predict different outcomes, such as deposition, splash, breakup, and rebound (i.e., Leidenfrost phenomenon). The present numerical method was used to construct a regime diagram for describing the impact of an iso-octane drop on a heated surface at various Weber numbers and wall temperatures

Simulation of Drop Impact on a Hot Wall using SPH Method with Peng-Robinson Equation of State

This study presents a smoothed particle hydrodynamics (SPH) method with Peng-Robinson equation of state for simulating drop vaporization and drop impact on a hot surface. The conservation equations of momentum and energy and Peng-Robinson equation of state are applied to describe both the liquid and gas phases. The governing equations are solved numerically by the SPH method. The phase change between the liquid and gas phases are simulated directly without using any phase change models. The numerical method is validated by comparing numerical results with analytical solutions for the vaporization of n-heptane drops at different temperatures. Using the SPH method, the processes of n-heptane drops impacting on a solid wall with different temperatures are studied numerically. The results show that the size of the film formed by drop impact decreases when temperature increases. When the temperature is high enough, the drop will rebound.Comment: 6 pages, 4 figures, 10th U.S. National Combustion Meeting, April 23-26, 2017, College Park, Marylan

Weakly Supervised Attention Learning for Textual Phrases Grounding

Grounding textual phrases in visual content is a meaningful yet challenging problem with various potential applications such as image-text inference or text-driven multimedia interaction. Most of the current existing methods adopt the supervised learning mechanism which requires ground-truth at pixel level during training. However, fine-grained level ground-truth annotation is quite time-consuming and severely narrows the scope for more general applications. In this extended abstract, we explore methods to localize flexibly image regions from the top-down signal (in a form of one-hot label or natural languages) with a weakly supervised attention learning mechanism. In our model, two types of modules are utilized: a backbone module for visual feature capturing, and an attentive module generating maps based on regularized bilinear pooling. We construct the model in an end-to-end fashion which is trained by encouraging the spatial attentive map to shift and focus on the region that consists of the best matched visual features with the top-down signal. We demonstrate the preliminary yet promising results on a testbed that is synthesized with multi-label MNIST data.Comment: 4 pages, 3 figure