A Fixed-Point Model for Pancreas Segmentation in Abdominal CT Scans

Deep neural networks have been widely adopted for automatic organ segmentation from abdominal CT scans. However, the segmentation accuracy of some small organs (e.g., the pancreas) is sometimes below satisfaction, arguably because deep networks are easily disrupted by the complex and variable background regions which occupies a large fraction of the input volume. In this paper, we formulate this problem into a fixed-point model which uses a predicted segmentation mask to shrink the input region. This is motivated by the fact that a smaller input region often leads to more accurate segmentation. In the training process, we use the ground-truth annotation to generate accurate input regions and optimize network weights. On the testing stage, we fix the network parameters and update the segmentation results in an iterative manner. We evaluate our approach on the NIH pancreas segmentation dataset, and outperform the state-of-the-art by more than 4%, measured by the average Dice-S{\o}rensen Coefficient (DSC). In addition, we report 62.43% DSC in the worst case, which guarantees the reliability of our approach in clinical applications.Comment: Accepted to MICCAI 2017 (8 pages, 3 figures

Recurrent Saliency Transformation Network: Incorporating Multi-Stage Visual Cues for Small Organ Segmentation

We aim at segmenting small organs (e.g., the pancreas) from abdominal CT scans. As the target often occupies a relatively small region in the input image, deep neural networks can be easily confused by the complex and variable background. To alleviate this, researchers proposed a coarse-to-fine approach, which used prediction from the first (coarse) stage to indicate a smaller input region for the second (fine) stage. Despite its effectiveness, this algorithm dealt with two stages individually, which lacked optimizing a global energy function, and limited its ability to incorporate multi-stage visual cues. Missing contextual information led to unsatisfying convergence in iterations, and that the fine stage sometimes produced even lower segmentation accuracy than the coarse stage. This paper presents a Recurrent Saliency Transformation Network. The key innovation is a saliency transformation module, which repeatedly converts the segmentation probability map from the previous iteration as spatial weights and applies these weights to the current iteration. This brings us two-fold benefits. In training, it allows joint optimization over the deep networks dealing with different input scales. In testing, it propagates multi-stage visual information throughout iterations to improve segmentation accuracy. Experiments in the NIH pancreas segmentation dataset demonstrate the state-of-the-art accuracy, which outperforms the previous best by an average of over 2%. Much higher accuracies are also reported on several small organs in a larger dataset collected by ourselves. In addition, our approach enjoys better convergence properties, making it more efficient and reliable in practice.Comment: Accepted to CVPR 2018 (10 pages, 6 figures

Influence of welding quality on stability of SUS304 tube-compression by viscous pressure forming

One of the major problems affecting viscous pressure forming (VPF) is the stability of tubecompression, whereas the main defect influencing the stability of welded tube-compression is the quality of welded joints. This article utilizes the finite element method to analyze the influence of weld joint strength and width on stability of SUS304 tube-compression by VPF. Meanwhile, SUS304 welded tube-blanks with different weld joint strength and width are obtained by plasma welding, TIG-Tungsten Inert Gas welding, laser welding and high frequency welding and then the stability test by VPF is carried out. The results showed that the weld joint strength and width affect the stability of tube-compression. The system and process of controlling weld joint width can improve the stability of tube-blank preferably relative to weld joint strength

Influence of welding quality on stability of SUS304 tube-compression by viscous pressure forming

One of the major problems affecting viscous pressure forming (VPF) is the stability of tubecompression, whereas the main defect influencing the stability of welded tube-compression is the quality of welded joints. This article utilizes the finite element method to analyze the influence of weld joint strength and width on stability of SUS304 tube-compression by VPF. Meanwhile, SUS304 welded tube-blanks with different weld joint strength and width are obtained by plasma welding, TIG-Tungsten Inert Gas welding, laser welding and high frequency welding and then the stability test by VPF is carried out. The results showed that the weld joint strength and width affect the stability of tube-compression. The system and process of controlling weld joint width can improve the stability of tube-blank preferably relative to weld joint strength

Visual Concepts and Compositional Voting

It is very attractive to formulate vision in terms of pattern theory \cite{Mumford2010pattern}, where patterns are defined hierarchically by compositions of elementary building blocks. But applying pattern theory to real world images is currently less successful than discriminative methods such as deep networks. Deep networks, however, are black-boxes which are hard to interpret and can easily be fooled by adding occluding objects. It is natural to wonder whether by better understanding deep networks we can extract building blocks which can be used to develop pattern theoretic models. This motivates us to study the internal representations of a deep network using vehicle images from the PASCAL3D+ dataset. We use clustering algorithms to study the population activities of the features and extract a set of visual concepts which we show are visually tight and correspond to semantic parts of vehicles. To analyze this we annotate these vehicles by their semantic parts to create a new dataset, VehicleSemanticParts, and evaluate visual concepts as unsupervised part detectors. We show that visual concepts perform fairly well but are outperformed by supervised discriminative methods such as Support Vector Machines (SVM). We next give a more detailed analysis of visual concepts and how they relate to semantic parts. Following this, we use the visual concepts as building blocks for a simple pattern theoretical model, which we call compositional voting. In this model several visual concepts combine to detect semantic parts. We show that this approach is significantly better than discriminative methods like SVM and deep networks trained specifically for semantic part detection. Finally, we return to studying occlusion by creating an annotated dataset with occlusion, called VehicleOcclusion, and show that compositional voting outperforms even deep networks when the amount of occlusion becomes large.Comment: It is accepted by Annals of Mathematical Sciences and Application

Permutation Polynomials and Their Differential Properties over Residue Class Rings

This paper mainly focuses on permutation polynomials over the residue class ring $\mathbb{Z}_{N}$, where $N>3$ is composite. We have proved that for the polynomial $f(x)=a_{1}x^{1}+\cdots +a_{k}x^{k}$ with integral coefficients, $f(x)\bmod N$ permutes $\mathbb{Z}_{N}$ if and only if $f(x)\bmod N$ permutes $S_{\mu}$ for all $\mu \mid N$, where $S_{\mu}=\{0< t <N: \gcd(N,t)=\mu\}$ and $S_{N}=S_{0}=\{0\}$. Based on it, we give a lower bound of the differential uniformities for such permutation polynomials, that is, $\delta (f)\geq \frac{N}{\#S_{a}}$, where $a$ is the biggest nontrivial divisor of $N$. Especially, $f(x)$ can not be APN permutations over the residue class ring \mathbb{Z}_{N}$. It is also proved that$f(x)\bmod N$and$(f(x)+x)\bmod N$can not permute$\mathbb{Z}_{N}$at the same time when$N$ is even