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

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

Constructing More Quadratic APN Functions with the QAM Method

We found 5412 new quadartic APN on F28 with the QAM method, thus bringing the number of known CCZ-inequivalent APN functions on F28 to 26525. Unfortunately, none of these new functions are CCZ-equivalent to permutations. A (to the best of our knowledge) complete list of known quadratic APN functions, including our new ones, has been pushed to sboxU for ease of study by others. In this paper, we recall how to construct new QAMs from a known one, and present how used the ortho-derivative method to figure out which of our new functions fall into different CCZ-classes. Based on these results and on others on smaller fields, we make to conjectures: that the full list of quadratic APN functions on F28 could be obtained using the QAM approached (provided enormous computing power), and that the total number of CCZ-inequivalent APN functions may overcome 50000

A Probabilistic Secret Sharing Scheme for a Compartmented Access Structure

In a compartmented access structure, there are disjoint participants C1, . . . ,Cm. The access structure consists of subsets of participants containing at least ti from Ci for i = 1, . . . ,m, and a total of at least t0 participants. Tassa [2] asked: whether there exists an efficient ideal secret sharing scheme for such an access structure? Tassa and Dyn [5] presented a solution using the idea of bivariate interpolation and the concept of dual program [9, 10]. For the purpose of practical applications, it is advantageous to have a simple scheme solving the problem. In this paper a simple scheme is given for this problem using the similar idea from [5]

Constructing differential 4-uniform permutations from know ones

It is observed that exchanging two values of a function over ${\mathbb F}_{2^n}$, its differential uniformity and nonlinearity change only a little. Using this idea, we find permutations of differential $4$-uniform over ${\mathbb F}_{2^6}$ whose number of the pairs of input and output differences with differential $4$-uniform is $54$, less than $63$, which provides a solution for an open problem proposed by Berger et al. \cite{ber}. Moreover, for the inverse function over $\mathbb{F}_{2^n}$ ($n$ even), various possible differential uniformities are completely determined after its two values are exchanged. As a consequence, we get some highly nonlinear permutations with differential uniformity $4$ which are CCZ-inequivalent to the inverse function on $\mathbb{F}_{2^n}$

A Matrix Approach for Constructing Quadratic APN Functions

We find a one to one correspondence between quadratic APN functions without linear or constant terms and a special kind of matrices (We call such matrices as QAMs). Based on the nice mathematical structures of the QAMs, we have developed efficient algorithms to construct quadratic APN functions. On $\mathbb{F}_{2^7}$, we have found more than 470 classes of new CCZ-inequivalent quadratic APN functions, which is 20 times more than the known ones. Before this paper, there are only 23 classes of CCZ-inequivalent APN functions on $\mathbb{F}_{2^{8}}$ have been found. With our method, we have found more than 2000 classes of new CCZ-inequivalent quadratic APN functions, and this number is still increasing quickly