In this paper, we introduce a new concept of list-decoding separable matrices with strength$d$and list size$L$, denoted as$(\overline{d}, L)$-LDSM, for non-adaptive combinatorial group testing, which is a generalized notion of several types of known test matrices such as d-disjunct matrices,$\overline{d}$-separable matrices, and d-union-free codes with fast decoding. We first provide a two-step identifying algorithm for$(\overline{d}, L)$-LDSM of size$n\times m$and show that it can determine all the$\leq d$positives among$m$items in time$O(\max\{nm,\ nL^{d}\})$. Furthermore, we derive a lower bound on the largest rate of$(\overline{d},\ L)$-LDSM for any$L\geq d\geq 2$by random coding with expurgation. In particular, when$L=m 1/d$, the identifying algorithm of$(d,\ m^{1/\overline{d}})$-LDSM is as efficient as that for d-disjunct matrices, while the rate of$(\overline{d},\ m^{1/d})$-LDSM can be significantly larger than that of d-disjunct matrices.

Secure codes with list decoding (SCLDs) were introduced due to their applications in collusion-resistant multimedia fingerprinting for copyright protection. A fundamental research problem is investigating the largest code rates and explicit constructions for SCLDs. So far, the largest code rates of SCLDs with length$n$have been investigated for asymptotically large alphabet size$q$, and explicit constructions of SCLDs are known for only a few specific cases. In this paper, we establish new lower bounds on the largest code rate of SCLDs for a broad range of alphabet size$q$by virtue of the Lovász local lemma, which particularly implies the known results when$q$is asymptotically large. Furthermore, we present a generic algorithmic construction for SCLDs by means of the Moser-Tardos algorithm and demonstrate its linear-time computational complexity.

In this paper, we study binary signature codes for the weighted binary adder channel (WbAC) and collusion-resistant multimedia fingerprinting. Let A(n, t) denote the maximum size of a t-signature code of length n, and A(n, w, t) denote the maximum size of a t-signature code of length n and constant-weight w. First, we derive asymptotic and general upper bounds on A(n, t) by relating signature codes to Bt codes and bipartite graphs with large girth respectively, and also show the upper bounds are tight for certain cases. Second, we determine the exact values of A(n, 2, 2) and A(n, 3, 2) for infinitely many n by connecting signature codes with C4-free graphs and union-free families, respectively. Third, we provide two explicit constructions for t-signature codes which have efficient decoding algorithms and applications to two-level signature codes. Furthermore, we show from a geometric viewpoint that there does not exist any binary code with complete traceability for noisy WbAC and multimedia fingerprinting. A new type of signature codes with a weaker requirement than complete traceability is introduced for the noisy scenario.

In this paper, we propose a method based on level set active contour model to sever the nucleus and cytoplast from the cervical smear image. The region of interest (ROI) which contained a main connected cell region has been separated from the smear image after the coarse segmentation by auto dual-threshold segmentation. In the process of fine segmentation, two independent level set functions based on the Chan-Vese model with intra-region similarity and inter-region diversity have been constructed to approximate the cytoplast and nucleus contours. While there may be more than one connected cell regions in the ROI, a method of main cell body and main cell nucleus contour curve extraction has been proposed. We validate the proposed models by numerical experiment and the results show that by means of the adjustment of weight coefficient λ1and λ2, most cervical cell image with weak edges can be segmented precisely.