Targets and objects registration and tracking in a sequence of images play an important role in various areas. One of the methods in image registration is feature-based algorithm which is accomplished in two steps. The first step includes finding features of sensed and reference images. In this step, a scale space is used to reduce the sensitivity of detected features to the scale changes. Afterw...

This paper presents a conception for computing gröbner basis. We convert some of gröbner-computing algorithms, e.g., F5, extended F5 and GWV algorithms into a special type of algorithm. The new algorithm’s finite termination problem can be described by equivalent conditions, so all the above algorithms can be determined when they terminate finitely. At last, a new criterion is presented. It is ...

Faugère's F5 algorithm computes a Gröbner basis incrementally, by computing a sequence of (non-reduced) Gröbner bases. The authors describe a variant of F5, called F5C, that replaces each intermediate Gröbner basis with its reduced Gröbner basis. As a result, F5C considers fewer polynomials and performs substantially fewer polynomial reductions, so that it terminates more quickly. We also provi...

A generalized criterion for signature-based algorithms to compute Gröbner bases is proposed in this paper. This criterion is named by “generalized criterion”, because it can be specialized to almost all existing criteria for signature-based algorithms which include the famous F5 algorithm, F5C, extended F5, GV and the GVW algorithm. The main purpose of current paper is to study in theory which ...

It has been shown recently that heuristic and width-based search can be combined to produce planning algorithms with a performance that goes beyond the state-of-the-art. Such algorithms are based on best-first width search (BFWS), a plain best-first search set with evaluations functions combined lexicographically to break ties, some of which express noveltybased preferences. In BFWS(f5), for ex...

We study the complexity of Gröbner bases computation, in particular in the generic situation where the variables are in simultaneous Noether position with respect to the system. We give a bound on the number of polynomials of degree d in a Gröbner basis computed by Faugère’s F5 algorithm ([Fau02]) in this generic case for the grevlex ordering (which is also a bound on the number of polynomials ...

Algebraic cryptanalysis usually requires to find solutions of several similar polynomial systems. A standard tool to solve this problem consists of computing the Gröbner bases of the corresponding ideals, and Faugère’s F4 and F5 are two well-known algorithms for this task. In this paper, we present a new variant of the F4 algorithm which is well suited to algebraic attacks of cryptosystems sinc...

PQ and F5 are two typical steganography methods of JPEG images and have been used widely. To compare the robustness of the above two algorithms, to withstand steganalytic attack a classification algorithm based on sensitive features is presented. SVM is used as a classifier using sensitive features extracted from two domains DCT and DWT. A comparison between the two types of features is also sh...