Fourier domain representation of planar curves for recognition in multiple views

Recognition of planar shapes is an important problem in computer vision and pattern recognition. The same planar object contour imaged from different cameras or from different viewpoints looks different and their recognition is non-trivial. Traditional shape recognition deals with views of the shapes that differ only by simple rotations, translations, and scaling. However, shapes suffer more serious deformation between two general views and hence recognition approaches designed to handle translations, rotations, and/or scaling would prove to be insufficient. Many algebraic relations between matching primitives in multiple views have been identified recently. In this paper, we explore how shape properties and multiview relations can be combined to recognize planar shapes across multiple views. We propose novel recognition constraints that a planar shape boundary must satisfy in multiple views. The constraints are on the rank of a Fourier-domain measurement matrix computed from the points on the shape boundary. Our method can additionally compute the correspondence between the curve points after a match is established. We demonstrate the applications of these constraints experimentally on a number of synthetic and real images.     

Planar shape representation and matching under projective transformation

This paper introduces a new representation for planar objects which is invariant to projective transformation. Proposed representation relies on a new shape basis which we refer to as the conic basis. The conic basis takes conic-section coefficients as its dimensions and represents the object as a convex combination of conic-sections. Pairs of conic-sections in this new basis and their projective invariants provides the proposed view invariant representation. We hypothesize that two projectively transformed versions of an object result in the same representation. We show that our hypothesis provides promising recognition performance when we use the nearest neighbor rule to match projectively deformed objects.     

A unifying framework for invariant pattern recognition

We introduce a group-theoretic model of invariant pattern recognition, the Group Representation Network. We show that many standard invariance techniques can be viewed as GRNs, including the DFT power spectrum, higher order neural network and fast translation-invariant transform.     

Simultaneous inner and outer approximation of shapes

For compact Euclidean bodiesP, Q, we define (P, Q) to be the smallest ratior/s wherer > 0,s > 0 satisfy . HeresQ denotes a scaling ofQ by the factors, andQ,Q are some translates ofQ. This function gives us a new distance function between bodies which, unlike previously studied measures, is invariant under affine transformations. If homothetic bodies are identified, the logarithm of this function is a metric. (Two bodies arehomothetic if one can be obtained from the other by scaling and translation.)For integerk 3, define (k) to be the minimum value such that for each convex polygonP there exists a convexk-gonQ with (P, Q) (k). Among other results, we prove that 2.118 ... <-(3) 2.25 and (k) = 1 + (k ^–2). We give anO(n ² log² n)-time algorithm which, for any input convexn-gonP, finds a triangleT that minimizes (T, P) among triangles. However, in linear time we can find a trianglet with (t, P)<-2.25.Our study is motivated by the attempt to reduce the complexity of the polygon containment problem, and also the motion-planning problem. In each case we describe algorithms which run faster when certain implicitslackness parameters of the input are bounded away from 1. These algorithms illustrate a new algorithmic paradigm in computational geometry for coping with complexity.Work of all authors was partially supported by the ESPRIT II Basic Research Actions Program of the EC under Contract No. 3075 (project ALCOM). Rudolf Fleischer and Kurt Mehlhorn acknowledge also DFG (Grant SPP Me 620/6). Chee Yap acknowledges also DFG (Grant Be 142/46-1) and NSF (Grants DCR-84-01898 and CCR-87-03458). This research was performed when Günter Rote and Chee Yap were at the Freie Universität Berlin.     

数据排列的上近似与数据识别

在传统信息系统中引入了n阶粒划分的概念,使信息系统通过n阶粒划分得以粒化,并随着n阶粒划分的变化呈现不同的粒化结构。进而,经对论域对象的特定排序,并通过对上近似和n阶粒划分的融合,确定了一种数据隐含与数据识别的方法,使在数据隐含与数据识别中具有独特的作用。通过调整论域对象的排列顺序,使得数据隐含与数据识别更具灵活性,达到了相同数据隐含及识别的多样性目的。     

Signal recognition: Fourier transform vs. Hartley transform

The new generic feature representation approach was utilized for Gaussian recognition. Approach consists of using simultaneously two new recognition features: real and imaginary Fourier components with taking into account the covariance between features.

Advanced time–frequency technique, short time Fourier transform was considered.

The recognition effectiveness between the new approach and Hartley based approach was compared. It was shown for Gaussian recognition that Hartley approach is not an optimal and is not even a particular case of the proposed approach. The use of the proposed approach provides an essential effectiveness gain in comparison with Hartley approach.     

Algebraic and geometric invariant of a pair of non-coplanar conics in space

It is easy to construct the geometric invariant of a pair of non-coplanar conics in space. It is the crossratio of the 4 intersection points of the two conics with the common line of the two conic planes. In this paper, the algebraic invariant of a pair of non-coplanar conics is derived from the invariant algebra of a pair of quaternary quadratic forms by using the dual representation of space conics. Then, the relationship between the algebraic invariant and the geometric invariant is established.     

Spherical approximation for multiple cameras in motion estimation: Its applicability and advantages

Estimating motions of a multi-camera system which may not have overlapping fields of view is generally complex and computationally expensive because of the non-zero offset between each camera’s center. It is conceivable that if we can assume that multiple cameras share a single optical center, and thus can be modeled as a spherical imaging system, motion estimation and calibration of this system would become simpler and more efficient.     

Pattern recognition with moment invariants: A comparative study and new results

Moment invariants have been proposed as pattern sensitive features in classification and recognition applications. In this paper, the authors present a comprehensive study of the effectiveness of different moment invariants in pattern recognition applications by considering two sets of data: handwritten numerals and aircrafts.

The authors also present a detailed study of Zernike and pseudo Zernike moment invariants including a new procedure for deriving the moment invariants. In addition, the authors introduce a new normalization scheme that reduces the large dynamic range of these invariants as well as implicit redundancies in these invariants.

Based on a comprehensive study with both handwritten numerals and aircraft data, the authors show that the new method of deriving Zernike moment invariants along with the new normalization scheme yield the best overall performance even when the data are degraded by additive noise.     

PHLST5: A Practical and Improved Version of Polyharmonic Local Sine Transform

We introduce a practical and improved version of the Polyharmonic Local Sine Transform (PHLST) called PHLST5. After partitioning an input image into a set of rectangular blocks, the original PHLST decomposes each block into a polyharmonic component and a residual. Each polyharmonic component solves a polyharmonic equation with the boundary conditions that match the values and normal derivatives of even orders along the boundary of the corresponding block with those of the original image block. Thanks to these boundary conditions, the residual component can be expanded into a Fourier sine series without facing the Gibbs phenomenon, and its Fourier sine coefficients decay faster than those of the original block. Due to the difficulty of estimating normal derivatives of higher orders, however, only the harmonic case (i.e., Laplace’s equation) has been implemented to date, which was called Local Laplace Sine Transform (LLST). In that case, the Fourier sine coefficients of the residual decay in the order O(‖k‖⁻³), where k is the frequency index vector. Unlike the original PHLST, PHLST5 only imposes the boundary values and the first order normal derivatives as the boundary conditions, which can be estimated using the information of neighbouring image blocks. In this paper, we derive a fast algorithm to compute a 5th degree polyharmonic function that satisfies such boundary conditions. Although the Fourier sine coefficients of the residual of PHLST5 possess the same decaying rate as in LLST, by using additional information of first order normal derivative from the boundary, the blocking artifacts are largely suppressed in PHLST5 and the residual component becomes much smaller than that of LLST. Therefore PHLST5 provides a better approximation result. We shall also show numerical experiments that demonstrate the superiority of PHLST5 over the original LLST in terms of the efficiency of approximation.

Object representation and recognition in shape spaces

In this paper, we describe a shape space based approach for invariant object representation and recognition. In this approach, an object and all its similarity transformed versions are identified with a single point in a high-dimensional manifold called the shape space. Object recognition is achieved by measuring the geodesic distance between an observed object and a model in the shape space. This approach produced promising results in 2D object recognition experiments: it is invariant to similarity transformations and is relatively insensitive to noise and occlusion. Potentially, it can also be used for 3D object recognition.