Abstract: The vibration analysis of horizontally curved beams is generally led to higher order shape functions using direct finite element method, resulting in more time-consuming computation process. In this paper, the weak-form mixed finite element method was used to reduce the order of shape functions. The shape functions were first considered linear which did not provide adequate accuracy....

The description of the object shape is an important characteristic of the image. In image processing and pattern recognition, several different shape descriptors are used. In human visual perception, the shapes are processed in multiple resolutions. Therefore multiscale shape representation is essential in the shape based image classification and retrieval. In the description of the object shap...

Progress in a novel wave-optical algorithm for synthesizing object waves of three-dimensional surface objects is reported. The algorithm has been proposed last year and has a feature of wave-optical calculation in diffraction by object surfaces. Numerical simulation of diffraction is implemented by a method based on coordinates rotation in Fourier spectrum. Source fields on a surface of objects...

The 2D Fourier Descriptor is an elegant and powerful technique for 2D shape analysis. This paper intends to extend such technique to 3D. Though conceptually natural, such an extension is not trivial in that two critical problems, the spherical parametrization and invariants construction, must be solved. By using a newly developed surface parametrization method–the discrete conformal mapping (DC...

In this paper, a new tool that is fractional Fourier Transform is introduced to 3D model retrieval. And we propose a 3D model descriptor based on 3D factional Fourier transform. Fractional Fourier transform is a general format of Fourier transform, and add a variables that is order. Our approach is based on volume. The first step of the approach is that voxelize these 3D models. A coarse voxeli...

Shape is one of the primary low level image features in Content Based Image Retrieval (CBIR). Many shape representations and retrieval methods exist. However, most of those methods either do not well capture shape features or are difficult to do normalization (making matching difficult). Among them, methods based Fourier descriptors (FDs) achieve both good representation (perceptually meaningfu...

In this study, we propose a compact shape descriptor, which represents the 2-D shape information by 1-D functions. For this purpose a two-step method is proposed. In the first step, the 2-D shape information is mapped into 1-D moment functions without using a predefined resolution. The mapping is based on the beams, which are originated from a boundary point, connecting that point with the rest...

It was shown [ 21 that any SFF can be decomposed in this manner. Thus, F(x) is an SFF if, and only if, it can be expressed as the sum of four functions in the form of the above equation. Additional SFF studies are reported in refs. [ 3-51. Another issue that has been recently investigated is the fractional Fourier transform [ 6-91. Two distinct definitions of the fractional Fourier transform ha...

‎The sequences of the form ${E_{mb}g_{n}}_{m‎, ‎ninmathbb{Z}}$,‎ ‎where $E_{mb}$ is the modulation operator‎, ‎$b>0$ and $g_{n}$ is the‎ ‎window function in $L^{2}(mathbb{R})$‎, ‎construct Fourier-like‎ ‎systems‎. ‎We try to consider some sufficient conditions on the window‎ ‎functions of Fourier-like systems‎, ‎to make a frame and find a dual‎ ‎frame with the same structure‎. ‎We also extend t...

Feedforward networks composed of units which compute a sigmoidal function of a weighted sum of their inputs have been much investigated. We tested the approximation and estimation capabilities of networks using functions more complex than sigmoids. Three classes of functions were tested: polynomials, rational functions, and flexible Fourier series. Unlike sigmoids, these classes can fit non-mon...