On the Affine Image of a Rational Surface of Revolution

We study the properties of the image of a rational surface of revolution under a nonsingular affine mapping. We prove that this image has a notable property, namely that all the affine normal lines, a concept that appears in the context of affine differential geometry, created by Blaschke in the first decades of the 20th century, intersect a fixed line. Given a rational surface with this property, which can be algorithmically checked, we provide an algorithmic method to find a surface of revolution, if it exists, whose image under an affine mapping is the given surface; the algorithm also finds the affine transformation mapping one surface onto the other. Finally, we also prove that the only rational affine surfaces of rotation, a generalization of surfaces of revolution that arises in the context of affine differential geometry, and which includes surfaces of revolution as a subtype, affinely transforming into a surface of revolution are the surfaces of revolution, and that in that case the affine mapping must be a similarity.

Robust Stabilised Visual Tracker for Vehicle Tracking

<p>Visual tracking is performed in a stabilised video. If the input video to the tracker algorithm is itself destabilised, incorrect motion vectors will cause a serious drift in tracking. Therefore video stabilisation is must before tracking. A novel algorithm is developed which simultaneously takes care of video stabilisation and target tracking. Target templates in just previous frame are stored in positive and negative repositories followed by Affine mapping. Then optimised affine parameters are used to stabilise the video. Target of interest in the next frame is approximated using linear combinations of previous target templates. Proposed modified L1 minimisation method is used to solve sparse representation of target in the target template subspace. Occlusion problem is minimised using the inherent energy of coefficients. Accurate tracking results have been obtained in destabilised videos.</p>

The stability of a generalized affine functional equation in fuzzy normed spaces

We obtain the general solution of the following functional equation f(kx1+x2+???+xk)+f(x1+kx2+???+xk)+???+f(x1+x2+???+kxk)+f(x1)+ f(x2)+???+ f(xk)= 2kf(x1+ x2+???+xk), k ? 2. We establish the Hyers-Ulam-Rassias stability of the above functional equation in the fuzzy normed spaces. More precisely, we show under suitable conditions that a fuzzy q-almost affine mapping can be approximated by an affine mapping. Further, we determine the stability of same functional equation by using fixed point alternative method in fuzzy normed spaces.

3-D from 2-D Using Warping Transformations .

Shown in this paper are methods on how to find the third dimension of a single image or from the two views of the image taking in a different angle using the method more accurate and faster to get to the third dimension in the following cases: One image of the same scene. Two views of the same scene from two different perspectives. Pictures of parts of the same scene. Set of pictures for different views of the work of the subject Panorama. This method is known Image Warping, which falls below a set of transfers such as (Affine - Bilinear - Projective - Mosaic – Similarity transformation) was compared to the work of transfers between the previous and this will be applied to more pictures. The idea is based on building code software is built on the programming language Visual C + + with the library for drawing an OpenGL program Matlab, which way can build a model of the following conversions, which fall under the so-called image warping of the conversion linear Bilinear Mapping and conversion Affine Mapping and conversion imagery Projective Mapping . shown in this paper are methods on how to correct camera exposure changes and how to blend the stitching line between the images. We will show panorama photos generated from both still image.

PERAN FAKTOR PENYEKALA PADA KONSTRUKSI INTERPOLASI FRAKTAL

Abstrak: Telah diketahui bahwa suatu fungsi fraktal yang menginterpolasi data sedemikian hingga untuk dapat dikonstruksi dari suatu Sistem Fungsi Iterasi (SFI) berdasarkan teorema titik tetap pada pemetaan kontraktif. Dengan mengambil suatu bentuk pemetaan Affine, yang merupakan salah satu bentuk pemetaan kontraktif untuk SFI, dapat dibuktikan eksistensi atraktor SFI dimaksud yang tidak lain merupakan interpolan fraktal dari data terkait. Faktor penyekala yang termuat di dalam pemetaan affine memegang peran sebagai syarat perlu eksistensi dan ketunggalan fungsi interpolasi fraktal suatu data. Syarat perlu tersebut berlaku pada batasan nilai . Kata kunci : interpolan fraktal, SFI, teorema titik tetap, pemetaan affine, faktor penyekala. Abstract: It is known that a fractal functions that interpolated the data such that , can be constructed from an Iterated Function System (IFS) based on The Fixed Point Theorem on contractive mappings. By taking a certain Affine Mapping, which is a form of contractive mapping on IFS, the existence of IFS’ attractor can be proven as the fractal interpolan of related data. The vertical scaling factor contained in the affine mapping role as a necessary condition of existence and uniqueness of a fractal interpolation function data. The necessary condition of is on the interval . Keywords : fractal interpolan, IFS, The Fixed Point Theorem, Affine Mapping, vertical scaling factor)