• International Journal of Contents
• /
• v.9 no.2
• /
• pp.1-7
• /
• 2013

This paper proposes an efficient matching algorithm based on ASIFT (Affine Scale-Invariant Feature Transform) which is fully invariant to affine transformation. In our approach, we proposed a method of reducing similar measure matching cost and the number of outliers. First, we combined the Manhattan and Chessboard metrics replacing the Euclidean metric by a linear combination for measuring the similarity of keypoints. These two metrics are simple but really efficient. Using our method the computation time for matching step was saved and also the number of correct matches was increased. By applying an Optimized Random Sampling Algorithm (ORSA), we can remove most of the outlier matches to make the result meaningful. This method was experimented on various combinations of affine transform. The experimental result shows that our method is superior to SIFT and ASIFT.

• Honam Mathematical Journal
• /
• v.42 no.1
• /
• pp.75-91
• /
• 2020

In this study, we have generalized pseudo-Finsler map by introducing the concept of semi-Riemannian map and have found pseudo-Finsler eikonal equations using pseudo-Finsler map. After that, we have obtained some sufficient theorems on pseudo-Finsler manifolds for the existence of solutions to the eikonal equation. At the same time, we have introduced a natural definition for the affine maps between pseudo-Finsler manifolds and have reached the affine solutions of them.

• Maxillofacial Plastic and Reconstructive Surgery
• /
• v.33 no.3
• /
• pp.233-240
• /
• 2011

Purpose: To apply a computer assisted navigation system to orthognathic surgery, a simple and efficient measuring algorithm calculation based on affine transformation was designed. A method of improving accuracy and reducing errors in orthognathic surgery by use of an optical tracking camera was studied. Methods: A total of 5 points on one surgical splint were measured and tracked by the Polaris $Vicra^{(R)}$ (Northern Digital Inc Co., Ontario, Canada) optical tracking system in two cases. The first case was to apply the transformation matrix at pre- and postoperative situations, and the second case was to apply an affine transformation only after the postoperative situation. In each situation, the predictive measuring value was changed to the final measuring value via an affine transformation algorithm and the expected coordinates calculated from the model were compared with those of the patient in the operation room. Results: The mean measuring error was $1.027{\pm}0.587$ using the affine transformation at pre- and postoperative situations and the average value after the postoperative situation was $0.928{\pm}0.549$. The farther a coordinate region was from the reference coordinates which constitutes the transform matrixes, the bigger the measuring error was found which was calculated from an affine transformation algorithm. Conclusion: Most difference errors were brought from mainly measuring process and lack of reproducibility, the affine transformation algorithm formula from postoperative measuring values by using of optic tracking system between those of model surgery and those of patient surgery can be selected as minimizing the difference error. To reduce coordinate calculation errors, minimum transformation matrices must be used and reference points which determine an affine transformation must be close to the area where coordinates are measured and calculated, as well as the reference points need to be scattered.

• East Asian mathematical journal
• /
• v.38 no.3
• /
• pp.321-329
• /
• 2022

For an ample divisor A of birational type on a singular del Pezzo surface S of degree 4 with A₁-singularity, we show that the affine cone of S defined by A is flexible

• International Journal of Control, Automation, and Systems
• /
• v.4 no.3
• /
• pp.293-301
• /
• 2006

A new discretization method for calculating a sampled-data representation of a nonlinear continuous-time system is proposed. The proposed method is based on the well-known Taylor series expansion and zero-order hold (ZOH) assumption. The mathematical structure of the new discretization method is analyzed. On the basis of this structure, a sampled-data representation of a nonlinear system with a time-delayed input is derived. This method is applied to obtain a sampled-data representation of a non-affine nonlinear system, with a constant input time delay. In particular, the effect of the time discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. 'Hybrid' discretization schemes that result from a combination of the 'scaling and squaring' technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method parameters to meet CPU time and accuracy requirements are examined as well. The performance of the proposed method is evaluated using a nonlinear system with a time-delayed non-affine input.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.4
• /
• pp.825-832
• /
• 2011

In this paper, we make a minute and detailed proof of a part which is omitted in the process of obtaining the value of the curvature tensor for an invariant affine connection at the point {H} of a reductive homogeneous space G/H in the paper 'Invariant affine connections on homogeneous spaces' by K. Nomizu.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.18 no.11
• /
• pp.778-784
• /
• 2017

We investigated the possibility of a bio-monitoring system for predicting toxic dinoflagellates (Genus Alexandrium) by the measuring shell valve movements(SVMs) of Pacific oyster, Crassostrea gigas (Mollusca: Bivalvia) using the Hall element sensor. We then described the SVMs of Pacific oyster exposed to the toxic algae under laboratory conditions. Pacific oyster used for experiment were fed Isochrysis galbana until they stabilized and kept under hunger conditions for three days to prevent the influence of food before the experiment. Pacific oyster were exposed to the toxic dinoflagellate, A. fundyense, and the potentially toxic dinoflagellate, A. affine. When Pacific oyster were exposed to A. fundyense, SVMs increased over 10 times/hr at low cell densities of 20 cells/mL. SVMs increased again at $14.1{\pm}5.7times/hr$ at 500 cells/mL, and $27.9{\pm}11.1times/hr$ at the high cell density of 5,000 cells/mL. However, in the presence of A. affine, SVMs increased at $6.7{\pm}3.9times/hr$ until 300 cells/mL, while they increased greatly to $15.3{\pm}10.8times/hr$ at 1,000 cells/mL. The SVMs of Pacific oyster indicated differences depending on species for toxic dinoflagellates. Therefore, the SVMs of Pacific oyster could be useful for A. fundyense, but would bedifficult to apply for A. affine.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.2
• /
• pp.213-219
• /
• 2011

In this paper, we will prove an equilibrium existence theorem of a non-compact acyclic strategic game with affine constraint correspondences which is comparable with equilibrium existence theorems due to Debreu, Nash, Kim-Kum, and Lu in several aspects.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.18 no.2
• /
• pp.181-192
• /
• 2014

In this paper, we propose a robust real-time myocardial border tracking algorithm for echocardiography. Commonly, after an initial contour of LV border is traced at one or two frame from the entire cardiac cycle, LV contour tracking is performed over the remaining frames. Among a variety of tracking techniques, optical flow method is the most widely used for motion estimation of moving objects. However, when echocardiography data is heavily corrupted in some local regions, the errors bring the tracking point out of the endocardial border, resulting in distorted LV contours. This shape distortion often occurs in practice since the data acquisition is affected by ultrasound artifacts, dropout or shadowing phenomena of cardiac walls. The proposed method deals with this shape distortion problem and reflects the motion realistic LV shape by applying global deformation modeled as affine transform partitively to the contour. We partition the tracking points on the contour into a few groups and determine each affine transform governing the motion of the partitioned contour points. To compute the coefficients of each affine transform, we use the least squares method with equality constraints that are given by the relationship between the coefficients and a few contour points showing good tracking results. Many real experiments show that the proposed method supports better performance than existing methods.

• Journal of Biomedical Engineering Research
• /
• v.16 no.1
• /
• pp.17-24
• /
• 1995

This paper presents a new compression method (or ECG data using iterated contractive transformations. The method represents any range of ECG signal by piecewise self-afrine fractal Interpolation (PSAFI). The piecewise self-afrine rractal model is used where a discrete data set is viewed as being composed of contractive arfine transformation of pieces of itself. This algorithm was evaluated using MIT/BIH arrhythmia database. PSAFI is found to yield a relatively low reconstruction error for a given compression ratio than conventional direct compression methods. The compression ratio achieved was 883.9 bits per second (bps) - an average percent rms difference (AFRD) of 5.39 percent -with the original 12b ECG samples digitized at 400 Hz.