Combined Invariants to Gaussian Blur and Affine Transformation

The Standard Metric

10.23943/princeton/9780691166902.003.0026 ◽

2017 ◽

Author(s):

Bernhard M¨uhlherr ◽

Holger P. Petersson ◽

Richard M. Weiss

Keyword(s):

Affine Transformation ◽

Convex Sets ◽

Finite Dimension ◽

Affine Subspace ◽

Affine Transformations ◽

Real Vector ◽

Euclidean Metric ◽

Affine Hyperplane ◽

Tits Building ◽

Convex Closure

This chapter presents some results about groups generated by reflections and the standard metric on a Bruhat-Tits building. It begins with definitions relating to an affine subspace, an affine hyperplane, an affine span, an affine map, and an affine transformation. It then considers a notation stating that the convex closure of a subset a of X is the intersection of all convex sets containing a and another notation that denotes by AGL(X) the group of all affine transformations of X and by Trans(X) the set of all translations of X. It also describes Euclidean spaces and assumes that the real vector space X is of finite dimension n and that d is a Euclidean metric on X. Finally, it discusses Euclidean representations and the standard metric.

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GESTURE RECOGNITION SYSTEM FOR NIGERIAN TRIBAL GREETING POSTURES USING SUPPORT VECTOR MACHINE

MALAYSIAN JOURNAL OF COMPUTING ◽

10.24191/mjoc.v5i2.10347 ◽

2020 ◽

Vol 5 (2) ◽

pp. 609

Author(s):

Segun Aina ◽

Kofoworola V. Sholesi ◽

Aderonke R. Lawal ◽

Samuel D. Okegbile ◽

Adeniran I. Oluwaranti

Keyword(s):

Support Vector Machine ◽

Gesture Recognition ◽

Recognition Rate ◽

Recognition Task ◽

Recognition System ◽

Human Interaction ◽

Support Vector ◽

System A ◽

Extraction Algorithm ◽

Gaussian Blur

This paper presents the application of Gaussian blur filters and Support Vector Machine (SVM) techniques for greeting recognition among the Yoruba tribe of Nigeria. Existing efforts have considered different recognition gestures. However, tribal greeting postures or gestures recognition for the Nigerian geographical space has not been studied before. Some cultural gestures are not correctly identified by people of the same tribe, not to mention other people from different tribes, thereby posing a challenge of misinterpretation of meaning. Also, some cultural gestures are unknown to most people outside a tribe, which could also hinder human interaction; hence there is a need to automate the recognition of Nigerian tribal greeting gestures. This work hence develops a Gaussian Blur – SVM based system capable of recognizing the Yoruba tribe greeting postures for men and women. Videos of individuals performing various greeting gestures were collected and processed into image frames. The images were resized and a Gaussian blur filter was used to remove noise from them. This research used a moment-based feature extraction algorithm to extract shape features that were passed as input to SVM. SVM is exploited and trained to perform the greeting gesture recognition task to recognize two Nigerian tribe greeting postures. To confirm the robustness of the system, 20%, 25% and 30% of the dataset acquired from the preprocessed images were used to test the system. A recognition rate of 94% could be achieved when SVM is used, as shown by the result which invariably proves that the proposed method is efficient.

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Enhancement of Principal Component Analysis using Gaussian Blur Filter

Iraqi Journal of Science ◽

10.24996/ijs.2018.59.3b.17 ◽

2018 ◽

Vol 59 (3B) ◽

Keyword(s):

Principal Component Analysis ◽

Principal Component ◽

Component Analysis ◽

Gaussian Blur

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A quasi-affine transformation artificial bee colony algorithm for global optimization

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-202712 ◽

2021 ◽

pp. 1-18

Author(s):

Baohua Zhao ◽

Tien-Wen Sung ◽

Xin Zhang

Keyword(s):

Affine Transformation ◽

Artificial Bee Colony ◽

Triangular Matrix ◽

Convergence Speed ◽

Test Set ◽

Abc Algorithm ◽

Bee Colony ◽

Search Mechanism ◽

Multiple Dimensions ◽

Collaborative Search

The artificial bee colony (ABC) algorithm is one of the classical bioinspired swarm-based intelligence algorithms that has strong search ability, because of its special search mechanism, but its development ability is slightly insufficient and its convergence speed is slow. In view of its weak development ability and slow convergence speed, this paper proposes the QABC algorithm in which a new search equation is based on the idea of quasi-affine transformation, which greatly improves the cooperative ability between particles and enhances its exploitability. During the process of location updating, the convergence speed is accelerated by updating multiple dimensions instead of one dimension. Finally, in the overall search framework, a collaborative search matrix is introduced to update the position of particles. The collaborative search matrix is transformed from the lower triangular matrix, which not only ensures the randomness of the search, but also ensures its balance and integrity. To evaluate the performance of the QABC algorithm, CEC2013 test set and CEC2014 test set are used in the experiment. After comparing with the conventional ABC algorithm and some famous ABC variants, QABC algorithm is proved to be superior in efficiency, development ability, and robustness.

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Single image super resolution based on multi-scale structure and non-local smoothing

EURASIP Journal on Image and Video Processing ◽

10.1186/s13640-021-00552-8 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Wenyi Wang ◽

Jun Hu ◽

Xiaohong Liu ◽

Jiying Zhao ◽

Jianwen Chen

Keyword(s):

Super Resolution ◽

Principal Component ◽

Feature Mapping ◽

Multi Scale ◽

Non Local ◽

Image Super Resolution ◽

Gaussian Blur ◽

Single Image Super Resolution ◽

Global And Local ◽

Bicubic Interpolation

AbstractIn this paper, we propose a hybrid super-resolution method by combining global and local dictionary training in the sparse domain. In order to present and differentiate the feature mapping in different scales, a global dictionary set is trained in multiple structure scales, and a non-linear function is used to choose the appropriate dictionary to initially reconstruct the HR image. In addition, we introduce the Gaussian blur to the LR images to eliminate a widely used but inappropriate assumption that the low resolution (LR) images are generated by bicubic interpolation from high-resolution (HR) images. In order to deal with Gaussian blur, a local dictionary is generated and iteratively updated by K-means principal component analysis (K-PCA) and gradient decent (GD) to model the blur effect during the down-sampling. Compared with the state-of-the-art SR algorithms, the experimental results reveal that the proposed method can produce sharper boundaries and suppress undesired artifacts with the present of Gaussian blur. It implies that our method could be more effect in real applications and that the HR-LR mapping relation is more complicated than bicubic interpolation.

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Affine transformation of virtual 3D object using 2D localization of fingertips

Virtual Reality & Intelligent Hardware ◽

10.1016/j.vrih.2020.10.001 ◽

2020 ◽

Vol 2 (6) ◽

pp. 534-555

Author(s):

Mohammad Mahmudul Alam ◽

S.M. Mahbubur Rahman

Keyword(s):

Affine Transformation ◽

3D Object

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Optimization Over the Boolean Hypercube Via Sums of Nonnegative Circuit Polynomials

Foundations of Computational Mathematics ◽

10.1007/s10208-021-09496-x ◽

2021 ◽

Author(s):

Mareike Dressler ◽

Adam Kurpisz ◽

Timo de Wolff

Keyword(s):

Computer Science ◽

Affine Transformation ◽

Optimization Problems ◽

Polynomial Optimization ◽

Theoretical Computer Science ◽

Sums Of Squares ◽

Theoretical Computer ◽

Complexity Bounds ◽

Polynomial Optimization Problems ◽

Transformation Of Variables

AbstractVarious key problems from theoretical computer science can be expressed as polynomial optimization problems over the boolean hypercube. One particularly successful way to prove complexity bounds for these types of problems is based on sums of squares (SOS) as nonnegativity certificates. In this article, we initiate optimization problems over the boolean hypercube via a recent, alternative certificate called sums of nonnegative circuit polynomials (SONC). We show that key results for SOS-based certificates remain valid: First, for polynomials, which are nonnegative over the n-variate boolean hypercube with constraints of degree d there exists a SONC certificate of degree at most $$n+d$$ n + d . Second, if there exists a degree d SONC certificate for nonnegativity of a polynomial over the boolean hypercube, then there also exists a short degree d SONC certificate that includes at most $$n^{O(d)}$$ n O ( d ) nonnegative circuit polynomials. Moreover, we prove that, in opposite to SOS, the SONC cone is not closed under taking affine transformation of variables and that for SONC there does not exist an equivalent to Putinar’s Positivstellensatz for SOS. We discuss these results from both the algebraic and the optimization perspective.

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