Tayeb Basta | Al Ghurair University (original) (raw)

Papers by Tayeb Basta

In stereo vision, the epipolar geometry is the intrinsic projective geometry between the two view... more In stereo vision, the epipolar geometry is the intrinsic projective geometry between the two views. The essential and fundamental matrices relate corresponding points in stereo images. The essential matrix describes the geometry when the used cameras are calibrated, and the fundamental matrix expresses the geometry when the cameras are uncalibrated. Since the nineties, researchers devoted a lot of effort to estimating the fundamental matrix. Although it is a landmark of computer vision, in the current work, three derivations of the essential and fundamental matrices have been revised. The Longuet-Higgins' derivation of the essential matrix where the author draws a mapping between the position vectors of a 3D point; however, the one-to-one feature of that mapping is lost when he changed it to a relation between the image points. In the two other derivations, we demonstrate that the authors established a mapping between the image points through the misuse of mathematics.

In stereo vision, the epipolar geometry is the intrinsic projective geometry between the two view... more In stereo vision, the epipolar geometry is the intrinsic projective geometry between the two views. The essential and fundamental matrices relate corresponding points in stereo images. The essential matrix describes the geometry when the used cameras are calibrated, and the fundamental matrix expresses the geometry when the cameras are uncalibrated. Since the nineties, researchers devoted a lot of effort to estimating the fundamental matrix. Although it is a landmark of computer vision, in the current work, three derivations of the essential and fundamental matrices have been revised. The Longuet-Higgins' derivation of the essential matrix where the author draws a mapping between the position vectors of a 3D point; however, the one-to-one feature of that mapping is lost when he changed it to a relation between the image points. In the two other derivations, we demonstrate that the authors established a mapping between the image points through the misuse of mathematics.

In stereo vision, the fundamental matrix encapsulates the epipolar geometric information which re... more In stereo vision, the fundamental matrix encapsulates the epipolar geometric information which relates corresponding points on two views of a scene. The eight-point algorithm is a frequently cited method for calculating the fundamental matrix. Some researchers criticized the performance of such algorithm as it is extremely susceptible to noise and hence virtually useless for most purposes. Such criticism prompted Richard Hartley to defend the algorithm. He asserted that preceding the matrix calculation with normalization of the coordinates of the matched points ensures a high performance of the algorithm. This paper presents an analysis showing that the raised question about the performance of the eight-point algorithm lies in the way by which the fundamental matrix equation is derived rather than in the eight-point algorithm itself. It demonstrates that calculated in the projection space is different of defined in the Euclidean space as a one-to-one correspondence.

Natural Language Processing (NLP) Trends

In stereo vision, the epipolar geometry is the intrinsic projective geometry between the two view... more In stereo vision, the epipolar geometry is the intrinsic projective geometry between the two views. The essential and fundamental matrices relate corresponding points in stereo images. The essential matrix describes the geometry when the used cameras are calibrated, and the fundamental matrix expresses the geometry when the cameras are uncalibrated. Since the nineties, researchers devoted a lot of effort to estimating the fundamental matrix. Although it is a landmark of computer vision, in the current work, three derivations of the essential and fundamental matrices have been revised. The Longuet-Higgins' derivation of the essential matrix where the author draws a mapping between the position vectors of a 3D point; however, the one-to-one feature of that mapping is lost when he changed it to a relation between the image points. In the two other derivations, we demonstrate that the authors established a mapping between the image points through the misuse of mathematics.

2019 International Conference on Digitization (ICD)

One of the big issues of security access to web and web services is authentication. Authenticatio... more One of the big issues of security access to web and web services is authentication. Authentication is verifying that the user is who he/she claims to be. Some of the mechanisms set to fight against intrusion are security questions, third-party account login, and (re)CAPTCHA. These solutions are sometimes vulnerable and can be easily exploited by hackers through bots and machine learning programs. We developed a system that enhances web and web services authentication. We tested it against an online OCR software program where it is proven robust. In addition, we conducted a survey about its ease-of-use and the results were promising.

In stereo vision, the fundamental matrix encapsulates the epipolar geometric information which re... more In stereo vision, the fundamental matrix encapsulates the epipolar geometric information which relates corresponding points on two views of a scene. The eight-point algorithm is a frequently cited method for calculating the fundamental matrix. Some researchers criticized the performance of such algorithm as it is extremely susceptible to noise and hence virtually useless for most purposes. Such criticism prompted Richard Hartley to defend the algorithm. He asserted that preceding the matrix calculation with normalization of the coordinates of the matched points ensures a high performance of the algorithm. This paper presents an analysis showing that the raised question about the performance of the eight-point algorithm lies in the way by which the fundamental matrix equation is derived rather than in the eight-point algorithm itself. It demonstrates that calculated in the projection space is different of defined in the Euclidean space as a one-to-one correspondence.

Proceedings of the 2020 3rd International Conference on Artificial Intelligence and Pattern Recognition

In this paper, we prove mathematically that the geometric derivation of the fundamental matrix F ... more In this paper, we prove mathematically that the geometric derivation of the fundamental matrix F of the two-view reconstruction problem is flawed. Although the fundamental matrix approach is quite classic, it is still taught in universities around the world. Thus, analyzing the derivation of F now is a non-trivial subject. The geometric derivation of E is based on the cross product of vectors in R3. The cross product (or vector product) of two vectors is x × y where x = ⟨x1, x2, x3⟩ and y = ⟨y1, y2, y3⟩ in R3. The relationship between the skew-matrix of a vector t in R3 and the cross product is [t]×y = t × y for any vector y in R3. In the derivation of the essential matrix we have E = [t]×R which is the result of replacing t × R by [t]×R, the cross product of a vector t and a 3×3 matrix R. This is an undefined operation and therefore the essential matrix derivation is flawed. The derivation of F, is based on the assertion that the set of all points in the first image and their corresponding points in the second image are protectively equivalent and therefore there exists a homography H&pgr; between the two images. An assertion that does not hold for 3D non-planar scenes.

Asian Journal of Information Technology

International Journal of Applied Physics and Mathematics, 2012

International Journal of Computer Theory and Engineering, 2013

Electronic learning is a type of education where the medium of instruction is information and com... more Electronic learning is a type of education where the medium of instruction is information and communication technologies (ICT). E-learning can be defined as the application of information and communication technologies to core institutional functions such as administration, materials development and distribution, course delivery and tuition, and the provision of learner services such as advising, prior learning assessment and program planning. E-Learning can be either blended learning in which the technology is used to enhance the face-to-face teaching, or it can be purely online learning, that is, the delivery of courses completely through information and communication technologies. This paper reports the different point of view about e-learning education in general and its credibility in particular. It demonstrates that one of the important factors of the e-learning credibility is the quality of assessment employed to measure how learners perceive the information. The paper recommends a way by which such assessments should be held to preserve the educational standards on one hand, and guarantee confidence in online learning, on the other.

asian-transactions.org

Abstract--The objective of most stereo vision work has been to extract the 3D shape of a world sc... more Abstract--The objective of most stereo vision work has been to extract the 3D shape of a world scene from two of its images which have been captured from two different standpoints. One of the major challenges in computer vision has been the elaboration of methods, ...

Journal of Image and Graphics, 2013

In computer stereo vision, the fundamental matrix is the algebraic representation of the epipolar... more In computer stereo vision, the fundamental matrix is the algebraic representation of the epipolar geometry that relates two images of a scene observed from two different viewpoints. The most important feature of the fundamental matrix is its independence of the scene structure. Different methods have been proposed to derive the fundamental matrix equation.  This paper reviews one of these methods and reveals that it is based on flawed statements to conclude the existence of a homography between the points on the two images. This derivation of the fundamental matrix equation is based on the existence of a homography between the two images.

During the last three decades, there has been a substantial research effort devoted to the proble... more During the last three decades, there has been a substantial research effort devoted to the problem of 3D extraction and construction from two views of a given scene. One of the major challenges in computer vision has been the elaboration of methods, which do not depend on scene structure, to compute the relationship between pairs of corresponding points from two views. Two landmark achievements, in this field, were the development of the essential matrix by Longuet-Higgins and the elaboration of the fundamental matrix by Olivier Faugeras. Basta [1] reviewed the work of Longuet-Higgins, discovering mathematical flaws in the derivation of the essential matrix. In a similar vein, this paper discusses mathematical flaws in the derivation of the fundamental matrix, which is based on the theory of a point lying on a line.

Proceedings of the 2019 5th International Conference on Computer and Technology Applications

International Journal of Machine Learning and Computing, 2012

In 1981 Longuet-Higgins represented the world point by two vectors in the two camera reference fr... more In 1981 Longuet-Higgins represented the world point by two vectors in the two camera reference frames and developed the essential matrix. Such a matrix is a relation between the corresponding image points on the two images of a world point on a rigid scene. The essential matrix is independent of the position and orientation of the cameras used to capture the two views. The calculation of the essential matrix requires the knowledge of at least five accurate pairs of corresponding points. The unavailability of a procedure that fulfills such a requirement led researchers to focus their attention on developing estimation methods of the essential matrix without questioning the mathematical correctness of its derivation. In this paper, we identify and expose flaws in Longuet-Higgins' derivation of the essential matrix. These flaws are the result of mixing up between the scalar product of vectors in a single reference frame and the transformation of vectors from one reference frame to another.

Asian Journal of Information Technology, 2006

In this paper, we have described an approach for a 3D scene reconstruction using 2 randomly selec... more In this paper, we have described an approach for a 3D scene reconstruction using 2 randomly selected adjacent colored video frames. We have used a single uncalibrated video camera to take a record for uncalibrated environment. The Selection of 2 frames based on the maximum homogeneity of points on these frames are favorable; could be any two adjacent frames. The use of Harris technique were very useful to find the edges and corners on each selected image (frame), then the use of the autocorrelation function ...

International Journal of Signal Processing, Image Processing and Pattern Recognition, Oct 31, 2014

In stereo vision, two images of a 3D scene are acquired from two viewpoints. One of the objective... more In stereo vision, two images of a 3D scene are acquired from two viewpoints. One of the objectives of stereo vision work is to recover the 3D structure of the scene. Epipolar geometry describes the relationship between the images, and the essential and fundamental matrices are the algebraic representations of this geometry. The most important feature of these matrices that is emphasized in the literature is that they are independent of the scene structure. This article illustrates-empirically and theoretically-that the fundamental matrix depends on the scene structure and demonstrates that the matrix in 0  l r Fm m not only represents a relationship between corresponding points of the two views but also represents a relationship between other non-corresponding points. Furthermore, we show empirically that the equation 0  l r Fm m does not hold for any pair of corresponding points. In scenes with objects of different depths, the value of l r Fm m depends on the depths of the 3D points and increases proportionally with an increasing baseline.

Proceedings of the 9th Wseas International Conference on Signal Speech and Image Processing and 9th Wseas International Conference on Multimedia Internet Video Technologies, Sep 1, 2009

Extracting 3D structure from two views is a flourishing subject in computer vision literature. In... more Extracting 3D structure from two views is a flourishing subject in computer vision literature. In 1981 Longuet-Higgins introduces what it seemed a mathematically founded theory that relates the corresponding points from the two images independently from the extrinsic camera parameters. Since then a number of contributions based on such a theory was emerged.

In stereo vision, the epipolar geometry is the intrinsic projective geometry between the two view... more In stereo vision, the epipolar geometry is the intrinsic projective geometry between the two views. The essential and fundamental matrices relate corresponding points in stereo images. The essential matrix describes the geometry when the used cameras are calibrated, and the fundamental matrix expresses the geometry when the cameras are uncalibrated. Since the nineties, researchers devoted a lot of effort to estimating the fundamental matrix. Although it is a landmark of computer vision, in the current work, three derivations of the essential and fundamental matrices have been revised. The Longuet-Higgins' derivation of the essential matrix where the author draws a mapping between the position vectors of a 3D point; however, the one-to-one feature of that mapping is lost when he changed it to a relation between the image points. In the two other derivations, we demonstrate that the authors established a mapping between the image points through the misuse of mathematics.

In stereo vision, the epipolar geometry is the intrinsic projective geometry between the two view... more In stereo vision, the epipolar geometry is the intrinsic projective geometry between the two views. The essential and fundamental matrices relate corresponding points in stereo images. The essential matrix describes the geometry when the used cameras are calibrated, and the fundamental matrix expresses the geometry when the cameras are uncalibrated. Since the nineties, researchers devoted a lot of effort to estimating the fundamental matrix. Although it is a landmark of computer vision, in the current work, three derivations of the essential and fundamental matrices have been revised. The Longuet-Higgins' derivation of the essential matrix where the author draws a mapping between the position vectors of a 3D point; however, the one-to-one feature of that mapping is lost when he changed it to a relation between the image points. In the two other derivations, we demonstrate that the authors established a mapping between the image points through the misuse of mathematics.

In stereo vision, the fundamental matrix encapsulates the epipolar geometric information which re... more In stereo vision, the fundamental matrix encapsulates the epipolar geometric information which relates corresponding points on two views of a scene. The eight-point algorithm is a frequently cited method for calculating the fundamental matrix. Some researchers criticized the performance of such algorithm as it is extremely susceptible to noise and hence virtually useless for most purposes. Such criticism prompted Richard Hartley to defend the algorithm. He asserted that preceding the matrix calculation with normalization of the coordinates of the matched points ensures a high performance of the algorithm. This paper presents an analysis showing that the raised question about the performance of the eight-point algorithm lies in the way by which the fundamental matrix equation is derived rather than in the eight-point algorithm itself. It demonstrates that calculated in the projection space is different of defined in the Euclidean space as a one-to-one correspondence.

Natural Language Processing (NLP) Trends

In stereo vision, the epipolar geometry is the intrinsic projective geometry between the two view... more In stereo vision, the epipolar geometry is the intrinsic projective geometry between the two views. The essential and fundamental matrices relate corresponding points in stereo images. The essential matrix describes the geometry when the used cameras are calibrated, and the fundamental matrix expresses the geometry when the cameras are uncalibrated. Since the nineties, researchers devoted a lot of effort to estimating the fundamental matrix. Although it is a landmark of computer vision, in the current work, three derivations of the essential and fundamental matrices have been revised. The Longuet-Higgins' derivation of the essential matrix where the author draws a mapping between the position vectors of a 3D point; however, the one-to-one feature of that mapping is lost when he changed it to a relation between the image points. In the two other derivations, we demonstrate that the authors established a mapping between the image points through the misuse of mathematics.

2019 International Conference on Digitization (ICD)

One of the big issues of security access to web and web services is authentication. Authenticatio... more One of the big issues of security access to web and web services is authentication. Authentication is verifying that the user is who he/she claims to be. Some of the mechanisms set to fight against intrusion are security questions, third-party account login, and (re)CAPTCHA. These solutions are sometimes vulnerable and can be easily exploited by hackers through bots and machine learning programs. We developed a system that enhances web and web services authentication. We tested it against an online OCR software program where it is proven robust. In addition, we conducted a survey about its ease-of-use and the results were promising.

In stereo vision, the fundamental matrix encapsulates the epipolar geometric information which re... more In stereo vision, the fundamental matrix encapsulates the epipolar geometric information which relates corresponding points on two views of a scene. The eight-point algorithm is a frequently cited method for calculating the fundamental matrix. Some researchers criticized the performance of such algorithm as it is extremely susceptible to noise and hence virtually useless for most purposes. Such criticism prompted Richard Hartley to defend the algorithm. He asserted that preceding the matrix calculation with normalization of the coordinates of the matched points ensures a high performance of the algorithm. This paper presents an analysis showing that the raised question about the performance of the eight-point algorithm lies in the way by which the fundamental matrix equation is derived rather than in the eight-point algorithm itself. It demonstrates that calculated in the projection space is different of defined in the Euclidean space as a one-to-one correspondence.

Proceedings of the 2020 3rd International Conference on Artificial Intelligence and Pattern Recognition

In this paper, we prove mathematically that the geometric derivation of the fundamental matrix F ... more In this paper, we prove mathematically that the geometric derivation of the fundamental matrix F of the two-view reconstruction problem is flawed. Although the fundamental matrix approach is quite classic, it is still taught in universities around the world. Thus, analyzing the derivation of F now is a non-trivial subject. The geometric derivation of E is based on the cross product of vectors in R3. The cross product (or vector product) of two vectors is x × y where x = ⟨x1, x2, x3⟩ and y = ⟨y1, y2, y3⟩ in R3. The relationship between the skew-matrix of a vector t in R3 and the cross product is [t]×y = t × y for any vector y in R3. In the derivation of the essential matrix we have E = [t]×R which is the result of replacing t × R by [t]×R, the cross product of a vector t and a 3×3 matrix R. This is an undefined operation and therefore the essential matrix derivation is flawed. The derivation of F, is based on the assertion that the set of all points in the first image and their corresponding points in the second image are protectively equivalent and therefore there exists a homography H&pgr; between the two images. An assertion that does not hold for 3D non-planar scenes.

Asian Journal of Information Technology

International Journal of Applied Physics and Mathematics, 2012

International Journal of Computer Theory and Engineering, 2013

Electronic learning is a type of education where the medium of instruction is information and com... more Electronic learning is a type of education where the medium of instruction is information and communication technologies (ICT). E-learning can be defined as the application of information and communication technologies to core institutional functions such as administration, materials development and distribution, course delivery and tuition, and the provision of learner services such as advising, prior learning assessment and program planning. E-Learning can be either blended learning in which the technology is used to enhance the face-to-face teaching, or it can be purely online learning, that is, the delivery of courses completely through information and communication technologies. This paper reports the different point of view about e-learning education in general and its credibility in particular. It demonstrates that one of the important factors of the e-learning credibility is the quality of assessment employed to measure how learners perceive the information. The paper recommends a way by which such assessments should be held to preserve the educational standards on one hand, and guarantee confidence in online learning, on the other.

asian-transactions.org

Abstract--The objective of most stereo vision work has been to extract the 3D shape of a world sc... more Abstract--The objective of most stereo vision work has been to extract the 3D shape of a world scene from two of its images which have been captured from two different standpoints. One of the major challenges in computer vision has been the elaboration of methods, ...

Journal of Image and Graphics, 2013

In computer stereo vision, the fundamental matrix is the algebraic representation of the epipolar... more In computer stereo vision, the fundamental matrix is the algebraic representation of the epipolar geometry that relates two images of a scene observed from two different viewpoints. The most important feature of the fundamental matrix is its independence of the scene structure. Different methods have been proposed to derive the fundamental matrix equation.  This paper reviews one of these methods and reveals that it is based on flawed statements to conclude the existence of a homography between the points on the two images. This derivation of the fundamental matrix equation is based on the existence of a homography between the two images.

During the last three decades, there has been a substantial research effort devoted to the proble... more During the last three decades, there has been a substantial research effort devoted to the problem of 3D extraction and construction from two views of a given scene. One of the major challenges in computer vision has been the elaboration of methods, which do not depend on scene structure, to compute the relationship between pairs of corresponding points from two views. Two landmark achievements, in this field, were the development of the essential matrix by Longuet-Higgins and the elaboration of the fundamental matrix by Olivier Faugeras. Basta [1] reviewed the work of Longuet-Higgins, discovering mathematical flaws in the derivation of the essential matrix. In a similar vein, this paper discusses mathematical flaws in the derivation of the fundamental matrix, which is based on the theory of a point lying on a line.

Proceedings of the 2019 5th International Conference on Computer and Technology Applications

International Journal of Machine Learning and Computing, 2012

In 1981 Longuet-Higgins represented the world point by two vectors in the two camera reference fr... more In 1981 Longuet-Higgins represented the world point by two vectors in the two camera reference frames and developed the essential matrix. Such a matrix is a relation between the corresponding image points on the two images of a world point on a rigid scene. The essential matrix is independent of the position and orientation of the cameras used to capture the two views. The calculation of the essential matrix requires the knowledge of at least five accurate pairs of corresponding points. The unavailability of a procedure that fulfills such a requirement led researchers to focus their attention on developing estimation methods of the essential matrix without questioning the mathematical correctness of its derivation. In this paper, we identify and expose flaws in Longuet-Higgins' derivation of the essential matrix. These flaws are the result of mixing up between the scalar product of vectors in a single reference frame and the transformation of vectors from one reference frame to another.

Asian Journal of Information Technology, 2006

In this paper, we have described an approach for a 3D scene reconstruction using 2 randomly selec... more In this paper, we have described an approach for a 3D scene reconstruction using 2 randomly selected adjacent colored video frames. We have used a single uncalibrated video camera to take a record for uncalibrated environment. The Selection of 2 frames based on the maximum homogeneity of points on these frames are favorable; could be any two adjacent frames. The use of Harris technique were very useful to find the edges and corners on each selected image (frame), then the use of the autocorrelation function ...

International Journal of Signal Processing, Image Processing and Pattern Recognition, Oct 31, 2014

In stereo vision, two images of a 3D scene are acquired from two viewpoints. One of the objective... more In stereo vision, two images of a 3D scene are acquired from two viewpoints. One of the objectives of stereo vision work is to recover the 3D structure of the scene. Epipolar geometry describes the relationship between the images, and the essential and fundamental matrices are the algebraic representations of this geometry. The most important feature of these matrices that is emphasized in the literature is that they are independent of the scene structure. This article illustrates-empirically and theoretically-that the fundamental matrix depends on the scene structure and demonstrates that the matrix in 0  l r Fm m not only represents a relationship between corresponding points of the two views but also represents a relationship between other non-corresponding points. Furthermore, we show empirically that the equation 0  l r Fm m does not hold for any pair of corresponding points. In scenes with objects of different depths, the value of l r Fm m depends on the depths of the 3D points and increases proportionally with an increasing baseline.

Proceedings of the 9th Wseas International Conference on Signal Speech and Image Processing and 9th Wseas International Conference on Multimedia Internet Video Technologies, Sep 1, 2009

Extracting 3D structure from two views is a flourishing subject in computer vision literature. In... more Extracting 3D structure from two views is a flourishing subject in computer vision literature. In 1981 Longuet-Higgins introduces what it seemed a mathematically founded theory that relates the corresponding points from the two images independently from the extrinsic camera parameters. Since then a number of contributions based on such a theory was emerged.