The Ellipse

The Ellipse: The Fall and Rise of the Human Soul, Secrets of the Cosmos describes the cosmic laws of the universe ruling the reality of the human experience and the destiny of humanity. It is an in depth study of the spiritual science that is the source of all religion, and the cause of the human condition. The term ellipse which means imperfect circle, as opposed to the perfect circle, is the updated metaphor that replaces the traditional concepts of God and the devil, and good and evil as the human race evolves out of the age of mythology to the era of the merging of science and spirituality. This spiritual saga describes the inner and outer soul of the universe, the apocalypse, and the destiny of the human race. Delving deeper than any metaphysical writer of the past or present, the book reveals new insights about the fall of man and the soul's journey to its ultimate destiny in unraveling the mysteries of its existence. It also clarifies pervasive distortions and misconceptions within religion and metaphysics.

Explores the development of the ellipse and presents mathematical concepts within a rich, historical context The Ellipse features a unique, narrative approach when presenting the development of this mathematical fixture, revealing its parallels to mankind's advancement from the Counter-Reformation to the Enlightenment. Incorporating illuminating historical background and examples, the author brings together basic concepts from geometry, algebra, trigonometry, and calculus to uncover the ellipse as the shape of a planet's orbit around the sun. The book begins with a discussion that tells the story of man's pursuit of the ellipse, from Aristarchus to Newton's successful unveiling nearly two millenniums later. The narrative draws insightful similarities between mathematical developments and the advancement of the Greeks, Romans, Medieval Europe, and Renaissance Europe. The author begins each chapter by setting the historical backdrop that is pertinent to the mathematical material that is discussed, equipping readers with the knowledge to fully grasp the presented examples and derive the ellipse as the planetary pathway. All topics are presented in both historical and mathematical contexts, and additional mathematical excursions are clearly marked so that readers have a guidepost for the materials' relevance to the development of the ellipse. The Ellipse is an excellent book for courses on the history of mathematics at the undergraduate level. It is also a fascinating reference for mathematicians, engineers, or anyone with a general interest in historical mathematics.

Because circular objects are projected to ellipses in images, ellipse fitting is a first step for 3-D analysis of circular objects in computer vision applications. For this reason, the study of ellipse fitting began as soon as computers came into use for image analysis in the 1970s, but it is only recently that optimal computation techniques based on the statistical properties of noise were established. These include renormalization (1993), which was then improved as FNS (2000) and HEIV (2000). Later, further improvements, called hyperaccurate correction (2006), HyperLS (2009), and hyper-renormalization (2012), were presented. Today, these are regarded as the most accurate fitting methods among all known techniques. This book describes these algorithms as well implementation details and applications to 3-D scene analysis. We also present general mathematical theories of statistical optimization underlying all ellipse fitting algorithms, including rigorous covariance and bias analyses and the theoretical accuracy limit. The results can be directly applied to other computer vision tasks including computing fundamental matrices and homographies between images. This book can serve not simply as a reference of ellipse fitting algorithms for researchers, but also as learning material for beginners who want to start computer vision research. The sample program codes are downloadable from the website: https://sites.google.com/a/morganclaypool.com/ellipse-fitting-for-computer-vision-implementation-and-applications.