Cylindrical Perspective: Cylindrical Perspective: Exploring Visual Perception in Computer Vision

By Fouad Sabry

What is Cylindrical Perspective

Cylindrical perspective is a form of distortion caused by fisheye and panoramic lenses which reproduce straight horizontal lines above and below the lens axis level as curved while reproducing straight horizontal lines on lens axis level as straight. This is also a common feature of wide-angle anamorphic lenses of less than 40mm focal length in cinematography, as well as the basis for creating the 146-degree peripheral vision of Cinerama when projected into a matching, cylindrically curved screen.

How you will benefit

(I) Insights, and validations about the following topics:

Chapter 1: Cylindrical perspective

Chapter 2: Optical aberration

Chapter 3: Map projection

Chapter 4: Panoramic photography

Chapter 5: Distortion (optics)

Chapter 6: Image stitching

Chapter 7: Cylindrical lens

Chapter 8: Image rectification

Chapter 9: Keystone effect

Chapter 10: Vertical and horizontal

(II) Answering the public top questions about cylindrical perspective.

(III) Real world examples for the usage of cylindrical perspective in many fields.

Who this book is for

Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Cylindrical Perspective.

• Language: English
• Publisher: One Billion Knowledgeable
• Release date: May 13, 2024

Book preview

Chapter 1: Cylindrical perspective

Cylindrical perspective is a type of perspective distortion created by fisheye and panoramic lenses that render straight horizontal lines above and below the lens axis level as curved while rendering straight horizontal lines on the lens axis level as straight. This is also a characteristic of cinematography's wide-angle anamorphic lenses with focal lengths of less than 40mm, as well as the basis for creating the 146-degree peripheral vision of Cinerama when projected onto a cylindrically curved screen.

Art has always been a reflection of how humans perceive the world around them. One of the most fascinating aspects of artistic representation is the use of perspective. Traditional linear perspective, with its vanishing points and horizon lines, has been the cornerstone of Western art for centuries. However, there's another perspective technique that offers a unique way of seeing and depicting space: cylindrical perspective.

Cylindrical perspective, also known as panoramic or wide-angle perspective, deviates from the strict rules of linear perspective. Instead of a single vanishing point on the horizon, cylindrical perspective employs a curved horizon line, resulting in a panoramic view that wraps around the viewer. This technique mimics how we perceive our surroundings in real life, especially when our field of vision extends beyond 180 degrees.

The roots of cylindrical perspective can be traced back to ancient art forms, such as panoramic paintings found in Egyptian tombs and Greek frescoes. However, it wasn't until the Renaissance that artists began to explore and formalize this technique. Early experiments can be seen in the works of artists like Paolo Uccello, who incorporated elements of cylindrical perspective in his paintings, albeit subtly.

One of the most notable proponents of cylindrical perspective was the Dutch painter, Pieter Bruegel the Elder. In his landscape paintings, such as The Harvesters and The Tower of Babel, Bruegel skillfully employed cylindrical perspective to create vast, immersive scenes that draw the viewer into the painting. The curvature of the horizon line in Bruegel's works not only adds depth and dimension but also enhances the sense of scale and grandeur.

The true potential of cylindrical perspective, however, was realized in the 19th century with the advent of panoramic photography. Pioneers like Robert Barker and Thomas Sutton developed techniques to capture wide-angle views using specialized cameras and lenses. These early panoramic photographs provided a new way of experiencing and documenting the world, from sweeping landscapes to bustling city streets.

In the realm of contemporary art, cylindrical perspective continues to inspire and intrigue artists across various mediums. Digital artists use 3D modeling software to create immersive virtual environments, where cylindrical perspective allows for interactive experiences that transcend traditional static imagery. Similarly, filmmakers and video game developers leverage cylindrical perspective to immerse audiences in expansive and lifelike worlds.

Architects and urban planners also recognize the value of cylindrical perspective in visualizing and designing spaces. By employing panoramic renderings and virtual reality simulations, they can accurately represent how buildings and landscapes will appear from different vantage points, providing clients and stakeholders with a more comprehensive understanding of their projects.

Beyond its artistic and practical applications, cylindrical perspective also offers a philosophical insight into the nature of perception. By embracing the curved horizon line, artists acknowledge the limitations of our linear understanding of space and time. Cylindrical perspective reminds us that reality is not confined to a single point of view but is instead a multifaceted and continuously evolving panorama.

In conclusion, cylindrical perspective represents a rich and dynamic approach to depicting space and form in art. From its ancient origins to its modern manifestations, this technique has captivated artists and viewers alike with its ability to convey depth, scale, and immersion. Whether used in painting, photography, digital art, or architectural visualization, cylindrical perspective invites us to see the world from a new angle and explore the boundless possibilities of perception.

{End Chapter 1}

Chapter 2: Optical aberration

Aberration is a feature of optical systems, such as lenses, that allows light to be dispersed across a certain region of space rather than being focussed to a single point. This phenomenon is known in the field of optics.

1: Imaging by a lens with chromatic aberration.

In addition, a lens that has a lower chromatic aberration

Image formation optical systems that are subject to aberration will result in the production of images that are not sharp. Optical instrument manufacturers are required to make adjustments to their optical systems in order to compensate for aberration.

The techniques of geometrical optics can be utilized in order to do an analysis of aberration. Some of the general characteristics of reflected and refracted rays are discussed in the articles that are devoted to reflection, refraction, and caustics.

Reflection from a spherical mirror.

Reflected rays (green) that are not directed toward the focal point are produced by incident rays (red) that are directed away from the center of the mirror, F.

Because of spherical aberration, this is the case.

An ideal lens would allow light from any point on an object to pass through it and converge at a single point in the picture plane (or, more generally, the image surface). This would be the case if the lens were perfect. Actual lenses, on the other hand, do not precisely concentrate light on a single spot, even when they are constructed to perfection. Aberrations of the lens are the term used to describe these deviations from the idealized performance of the lens.

The two categories of aberrations are known as monochromatic and chromatic aberrations. When light is reflected or refracted, monochromatic aberrations can develop. These aberrations are created by the geometry of the lens or mirror, and they can occur in either of these two processes. The name comes from the fact that they are visible even when employing monochromatic light.

Chromatic aberrations are brought about by dispersion, which is the change in the refractive index of a lens that occurs regardless of the wavelength. It is because of dispersion that distinct wavelengths of light come to focus at different spots in specific locations. The use of monochromatic light does not result in the appearance of chromatic aberration because.

In terms of monochromatic aberrations, the most common ones are:

Defocus

Spherical aberration

Coma

Astigmatism

Field curvature

Image distortion

In spite of the fact that defocus is theoretically the lowest-order of the optical aberrations, it is not typically considered to be a lens aberration. This is because it can be rectified by shifting the lens (or the picture plane) in order to bring the image plane closer to the optical focus of the lens.

These aberrations are not the only factors that can cause the focal point to shift; the piston and tilt effects are further examples of such effects. When an otherwise perfect wavefront is altered by piston and tilt, it will still create a flawless, aberration-free image; the only difference is that it will be displaced to a new position. This is why piston and tilt are not considered to constitute actual optical aberration errors.

Comparison of an ideal image of a ring (1) and ones with only axial (2) and only transverse (3) chromatic aberration

When different wavelengths are not focused to the same place, a phenomenon known as chromatic aberration has occurred. Some examples of chromatic aberration include::

Chromatic aberration that is axial, often known as longitudinal

It is also referred to as transverse chromatic aberration.

In the classical theory of optics, a perfect optical system involves the following:, The inquiries that were conducted by James Clerk Maxwell

Figure 1

In the event where S (figure 1) is any optical system, rays that are traveling from an axis point O and are under an angle u1 will merge in the axis point O'1, while rays that are traveling under an angle u2 will unite in the axis point O'2. If there is refraction at a collective spherical surface or through a thin positive lens, then O'2 will lie in front of O'1 as long as the angle u2 is greater than u1 (under correction). On the other hand, if there is refraction at a dispersive surface or lenses, then O'2 will lie in front of O'1 (over correction). In the first scenario, the caustic is comparable to the symbol >, which stands for larger than, while in the second scenario, it is similar to the symbol <, which stands for less than. When the angle u1 is very tiny, the Gaussian image is denoted by O'1. The longitudinal aberration of the pencils with aperture u2 is referred to as O'1 O'2, while the lateral aberration is denoted as O'1R. If the pencil with the angle u2 is the one that has the greatest aberration of all the pencils that have been transmitted, then there is a circular disc of confusion with a radius of O'1R in a plane that is perpendicular to the axis at O'1, and another one