Joseph Mundy
Encyclopedia
Computer vision
Computer vision is a field that includes methods for acquiring, processing, analysing, and understanding images and, in general, high-dimensional data from the real world in order to produce numerical or symbolic information, e.g., in the forms of decisions...
and projective geometry using LISP
Lisp
A lisp is a speech impediment, historically also known as sigmatism. Stereotypically, people with a lisp are unable to pronounce sibilants , and replace them with interdentals , though there are actually several kinds of lisp...
, when computer vision still was a new area of research. In 1987 he presented his work in a video, which now is available for free at archive.org.
Here is an extract of the interview, which took place in the end of the video.
"What do students need to learn to be prepared to meet the challenges?" -
"I would like to comment on the necessary courses a student should take to really be prepared to carry out research in model-based vision.
As we can see the geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
of image projection and the mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
of transformation
Affine transformation
In geometry, an affine transformation or affine map or an affinity is a transformation which preserves straight lines. It is the most general class of transformations with this property...
is a very key element in studying this field, but there are many other issues the student has to be prepared for.
If we are going to talk about segmenting images
Image segment
In computer vision segmentation of an image is the division of a given image into contiguous regions. In current computer vision algorithms the similarity of image parts is usually defined in terms of color and texture. The goal to automatically segment images into semantically meaningful parts is...
and getting good geometric clues, we have to understand the relationship between the intensity of image data and its underlying geometry. And this would lead the student into such areas as optics
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
, illumination
Lighting
Lighting or illumination is the deliberate application of light to achieve some practical or aesthetic effect. Lighting includes the use of both artificial light sources such as lamps and light fixtures, as well as natural illumination by capturing daylight...
theory, theory of shadow
Shadow
A shadow is an area where direct light from a light source cannot reach due to obstruction by an object. It occupies all of the space behind an opaque object with light in front of it. The cross section of a shadow is a two-dimensional silhouette, or reverse projection of the object blocking the...
s and the like. And also the mathematics underlying this kind of computations would of course require signal processing
Signal processing
Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...
theory, fourier transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
theory and the like. And in dealing with algebraic surfaces such as this curved surface
Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball...
s as we talked about here, courses in algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
and higher pure forms of algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
will prove to be necessary in order to make any kind of progress in research to handle curved surface
Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball...
s.
So, I guess the bottom line of what I'm saying is: math courses, particularly those associated with geometric aspects will be key in all of this."