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- [[image:boys and balls.png| center]] [[image:boys and balls -- union.png| center]]142 KB (23,566 words) - 02:01, 23 February 2019
- [[image:road and nothing.png| center]] [[image:coordinate system dim 1.png| center]]100 KB (16,148 words) - 20:04, 18 January 2017
- [[image:solution of linear system.png| center]] [[image:solution of linear system 2.png| center]]113 KB (18,750 words) - 02:33, 10 December 2018
- [[Image:light bounce off a curved mirror.png| center]] [[image:secant.png| center]]75 KB (13,000 words) - 15:12, 7 December 2018
- [[image:constant speed.png| center]] [[image:constant acceleration.png| center]]76 KB (13,017 words) - 20:26, 23 February 2019
- [[image:limits of functions.png| center]] [[image:lim f(x) via lim a_n.png| center]]107 KB (18,743 words) - 17:00, 10 February 2019
- [[image:time-location-altitude.png| center]] [[image:composition -- time-location-altitude.png| center]]113 KB (19,680 words) - 00:08, 23 February 2019
- [[image:boys and balls -- constant.png| center]] [[image:constant map.png| center]]143 KB (24,052 words) - 13:11, 23 February 2019
- [[image:Sum Rule for differentials.png| center]] [[image:Constant Multiple Rule for differentials.png| center]]82 KB (14,116 words) - 19:50, 6 December 2018
- [[image:parabola on grid.png| center]] [[image:area between parabola and horizontal line.png| center]]17 KB (2,933 words) - 19:37, 30 July 2018
- ...y is the science of spatial properties that are preserved under continuous transformations.'' To elaborate a bit: you can bend, stretch, and shrink but '''not''' tear <!--100-->[[image:topology-algebra-geometry 1.png|center]]20 KB (3,407 words) - 21:46, 30 November 2015
- <!--200-->[[Image:continuous vs discontinuous.png|center]] <!--200-->[[Image:continuous function.png|center]]42 KB (7,138 words) - 19:08, 28 November 2015
- ==Functions as transformations== [[image:solution of linear system.png| center]]46 KB (7,625 words) - 13:08, 26 February 2018
- [[image:circles.png|center]] <!--150-->[[image:circle homotopy type.png|center]]46 KB (7,846 words) - 02:47, 30 November 2015
- ...<!--\index{Topology}--> would be incomplete without considering continuous transformations of objects, also known as maps<!--\index{maps}-->. <!--250-->[[image:components and holes under maps.png|center]]29 KB (5,042 words) - 17:57, 28 November 2015
- *develop further methods for studying transformations of these structures. [[Image:graph examples.png|center]]25 KB (4,214 words) - 16:08, 28 November 2015
- [[image:Calculus Illustrated.png|right]] 16 The image: the range of values of a function16 KB (1,933 words) - 19:50, 28 June 2021
- ...and objects are large. So the question is, what changes to the image will produce "small" changes to the output of analysis, especially [[Measur <p>Let’s consider a very simple example. Suppose we have an image containing a 1x1 black square on white background. Suppose also that the re4 KB (604 words) - 16:35, 12 March 2010
- ...dding a single pixel shouldn't dramatically change the [[topology]] of the image. But it does! The example on the right shows that adding the red pixel merg [[Image:Adding_whole_pixel.JPG|center]]5 KB (784 words) - 13:28, 28 August 2015
- ...y different from "image recognition". The latter is essentially [[image-to-image search]]. ...a few examples: Numenta (below) and others that try object recognition for image search:3 KB (520 words) - 22:59, 6 September 2010
- <p>[[Pixcavator image search]] searches for images based on similarity, a potential application o ...nly used in information retrieval. Below, we just replace “document” with “image”.</p>4 KB (669 words) - 03:34, 6 September 2010
- This is an introduction into the mathematics of computer vision and digital image analysis: [[topology]] and [[geometry]]. (For a more advanced approach see [[image:Topology_graph.jpg|right|400px]]3 KB (436 words) - 15:05, 24 October 2015
- ==Example of image analysis== [[Image:CellsMATLABoriginal.jpg|300px]] [[Image:CellsMATLAB.jpg|330px]][[Image:CellsMATLABoriginal_2000_60.jpg|300px]]4 KB (548 words) - 14:55, 9 October 2010
- [[Image:Torus.JPG|thumb|right|300px|Betti Numbers: B<sub>0</sub> = 1 (parts), B<sub We will compute the spacial properties that are preserved under topological transformations, i.e. you can bend, stretch, or shrink but not tear or glue. We determine t9 KB (1,431 words) - 16:57, 20 February 2011
- ...ed like this is rather difficult. It is obvious that simply looking at the image, one may determine how circular the object is, but getting a computer to lo [[image:ExcelFail.jpg]]31 KB (5,254 words) - 17:57, 21 July 2012
- ...rnel of a linear operator. Find the image and the kernel for the following transformations of the plane: (a) rotation around the origin, (b) flip about the diagonal,2 KB (351 words) - 20:49, 30 April 2018
- [[image:no cellphones.png|right]] ...tems of linear equations, matrices and determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, and applications. PR: ACT Math 27 or MTH1324 KB (573 words) - 13:07, 7 April 2018
- [[image:no cellphones.png|right]] ...tems of linear equations, matrices and determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, and applications. PR: ACT Math 27 or MTH1323 KB (321 words) - 21:06, 19 February 2019