This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages)
This article possibly contains original research. Please improve it by verifying the claims made and adding inline citations. Statements consisting only of original research should be removed.(October 2014) (Learn how and when to remove this message)
This article may contain excessive or inappropriate references to self-published sources. Please help improve it by removing references to unreliable sources where they are used inappropriately.(October 2014) (Learn how and when to remove this message)
(Learn how and when to remove this message)
Boundary tracing, also known as contour tracing, of a binary digital region can be thought of as a segmentation technique that identifies the boundary pixels of the digital region. Boundary tracing is an important first step in the analysis of that region.
Boundary is a topological notion. However, a digital image is no topological space. Therefore, it is impossible to define the notion of a boundary in a digital image mathematically exactly. Most publications about tracing the boundary of a subset S of a digital image I describe algorithms which find a set of pixels belonging to S and having in their direct neighborhood pixels belonging both to S and to its complement I - S. According to this definition the boundary of a subset S is different from the boundary of the complement I – S which is a topological paradox.
To define the boundary correctly it is necessary to introduce a topological space corresponding to the given digital image. Such space can be a two-dimensional abstract cell complex. It contains cells of three dimensions: the two-dimensional cells corresponding to pixels of the digital image, the one-dimensional cells or “cracks” representing short lines lying between two adjacent pixels, and the zero-dimensional cells or “points” corresponding to the corners of pixels. The boundary of a subset S is then a sequence of cracks and points while the neighborhoods of these cracks and points intersect both the subset S and its complement I – S.
The boundary defined in this way corresponds exactly to the topological definition and corresponds also to our intuitive imagination of a boundary because the boundary of S should contain neither elements of S nor those of its complement. It should contain only elements lying between S and the complement. This are exactly the cracks and points of the complex.
This method of tracing boundaries is described in the book of Vladimir A. Kovalevsky[1] and in the web site.[2]
^Kovalevsky, V., Image Processing with Cellular Topology, Springer 2021, ISBN 978-981-16-5771-9
^http://www.kovalevsky.de, Lecture "Tracing Boundaries in 2D Images"
Boundarytracing, also known as contour tracing, of a binary digital region can be thought of as a segmentation technique that identifies the boundary...
faithful to reality Ray tracing (graphics), techniques in computer graphics Boundarytracing (also known as contour tracing), a segmentation technique...
April 2023. {{cite journal}}: Cite journal requires |journal= (help) "BoundaryTracing Method". Archived from the original on 20 February 2015. Dewdney, A...
cell coverage area finding boundaries of level sets after image segmentation Edge detection Level-set method Boundarytracing Active contour model To maximize...
Process tracing is a qualitative research method used to develop and test theories. Process-tracing can be defined as the following: it is the systematic...
standards such as DjVu and JBIG2. Image compression Blob detection Boundarytracing Triangle strip Freeman, Herbert (June 1961). "On the Encoding of Arbitrary...
Tracing boards are painted or printed illustrations depicting the various emblems and symbols of Freemasonry. They can be used as teaching aids during...
In computer graphics, image tracing, raster-to-vector conversion or raster vectorization is the conversion of raster graphics into vector graphics. An...
processing, spreading activation over an area delimited by boundaries, tracingboundaries, and marking a location or object for future reference. When...
for boundary scan testing: ARM architecture processors come with JTAG support, sometimes supporting a two-wire "SWD" variant or high speed tracing of traffic...
problem and some tricks for its solution can be found in an issue of the Ray Tracing News. One simple way of finding whether the point is inside or outside...
Minesweeper for determining which pieces are cleared. A variant called boundary fill uses the same algorithms but is defined as the area connected to a...
RTX cards, the first in the industry to implement realtime hardware ray tracing in a consumer product. In a departure from Nvidia's usual strategy, the...
Rendering of constructive solid geometry is particularly simple when ray tracing. Ray tracers intersect a ray with both primitives that are being operated...
reconstruction of contour lines from scattered data points, and in boundarytracing in image analysis. Denjoy–Riesz theorem, on sets of infinitely many...
scattering in small size parameter regime x ≪ 1 {\displaystyle x\ll 1} . Ray tracing techniques can approximate light scattering by not only spherical particles...
for tracingboundaries in 2D and 3D, for economically encoding the boundaries and for exactly reconstructing a subset from the code of its boundary. Using...
Dubai. Retrieved 5 August 2019. Küng, Hans (31 August 2006). Hans Kung, Tracing the Way: Spiritual Dimensions of the World Religions, éd. Continuum International...
to the interior angle. Tracing around a convex n-gon, the angle "turned" at a corner is the exterior or external angle. Tracing all the way around the...
ray tracing to incorporate path tracing where diffused light will also bounce across duller surfaces in addition to reflective ones. Path tracing's computational...
paper; these were then traced on to tracing paper using India ink for reproduction whenever needed. The tracing paper drawing is placed on top of the...
Fort Collins, Colorado, USA, December 102 pages. Joseph R. Curray, 1961, Tracing sediment masses by grain size modes; Proc. Internat. Association of Sedimentology...