Results 1  10
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196
On the Removal of Shadows from Images
, 2006
"... This paper is concerned with the derivation of a progression of shadowfree image representations. First, we show that adopting certain assumptions about lights and cameras leads to a 1D, grayscale image representation which is illuminant invariant at each image pixel. We show that as a consequenc ..."
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Cited by 236 (18 self)
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consequence, images represented in this form are shadowfree. We then extend this 1D representation to an equivalent 2D, chromaticity representation. We show that in this 2D representation, it is possible to relight all the image pixels in the same way, effectively deriving a 2D image representation which
Grid Representations and the Chromatic Number
, 2014
"... A grid drawing of a graph maps vertices to grid points and edges to line segments that avoid grid points representing other vertices. We show that there is a number of grid points that some line segment of an arbitrary grid drawing must intersect. This number is closely connected to the chromatic nu ..."
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A grid drawing of a graph maps vertices to grid points and edges to line segments that avoid grid points representing other vertices. We show that there is a number of grid points that some line segment of an arbitrary grid drawing must intersect. This number is closely connected to the chromatic
Chromatic polynomials and representations of the symmetric group
, 2001
"... The chromatic polynomials considered in this paper are associated with graphs constructed in the following way. Take n copies of a complete graph Kb and, for i = 1, 2,..., n, join each vertex in the ith copy to the same vertex in the (i + 1)th copy, taking n + 1 = 1 by convention. Previous calculati ..."
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Cited by 3 (2 self)
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calculations for b = 2 and b = 3 suggest that the chromatic polynomial contains terms that occur in ‘levels’. In the present paper the levels are explained by using a version of the sieve principle, and it is shown that the terms at level ℓ correspond to the irreducible representations of the symmetric group
Chromatic structure of natural scenes
, 2001
"... We applied independent component analysis (ICA) to hyperspectral images in order to learn an efficient representation of color in natural scenes. In the spectra of single pixels, the algorithm found basis functions that had broadband spectra and basis functions that were similar to natural reflectan ..."
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Cited by 50 (5 self)
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We applied independent component analysis (ICA) to hyperspectral images in order to learn an efficient representation of color in natural scenes. In the spectra of single pixels, the algorithm found basis functions that had broadband spectra and basis functions that were similar to natural
Algebraic methods for chromatic polynomials
, 2001
"... In this paper we discuss the chromatic polynomial of a ‘bracelet’, when the base graph is a complete graph and arbitrary links between the copies are allowed. The resulting graph will be denoted by Ln(b). We show that the chromatic polynomial of Ln(b) can be written in the form b ∑ ∑ P (Ln(b); k) ..."
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Cited by 22 (7 self)
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In this paper we discuss the chromatic polynomial of a ‘bracelet’, when the base graph is a complete graph and arbitrary links between the copies are allowed. The resulting graph will be denoted by Ln(b). We show that the chromatic polynomial of Ln(b) can be written in the form b ∑ ∑ P (Ln(b); k
Chromatic parameter space representation of LCD operating modes
, 1997
"... : A chromatic parameter space (CPS) representation is proposed to represent the operation of LCDs. Both chrominance and luminance are visualized in the CPS diagrams. All the usual display modes, both transmissive and reflective, such as TN, ECB, OMI, STN, and SBE are shown clearly on the diagrams. T ..."
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Cited by 1 (0 self)
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: A chromatic parameter space (CPS) representation is proposed to represent the operation of LCDs. Both chrominance and luminance are visualized in the CPS diagrams. All the usual display modes, both transmissive and reflective, such as TN, ECB, OMI, STN, and SBE are shown clearly on the diagrams
Specht modules and chromatic polynomials
, 2003
"... An explicit formula for the chromatic polynomials of certain families of graphs, called ‘bracelets’, is obtained. The terms correspond to irreducible representations of symmetric groups. The theory is developed using the standard bases for the Specht modules of representation theory, and leads to an ..."
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Cited by 4 (4 self)
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An explicit formula for the chromatic polynomials of certain families of graphs, called ‘bracelets’, is obtained. The terms correspond to irreducible representations of symmetric groups. The theory is developed using the standard bases for the Specht modules of representation theory, and leads
On the quantum chromatic number of a graph
"... We investigate the notion of quantum chromatic number of a graph, which is the minimal number of colours necessary in a protocol in which two separated provers can convince a referee that they have a colouring of the graph. After discussing this notion from first principles, we go on to establish re ..."
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Cited by 12 (2 self)
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relations with the clique number and orthogonal representations of the graph. We also prove several general facts about this graph parameter and find large separations between the clique number and the quantum chromatic number by looking at random graphs. Finally, we show that there can be no separation
Bounds On The Complex Zeros Of (Di)Chromatic Polynomials And PottsModel Partition Functions
 Chromatic Roots Are Dense In The Whole Complex Plane, Combinatorics, Probability and Computing
"... I show that there exist universal constants C(r) < ∞ such that, for all loopless graphs G of maximum degree ≤ r, the zeros (real or complex) of the chromatic polynomial PG(q) lie in the disc q  < C(r). Furthermore, C(r) ≤ 7.963907r. This result is a corollary of a more general result on the ..."
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Cited by 61 (14 self)
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I show that there exist universal constants C(r) < ∞ such that, for all loopless graphs G of maximum degree ≤ r, the zeros (real or complex) of the chromatic polynomial PG(q) lie in the disc q  < C(r). Furthermore, C(r) ≤ 7.963907r. This result is a corollary of a more general result
Results 1  10
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196