Bio-medical Ontologies Maintenance and Change Management

3-D color histogram
M
Tc Qc -1 M -1
T (Qc ) c
Multimedia Medical Databases 97
Fig. 3.4. Transformation between 3-D color histogram and binary color set
University of Columbia [83, 84, 85, 87]. The binary color sets can be obtained
by selection from M colors. The process is represented in the following figure
[84, 86]:
Let B M be an M dimensional binary space, such that each index value m
corresponds to one axis in B M .
The following definition can be given [86]:
The color set s c is a binary vector in B M . A color set corresponds to a selection
of colors from the quantized color space.
A binary set is equivalent with a limited histogram. For example, having the
threshold τ m for a color m, the color set is obtained using the following equation:
Sc [m] = 1, if hc [m] ≥ τm , otherwise Sc [m] = 0 (3.14)
The color set specifies only the colors that are above the specified threshold.
The color sets give a good representation of colors, images and regions. If a
color is not representative in a region and it is under the threshold τm it is ignored.
In this manner, with the color set, the color content is represented using only the
most preeminent colors from image or region.
3.5.3 Color Quantization
Because the color spaces are multi-dimensional, a partitioning of the color space is
described by a spece vector quantization [84, 85]. Generally speaking, a vector
quantization Qc of dimension k and size M is a mapping of a vector from a kdimensional
space, in a finite set C which has M outputs. Qc can be defined as a
function Qc : ℜ k
→C, where C = (y0 , y1 , …, yM-1 ) and ym ∈ ℜ k
for each m ∈ 0,1, …,
M-1 [84, 86].
The set C is called the collection of cods and has the size M. For the case of
vector quantization of a color space, k = 3 and for each input in the codes
collection, the y corresponds to a color point.
m
There is a coverage of ℜ k with M partitions that is associated with the vector
quantization, where each partition R has all the points w assigned to the same
m c
code y : m
1
B M
1
Binary color sets
1