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Image gradients can also be used for robust feature and texture matching. Different lighting or camera properties can cause two images of the same scene to have drastically different pixel values. This can cause matching algorithms to fail to match very similar or identical features. One way to solve
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intensity function which has been sampled at the image points. With some additional assumptions, the derivative of the continuous intensity function can be computed as a function on the sampled intensity function, i.e., the digital image. Approximations of these derivative functions can be defined at
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On the left, an intensity image of a cat. In the center, a gradient image in the x direction measuring horizontal change in intensity. On the right, a gradient image in the y direction measuring vertical change in intensity. Gray pixels have a small gradient; black or white pixels have a large
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One of the most common uses is in edge detection. After gradient images have been computed, pixels with large gradient values become possible edge pixels. The pixels with the largest gradient values in the direction of the gradient become edge pixels, and edges may be traced in the direction
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273:) for this purpose. Each pixel of a gradient image measures the change in intensity of that same point in the original image, in a given direction. To get the full range of direction, gradient images in the x and y directions are computed.
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in the horizontal and vertical directions. At each image point, the gradient vector points in the direction of largest possible intensity increase, and the length of the gradient vector corresponds to the rate of change in that direction.
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this is to compute texture or feature signatures based on gradient images computed from the original images. These gradients are less susceptible to lighting and camera changes, so matching errors are reduced.
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Since the intensity function of a digital image is only known at discrete points, derivatives of this function cannot be defined unless we assume that there is an underlying
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422:{\displaystyle \nabla f={\begin{bmatrix}g_{x}\\g_{y}\end{bmatrix}}={\begin{bmatrix}{\frac {\partial f}{\partial x}}\\{\frac {\partial f}{\partial y}}\end{bmatrix}}}
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denotes the 1-dimensional convolution operation. This 2×1 filter will shift the image by half a pixel. To avoid this, the following 3×1 filter
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is a directional change in the intensity or color in an image. The gradient of the image is one of the fundamental building blocks in
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perpendicular to the gradient direction. One example of an edge detection algorithm that uses gradients is the
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from low to high values, as used from white to black in the images to the right. Another name for this is
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varying degrees of accuracy. The most common way to approximate the image gradient is to
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994:(3rd ed.). Upper Saddle River, New Jersey: Pearson Education, Inc.
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can be used. The gradient direction can be calculated by the formula:
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is the derivative with respect to y (gradient in the y direction).
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is the derivative with respect to x (gradient in the x direction)
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1054:. Upper Saddle River, New Jersey: Prentice-Hall, Inc. pp.
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850:{\displaystyle \theta =\operatorname {tan{^{-}}{^{1}}} \left}
562:{\displaystyle \textstyle {\frac {\partial f}{\partial y}}}
511:{\displaystyle \textstyle {\frac {\partial f}{\partial y}}}
468:{\displaystyle \textstyle {\frac {\partial f}{\partial x}}}
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Directional change in the intensity or color in an image
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530:. If central difference is used, to calculate
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911:{\displaystyle {\sqrt {g_{y}^{2}+g_{x}^{2}}}}
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988:Gonzalez, Rafael; Richard Woods (2008).
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1879:Color Association of the United States
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118:Image gradients are often utilized in
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178:adding citations to reliable sources
122:and other visual representations of
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67:is also used for a gradual blend of
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71:which can be considered as an even
1743:Blue–green distinction in language
975:." Class Notes for CMSC 426 (2005)
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1016:"Edges: Gradient Edge Detection"
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861:and the magnitude is given by:
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1884:International Colour Authority
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1960:List of Crayola crayon colors
584:{\displaystyle \mathbf {A} }
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1423:Multi-primary color display
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1623:Color realism (art style)
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1281:Evolution of color vision
953:Total variation denoising
1940:List of colors (compact)
1758:Color in Chinese culture
1408:Digital image processing
1141:Electromagnetic spectrum
1058:–158, 215–216, 299–300.
991:Digital Image Processing
51:uses image gradient for
1945:List of colors by shade
63:, the term gradient or
1950:List of color palettes
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1930:List of colors: G–M
1925:List of colors: A–F
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47:. For example, the
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1977:List of RAL colors
1383:Color reproduction
1348:Lüscher color test
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1396:Color balance
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1313:Tetrachromacy
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1237:Achromatopsia
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1220:Chromesthesia
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1134:Color physics
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943:Posterization
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938:Color banding
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195: –
194:
190:
189:Find sources:
183:
179:
175:
169:
168:
164:
159:This section
157:
153:
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29:
21:
1835:Fluorescence
1798:Colorfulness
1791:Dichromatism
1635:
1627:
1597:Chromaticity
1580:Color mixing
1572:Color theory
1505:Color scheme
1368:Chromophobia
1317:
1049:
1023:. Retrieved
1019:
1010:
990:
967:
860:
762:
680:
521:
432:
292:
283:
275:
271:Sobel filter
264:
240:
231:
221:
214:
207:
200:
188:
172:Please help
160:
117:
97:
81:
76:
40:
38:
1972:Color chart
1830:Iridescence
1662:Basic terms
1653:Color terms
1607:Color wheel
1602:Color solid
1466:Color space
1452:subtractive
1435:Color model
1306:Unique hues
1202:Colorimetry
1168:Chromophore
593:convolution
289:Mathematics
92:derivatives
2140:Categories
1992:Shades of:
1825:Brightness
1557:Web colors
1513:Color tool
1496:philosophy
1401:Color cast
1301:Afterimage
1291:Metamerism
1264:Color code
1259:Color task
1242:Dichromacy
1025:2023-04-09
959:References
524:derivative
204:newspapers
100:continuous
1842:Grayscale
1815:Lightness
1810:Luminance
1619:(fashion)
1319:The dress
813:
774:θ
720:−
689:∗
661:∗
637:−
617:∂
609:∂
550:∂
542:∂
499:∂
491:∂
456:∂
448:∂
403:∂
395:∂
379:∂
371:∂
308:∇
261:gradient.
161:does not
132:elevation
73:gradation
2115:Category
2097:Lighting
1820:Darkness
1640:(Goethe)
1440:additive
1428:Quattron
1082:function
928:Acutance
922:See also
295:partials
105:convolve
84:gradient
2079:Related
2040:Magenta
1965:history
1869:Pantone
1156:Visible
1151:Rainbow
433:where:
218:scholar
182:removed
167:sources
2092:Qualia
2087:Vision
2035:Purple
2030:Violet
2010:Yellow
2005:Orange
1700:Orange
1695:Purple
1685:Yellow
1119:topics
1062:
998:
681:where
220:
213:
206:
199:
191:
88:vector
2125:Index
2065:Black
2055:White
2050:Brown
2015:Green
1917:Lists
1909:Names
1891:(CIE)
1860:Color
1720:Brown
1715:White
1705:Black
1675:Green
1494:Color
1190:Water
1146:Light
1117:Color
225:JSTOR
211:books
69:color
55:. In
2060:Gray
2045:Pink
2025:Blue
2020:Cyan
1710:Gray
1690:Pink
1670:Blue
1457:CMYK
1060:ISBN
996:ISBN
522:The
197:news
165:any
163:cite
134:and
124:data
120:maps
59:for
2000:Red
1786:Hue
1680:Red
1445:RGB
1056:157
591:by
265:In
176:by
128:GIS
111:or
39:An
2142::
1018:.
980:^
595::
297::
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115:.
79:.
1109:e
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817:[
806:1
795:-
787:n
784:a
781:t
777:=
746:]
740:1
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730:0
723:1
714:[
665:A
656:]
650:1
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631:[
626:=
620:y
612:f
578:A
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415:]
406:y
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382:x
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362:[
357:=
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344:y
340:g
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326:g
319:[
314:=
311:f
247:)
241:(
236:)
232:(
222:·
215:·
208:·
201:·
184:.
170:.
35:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
