Segmenting multi bands images by color and

texture

Eldman O. Nunes - Aura Conci

IC - UFF

Introduction

•Use of fractals and image multiespectral bands to characterize texture.

•Considering inter-relation among bands the image FD є [ 0 , number of bands + 2] .

•Improve the possibilies of usual false color segmentations (assigning satellite bands to RGB color). It is not now limited to 3 band.

• The color sensations noticed by humans are combination of the intensities received by 3 types of cells cones.

• Combination of the 3 primary colors produces the others

• In the video: R=700 nm, G = 546,1 nm, B=435,1 nm.

Monocromatic : one color channel or one band.

• binary image:

each pixel only

0 or 1 values.

• intensity level (grey level):

each pixel one value

from 0 to 255.

Digital images

• Multiband images: n band value for each pixel.

• examples: »color images »sattelite images»medical images

color images

each pixel 3 values ( from 0 to 255 )

3 bands: Red - Green -Blue.

 

   

 

 

 

  

  

 

Band 1 Band 2 Band 3

Band 4 Band 5 Band 6 Band 7

example : a LandSat-7 image is a collection of 7 images of same scene

sensor characteristics

TM HRV AVHRR

spacial resolution

30 m120 m (Band 6)

20 m (Band 1 a 3)10 m (Pan)

1.1 Km (nominal)

spectralBands (micro meters)

Band 1 - 0.45-0.52Band 2 - 0.52-0.60Band 3 - 0.63-0.69Band 4 - 0.76-0.90Band 5 - 1.55-1.75Band 6 - 10.74-12.5Band 7 - 2.08-2.35

Band 1 - 0.50-0.59Band 2 - 0.61-0.68Band 3 - 0.79-0.89Pan - 0.51-0.73

Band 1 - 0.58-0.68Band 2 - 0.725-1.1Band 3 - 3.55-3.93Band 4 - 10.30-11.30Band 5 - 11.50-12.50

Radiometric resolution

8 bits8 bits (1-3) 6 bits (Pan)

10 bits

Temporalresolution 16 days 26 days 2 times a days

Landsat 7 - Sensor TM

Channel spectral band (um) main applications

1 0.45 - 0.52Differentiation between soil and vegetation, conifers and deciduous trees

2 0.52 - 0.60 healthy vegetation

3 0.63 - 0.69 chlorophyll absortion, vegetation types

4 0.76 - 0.90 biomass , water bodies

5 1.55 - 1.75 penetrate smokes, snow

6 10.4 - 12.5 surface temperature from -100 to 150 C

7 2.08 - 2.35 hidrotermal map, buildings, soil trafficability

Band 4 (R), 5 (G), 3 (B)

Band 4 (R), 3 (G), 2 (B)

Multiespectral false color :

l , m, n Bands to Red, Green and Blue.

TexturesTexture is characterized by the repetition of a model on an area.

Textons : size, format, color and orientation of the elements.

Textons can be repeated in an exact way or with small variations on a same theme.

Texture 1

Texture 2

Fractal Geometry

• self similar sets

• fractal dimensions and measures used to classify textures

FD for binary image

• Box Counting Theorem - 2D images.

• For a set A, Nn(A) = number of boxes of side 1/2n

which interser the set A:

DF = lim n log Nn (A) / log 2n

n Nn (A) 2n log Nn (A) log 2n

1 4 2 1,386 0,693

2 12 4 2,484 1,386

3 36 8 3,583 2,079

4 108 16 4,682 2,772

5 324 32 5,780 3,465

6 972 64 6,879 4,158

0

2

4

6

8

0 1 2 3 4 5

log (2n )

log

Nn

(A)

gray level images• Box Counting Theorem extension for 3-dimensional object: third

coordinate represents the intensity of the pixel.

• DF between 2 e 3.

Blanket Dimension - Blanket Covering Method

The space is subdivided in cubes of sides SxSxS ’.

Nn(A) denotes the number of cubes intercept a blanket covering the image: Nn = nn (i,j)

On each grid (i,j), nn (i,j) = int ( ( max – min ) / s’ ) + 1

for multi-bands image

•a color R G B image is a subset of the 5-dimensional space : N5). Each pixel is defined by: (x, y, r, g, b)

•FD of this images: values from 2 to 5.

Generalizing: d-cube

• points (0D), segments (1D), squares (2D), cubes (3D) and

• for a n-dimensional : n-cube (nD)

• But what is d-cubos , and how many d-cubes appear in a divison of Nd space?

r

r

r

rr

r

SEGMENTO

QUADRADO CUBO

Sweep representation :

• n-cube as translational swepps of (n-1) cube

Generalizing: d-Cube Counting - DCC:

• the experimental determination of the fractal dimension of images with multiple channels;

• will imply in the recursive division of the N space in d-cubes of size r;

• followed by the contagem of the numbers of d-cubes that intercept the image.

• monochrome images: the space N3 is divided by 3-cubos of size 1/2n, and the number of 3-cubos that intercept the image it is counted.

• color images: the space N5 is divided by 5-cubos of the same size 1/2n, and the number of 5-cubos that intercept the image is counted.

• satellite images: the space Nd is divided by d-cubes of size 1/2n and the number of d-cubes that intercept the image is counted.

• number of 1-cubes: Nn

1-cubos = 2 1x n, where n is the number of divisions.

• number of 2-cubes: Nn

2-cubos = 2 2x n, where n is the number of divisions.

• number of 3-cubos: Nn

3-cubos = 2 3x n, where n is the number of divisions.

• Generalizing, the number of identical d-cube: Nn

d-cubes = 2 d x n, where d is the space dimension and n it is the number of divisions.

Then FD of d-dimensional images can be obtained by:

DFn = log (Nn,d-cubo) /log (2n )

Results binary images

gray scale

colored images

satellite images

CDC invariance to resolution (FD 3,465)

CDC invariance on colors reflection (second image) and affine transformations (FD 3,465)

CDC invariance to band combinations(FD 3,465) : RGB (4-5-6, 4-6-5, 5-4-6, 5-6-4, 6-4-5, 6-5-4)

Mosaic of textures: original x CDCSegmentation result: same color means same texture.

comparison: original - SEGWINSPRING - CDC

Region on the city of Patriocínio - MG

(from Landsat 5-TM, 5-4-3 spectral band to RGB)

Segmentation results by CDC