Bài giảng xử lí ảnh Học viện kĩ thuật quân sự Point Processing

Point Processing 1.In a digital image point is called pixel (point ≡ ≡≡ ≡ pixel); 2.Point Processing transforms a pixel’s value to function of its value alone: T: f(x,y) → →→ → g(x,y) or G(x,y) = T(f(x,y)) where a=f(x,y), s=g(x,y) 3. Point Processing does not depend on the values of the neighbors. 1192013 2 Image Processing Point Processing 1. Brightness and contrast adjustment 2. Gamma correction 3. Histogram equalization 4. Histogram matching 5. Color correction 1192013 3 Image Processing Point Processing Origin image Histogram equalization brightness +brightness +contrast contrast γ γγ γ γγ γ =1.25 γ γγ γ γγ γ =0.9 negative bitplan 5 1192013 4 Image Processing Point Processing Negative image of image I Let I is an image with gray levels in the range L , L , i.e., L ≤ ≤≤ ≤ ≤≤ ≤ f(x,y) ≤ ≤≤ ≤ ≤≤ ≤ L , for all (x,y) in an image I. The negative transformation is given by: g(x,y) = L f(x,y), for all (x,y) ∈ ∈∈ ∈ ∈∈ ∈I 1192013 5 Image Processing Point Processing Ảnh I Ảnh âm bản của I 1192013 6 Image Processing Point Processing Negative image of image I For a color image I: g(x,y).R = LR f(x,y).R g(x,y).G = LG f(x,y).G g(x,y).B = LB f(x,y).B In general, can be choosen LR=LG=LB 1192013 7 Image Processing Point Processing The original color image and the negative image Negative image

Point Processing

1.In a digital image point is called pixel (point ≡ ≡

pixel);

2.Point Processing transforms a pixel’s value to

function of its value alone:

or G(x,y) = T(f(x,y))

where a=f(x,y), s=g(x,y)

3 Point Processing does not depend on the

values of the neighbors.

Origin image

Histogram equalization

-brightness +brightness γγγγ=1.25 γγγγ=0.9

Point Processing

Negative image of image I

Let I is an image with gray levels in the range [L*, L*], i.e.,

L* ≤ f(x,y) ≤ L*,

for all (x,y) in an image I

The negative transformation is given by:

g(x,y) = L* - f(x,y),

for all (x,y) ∈I

Point Processing

Ảnh I Ảnh âm bản của I

Point Processing

Negative image of image I

For a color image I:

g(x,y).R = LR* - f(x,y).R g(x,y).G = LG* - f(x,y).G g(x,y).B = LB* - f(x,y).B

In general, can be choosen

LR*=LG*=LB*

Point Processing

The original color image

and the negative image

Negative image

αα=0.55

For color image:

g(x,y).R = min{255, αR*f(x,y).R}

g(x,y).G = min{255, αG*f(x,y).G}

g(x,y).B = min{255, αB*f(x,y).B}

αα=5

αα=0.55

Point Processing

Logarithm transform

where c, β β are constants

abc

(a) The origin image(b) After Log transform: c=50, βββ=20(c) After Log transform: c=50, βββ=1

g(x,y) = c*Log(f(x,y)+β β β)

for all (x,y) in image

(a) The origin image(b) After gamma transformation: c=1, βββ=1, Γ=1.25(c) After gamma transformation: c=1, βββ=1, Γ=0.90

Let amin ≤ f(x, y) ≤ amax, for all (x,y) in image

then the interval

[amin, amax]

is called the gray scale

Contrast stretching

amax and amin are the maximum and minimum intensities of a region or image

amin=0, amax=79

amin=100, amax=150

amin = 0, amax = 255

Contrast stretching

min max

min min

max

) ,

(

) ,

a a

a y

x

f L

L y

• f(x,y) = amin ⇒ g(x,y) = Lmin

• f(x,y) = amax ⇒ g(x,y) = Lmax

Contrast stretching

Lmin = 100Lmax = 179

amin = 0

amax = 79

Lmin = 176Lmax = 255

Lmin = 0Lmax = 255

Contrast stretching

amin = 0amax = 255

Lmin = 0Lmax = 255

Contrast stretching

amin = 0 amax = 123

Lmin = 0 Lmax = 255

Contrast stretching

amin = 0 amax = 104

Lmin = 0 Lmax = 255

Contrast stretching

amin = 0 amax = 233

Lmin = 0 Lmax = 255

, )

, ( ,

) ,

(

, )

, ( ,

) ,

(

2 max

2 1

min 1

2

1 min

max

1 min

y x f a

L

a y

x f a

L a

a

a y

x

f L

L

a y

x f L

y x

g

where Lmin ≤ a ≤ 1 < a2 ≤ ≤ Lmax

This formula, however, can be somewhat sensitive to outliers and a less sensitive and more general version is given by:

Contrast stretching

amin = 0 amax = 233

a 1 = 0, a 2 = 50 Lmin = 0, Lmax = 255

Histogram and its transformation

The intensity of a gray image at any coordinates (x,

y) is called gray level (brightness) a of the image at

that point That is

a = f(x, y)

A histogram, h[a], is the number of times that gray level a occurs in the image.

Histogram and its transformation

Histogram and its transformation

Histogram and its transformation

The histogram can

Histogram and its transformation

h(0) = 1180

amin = 0, amax = 79 Lmin = 0, Lmax = 255

Contrast stretching

Contrast stretching

Equalization

The most common histogram normalization technique is

histogram equalization where one attempts to change the histogram through the use of a function

b = T(a)

where:

a and b is a brightness (gray level).

T(a) satisfies the following conditions:

(1) T(a) is single-valued and monotonically increasing in the interval [0 , L]

(2) T(a) ∈ [0, L] for a ∈ [0, L]

Equalization

Remark:

1 The requirement in (1) that T(r) be single valued is

needed to guarantee that the inverse transformation will exist, and the monotonicity condition preserves the

increasing order from black to white in the output image.

a = T −1 (b) for b ∈ [0, L]

2 Condition (2) guarantees that the output gray levels will

be in the same range as the input levels

Equalization

Example:

Define

a :gray level in an immage

Γ :total number of pixels in the image

h(a): number of pixel with gray level a in the image

Equalization

Bài tập

• Cho một ảnh xám kích thước 6×6, mỗi điểm ảnh là một số nằm trong

khoảng [0,100] Ảnh thu được gọi là ảnh F Thực hiện thay đổi sự tương phản với dải xám mới là [0,255].

• Thực hiện biến đổi âm bản và các biến đổi logarit, mũ đối với ảnh F.

• Tính ảnh được cắt theo mặt phẳng bit số 5.

• Vẽ lược đồ xám của ảnh F, đánh giá sơ bộ ảnh F dựa trên lược đồ đó

Biến đổi cân bằng mức xám đối với ảnh F.

• Viết chương trình thực hiện các phép biến đổi điểm ảnh đối với ảnh xám.

• Viết chương trình thực hiện thay đổi độ tương phản.

• Viết chương trình thực hiện phép cân bằng lược đồ mức xám.