Xử lý ảnh trong cơ điện tử: Machine Vision. Chapter 3. Intensity Transformations and Spatial Filtering91

Some Basic Intensity Transformatio❖ Power-Law Gamma Transformations ➢ Contrast enhancement using power-law intensity transform a Magnetic resonance image MRI of a fractured human spine t

XỬ LÝ ẢNH TRONG CƠ ĐIỆN

Machine Vision

TRƯỜNG ĐẠI HỌC BÁCH KHOA

Giảng viên: TS Nguyễn Thành Hùn

Đơn vị : Bộ môn Cơ điện tử , Viện Cơ

Chapter 3 Intensity Transformations and

❖ Two principal categories of spatial processing are intens spatial filtering.

➢ Intensity transformations operate on single pixels of an

as contrast manipulation and image thresholding.

➢ Spatial filtering performs operations on the neighborhoo

image.

➢ Examples of spatial filtering include image smoothing an

Chapter 3 Intensity Transformations and

1 Background

2 Some Basic Intensity Transformation Functions

3 Histogram Processing

4 Fundamentals of Spatial Filtering

5 Smoothing (Lowpass) Spatial Filters

6 Sharpening (Highpass) Spatial Filters

7 Highpass, Bandreject, and Bandpass Filters from

8 Combining Spatial Enhancement Methods

1 Background

❖ The Basics of Intensity Transformations and Spatial F

➢ The spatial domain processes are based on the expressio

where ( f x , y ) is an input image, ( g x , y ) is th e

output image, and is an operator on de T f fined

over a neighborhood of point (x, y).

A 3x3 neighborhood about a poin

is moved from pixel to pixel in the

1 Background

❖ The Basics of Intensity Transformations and Spatial F

➢ intensity (also called a gray-level , or mapping ) transformatio

Inte (a) (b)

Chapter 3 Intensity Transformations and

1 Background

2 Some Basic Intensity Transformation Functions

3 Histogram Processing

4 Fundamentals of Spatial Filtering

5 Smoothing (Lowpass) Spatial Filters

6 Sharpening (Highpass) Spatial Filters

7 Highpass, Bandreject, and Bandpass Filters from

8 Combining Spatial Enhancement Methods

❖ Three basic types of functions

➢ linear (negative and identity transformations)

➢ logarithmic (log and inverse-log transformations)

➢ power-law ( th power and nth root n

transformations)

2 Some Basic Intensity Transformatio

❖ Image Negatives

(a) A digital mammogram (b) Negative image obtained using (Image (a) Courtesy of General Electric Medical Systems.)

2 Some Basic Intensity Transformatio

❖ Log Transformations

where is a co c

2 Some Basic Intensity Transformatio

❖ Power-Law (Gamma) Transformations

w

Plots of the gamma e

of ( = 1 in all case c

2 Some Basic Intensity Transformatio

❖ Power-Law (Gamma) Transformations

(a) Image

as it appe setting of Gammac image, a (compare (a) courte NIH)

2 Some Basic Intensity Transformatio

❖ Power-Law (Gamma) Transformations

➢ Contrast enhancement using power-law intensity transform

a) Magnetic resonance image (MRI) of a fractured human spine (the region of the fracture is e Results of applying the transformation in Eq (3-5) with and and 0.3, respectively (Original ima Department of Radiology and Radiological Sciences, Vanderbilt University Medical Center.)

2 Some Basic Intensity Transformatio

❖ Power-Law (Gamma) Transformations

➢ Another illustration of power-law transformations.

2 Some Basic Intensity Transformatio

❖ Piecewise Linear Transformation Functions

➢ Contrast Stretching

where rmin and rmax denote

the minimum and maximum

intensity levels in the input

image, respectively

2 Some Basic Intensity Transformatio

❖ Piecewise Linear Transformation Functions

➢ Intensity-Level Slicing

Figure 2: (a) Aortic angiogram

2 Some Basic Intensity Transformatio

❖ Piecewise Linear Transformation Functions

➢ Bit-Plane Slicing

Bit-planes of an 8-bit image.

2 Some Basic Intensity Transformatio

❖ Piecewise Linear Transformation Functions

➢ Bit-Plane Slicing

2 Some Basic Intensity Transformatio

❖ Piecewise Linear Transformation Functions

➢ Bit-Plane Slicing

Image reconstructed from bit planes: (a) 8 and 7; (b) 8, 7, and 6; (

Chapter 3 Intensity Transformations and

1 Background

2 Some Basic Intensity Transformation Functions

3 Histogram Processing

4 Fundamentals of Spatial Filtering

5 Smoothing (Lowpass) Spatial Filters

6 Sharpening (Highpass) Spatial Filters

7 Highpass, Bandreject, and Bandpass Filters from

8 Combining Spatial Enhancement Methods

3 Histogram Processing

❖ Histogram

➢ The unnormalized histogram:

where rk is the - intensity level of an -level k th L

digital image ( f x , y n ); k is the number of pixels

in with intensity f rk and the subdivisions of the

intensity scale are called histogram bins.

3 Histogram Processing

❖ Histogram

➢ The normalized histogram:

where M and N are the number of image rows and columns, respectively.

3 Histogram Processing

❖ Histogram

Four image types and their corresponding histograms (a) dark; (b) light; The horizontal axis of the histograms are values of rk and the vertical ax

3 Histogram Processing

❖ Histogram Equalization

➢ Example: Illustration of the mechanics of histogram equali

in Table

3 Histogram Processing

❖ Histogram Equalization

➢ Example: Illustration of the mechanics of histogram equali

We round them to their nearest integer values in the range

3 Histogram Processing

❖ Histogram Equalization

➢ Example: Illustration of the mechanics of histogram equali

Histogram equalization (a) Original histogram (b) Transformation function

3 Histogram Processing

❖ Histogram Equalization

➢ Algorithm for Histogram Equalization

3 Histogram Processing

❖ Histogram Equalization

equalized images

eq Source images

3 Histogram Processing

❖ Histogram Equalization

(a) Image fro histogram eq (a) (d) Histog courtesy of N

Chapter 3 Intensity Transformations and

1 Background

2 Some Basic Intensity Transformation Functions

3 Histogram Processing

4 Fundamentals of Spatial Filtering

5 Smoothing (Lowpass) Spatial Filters

6 Sharpening (Highpass) Spatial Filters

7 Highpass, Bandreject, and Bandpass Filters from

8 Combining Spatial Enhancement Methods

4 Fundamentals of Spatial Filt

❖ The Mechanics of Linear Spatial Filtering

➢ Spatial filter kernel: filter kernel, kernel, mask,

template , and window

➢ Linear spatial filtering

4 Fundamentals of Spatial Filt

❖ Spatial Correlation

and Convolution

➢ 1-D illustration

4 Fundamentals of Spatial Filt

❖ Spatial Correlation and Convolution

➢ 2-D illustration

➢ Correlation

➢ Convolution

4 Fundamentals of Spatial Filt

❖ Spatial Correlation and Convolution

Chapter 3 Intensity Transformations and

1 Background

2 Some Basic Intensity Transformation Functions

3 Histogram Processing

4 Fundamentals of Spatial Filtering

5 Smoothing (Lowpass) Spatial Filters

6 Sharpening (Highpass) Spatial Filters

7 Highpass, Bandreject, and Bandpass Filters from

8 Combining Spatial Enhancement Methods

5 Smoothing (Lowpass) Spatial

➢ Smoothing (also called averaging ) spatial filters are used to transitions in intensity.

➢ Application: noise reduction, reduce aliasing, reduce irrele smoothing the false contours, …

➢ Linear spatial filtering

➢ Nonlinear smoothing filters

5 Smoothing (Lowpass) Spatial

❖ Box Filter Kernels

5 Smoothing (Lowpass) Spatial

❖ Box Filter Kernels

➢ Example: Lowpass filtering with a box

kernel

(a) Test pattern of size 1024x1024 pixels (b)-(d)

Results of lowpass filtering with box kernels of

sizes 3x3, 11x11, and 21x21 respectively.

5 Smoothing (Lowpass) Spatial

❖ Lowpass Gaussian Filter Kernels

➢ Gaussian kernels of the form

5 Smoothing (Lowpass) Spatial

❖ Lowpass Gaussian Filter Kernels

(a) Sampling a Gaussian function to obtain a discrete Gauss The values shown are for = 1 and = 1 (b) Resulting ker K

5 Smoothing (Lowpass) Spatial

❖ Lowpass Gaussian Filter Kernels

➢ Example: Lowpass filtering with a Gaussian kernel

5 Smoothing (Lowpass) Spatial

❖ Lowpass Gaussian Filter Kernels

➢ Example: Lowpass filtering with a Gaussian kernel

(a) Result of filtering using a Gaussian kernels of size43x43, with = 7.

a kernel of 85x85, with the same value of (c) Difference image

5 Smoothing (Lowpass) Spatial

➢ Example: Comparison of Gaussian and box filter smoothi

5 Smoothing (Lowpass) Spatial

➢ Example: Using lowpass filtering and thresholding for reg

5 Smoothing (Lowpass) Spatial

❖ Order-Statistic (Nonlinear) Filters

➢ Median filter : replaces the value of the center pixel by the values in the neighborhood of that pixel

→ Effective in the presence of impulse noise salt- - ( and pepper n

→ The 50th percentile of a ranked set of numbers

➢ Max filter :

→ Finding the brightest points in an image or for eroding dar regions

5 Smoothing (Lowpass) Spatial

❖ Order-Statistic (Nonlinear) Filters

➢ Min filter:

→ used for the opposite purpose

→ The 0th percentile filter

5 Smoothing (Lowpass) Spatial

❖ Order-Statistic (Nonlinear) Filters

➢ Example: Median filtering

Chapter 3 Intensity Transformations and

1 Background

2 Some Basic Intensity Transformation Functions

3 Histogram Processing

4 Fundamentals of Spatial Filtering

5 Smoothing (Lowpass) Spatial Filters

6 Sharpening (Highpass) Spatial Filters

7 Highpass, Bandreject, and Bandpass Filters from

8 Combining Spatial Enhancement Methods

6 Sharpening (Highpass) Spatia

❖ Foundation

➢ First-order derivative

➢ Second-order derivative

6 Sharpening (Highpass) Spatia

❖ Image Sharpening the Laplacian —

➢ Laplacian

6 Sharpening (Highpass) Spatia

❖ Image Sharpening the Laplacian —

➢ Laplacian kernel

6 Sharpening (Highpass) Spatia

❖ Image Sharpening the Laplacian —

➢ The basic way in which the Laplacian is used for image sh

▪ c = 1 if the center element of the Laplacian kernel is posit

▪ c = -1 if the center element of the Laplacian kernel is nega

6 Sharpening (Highpass) Spatia

❖ Image Sharpening the Laplacian —

➢ Example: Image sharpening using the Laplacian

6 Sharpening (Highpass) Spatia

❖ Unsharp Masking and Highboost Filtering

➢ Unsharp masking

6 Sharpening (Highpass) Spatia

❖ Unsharp Masking and Highboost Filtering

6 Sharpening (Highpass) Spatia

❖ Unsharp Masking and Highboost Filtering

(a) Unretouched “soft tone” digital image of size 469x600 pixels (b) Image blurred using a 3 filter with = 5 (c) Mask (d) Result of unsharp masking using Eq (3-65) with k = 1 filtering with k = 2 and k = 3 respectively.

-6 Sharpening (Highpass) Spatia

❖ Image Sharpening the Gradient —

➢ The gradient of an image f at coordinates (x, y)

➢ The magnitude length ( ) of vector f

6 Sharpening (Highpass) Spatia

❖ Image Sharpening the Gradient —

➢ Roberts cross-gradient operators

6 Sharpening (Highpass) Spatia

❖ Image Sharpening the Gradient —

➢ Sobel operators

6 Sharpening (Highpass) Spatia

❖ Image Sharpening the Gradient —

➢ Filter masks

(a) A 3x3 region of an image, where the zs are intensity values (b) (c) Rob – (d) (e) Sobel operators All the kernel coefficients sum to zero, as expected –

6 Sharpening (Highpass) Spatia

❖ Image Sharpening the Gradient —

➢ Example: Using the gradient for edge enhancement.

Chapter 3 Intensity Transformations and

1 Background

2 Some Basic Intensity Transformation Functions

3 Histogram Processing

4 Fundamentals of Spatial Filtering

5 Smoothing (Lowpass) Spatial Filters

6 Sharpening (Highpass) Spatial Filters

7 Highpass, Bandreject, and Bandpass Filters from

8 Combining Spatial Enhancement Methods

7 Highpass, Bandreject, and Bandpass Filters f

❖ Transfer functions of ideal 1-D filters

7 Highpass, Bandreject, and Bandpass Filters f

❖ Transfer functions of ideal 1-D filters

7 Highpass, Bandreject, and Bandpass Filters f

❖ Transfer functions of ideal 1-D filters

(a) A 1-D spatial lowpass

7 Highpass, Bandreject, and Bandpass Filters f

❖ Transfer functions of ideal 1-D filters

(a) Zone plate image filtered with a separable lowpass kernel (b filtered with the isotropic lowpass kernel in Fig 3.60(b).

7 Highpass, Bandreject, and Bandpass Filters f

❖ Transfer functions of ideal 1-D filters

Chapter 3 Intensity Transformations and

1 Background

2 Some Basic Intensity Transformation Functions

3 Histogram Processing

4 Fundamentals of Spatial Filtering

5 Smoothing (Lowpass) Spatial Filters

6 Sharpening (Highpass) Spatial Filters

7 Highpass, Bandreject, and Bandpass Filters from

8 Combining Spatial Enhancement Methods

8 Combining Spatial Enhancemen

8 Combining Spatial Enhancemen

(e) Sobel image smoothed with a 3x3 box filter (f) Mask image formed by the product of obtained by the adding images (a) and (f) (h) Final result obtained by applying a power- images (g) and (h) with (a) (Original image courtesy of G.E Medical Systems.)