Xử lý ảnh trong cơ điện tử machine vision chapter 3 intensity transformations and spatial filtering

Background❖The Basics of Intensity Transformations and Spatial Filtering ➢ intensity also called a gray-level, or mapping transformation function Intensity transformation functions... ➢

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XỬ LÝ ẢNH TRONG CƠ ĐIỆN TỬ

Machine Vision

TRƯỜNG ĐẠI HỌC BÁCH KHOA HÀ NỘI

Giảng viên: TS Nguyễn Thành Hùng Đơn vị: Bộ môn Cơ điện tử, Viện Cơ khí

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Chapter 3 Intensity Transformations and Spatial Filtering

❖Two principal categories of spatial processing are intensity transformations and

spatial filtering.

➢ Intensity transformations operate on single pixels of an image for tasks such

as contrast manipulation and image thresholding.

➢ Spatial filtering performs operations on the neighborhood of every pixel in an

image.

➢ Examples of spatial filtering include image smoothing and sharpening.

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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 Lowpass Filters

8 Combining Spatial Enhancement Methods

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1 Background

❖The Basics of Intensity Transformations and Spatial Filtering

➢ The spatial domain processes are based on the expression

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

output image, and T is an operator on f defined

over a neighborhood of point (x, y).

A 3x3 neighborhood about a point (x0, y0) in an image The neighborhood

is moved from pixel to pixel in the image to generate an output image.

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1 Background

❖The Basics of Intensity Transformations and Spatial Filtering

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

Intensity transformation functions (a) Contrast stretching function

(b) Thresholding function.

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1 Background

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❖Three basic types of functions

➢ linear (negative and identity transformations)

➢ logarithmic (log and inverse-log transformations)

➢ power-law (nth power and nth root

transformations)

Some basic intensity transformation functions.

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❖Image Negatives

(a) A digital mammogram (b) Negative image obtained using Eq (3-3) (Image (a) Courtesy of General Electric Medical Systems.)

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❖Log Transformations

where c is a constant and it is assumed that r  0

(a) Fourier spectrum displayed as a grayscale image (b) Result of applying the log

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❖Power-Law (Gamma) Transformations

where c and are positive constants

Plots of the gamma equation s = cr for various values

of  (c = 1 in all cases).

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(a) Image of a human retina (b) Image as

as it appears on a monitor with a gamma setting of 2.5 (note the darkness) (c) Gammacorrected image (d) Corrected image, as it appears on the same monitor (compare with the original image) (Image (a) courtesy of the National Eye Institute, NIH)

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➢ Contrast enhancement using power-law intensity transformations.

a) Magnetic resonance image (MRI) of a fractured human spine (the region of the fracture is enclosed by the circle) (b)–(d)

Results of applying the transformation in Eq (3-5) with and and 0.3, respectively (Original image courtesy of Dr David R Pickens, Department of Radiology and Radiological Sciences, Vanderbilt University Medical Center.)

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➢ Another illustration of power-law transformations.

(a) Aerial image (b)–(d) Results of applying the transformation in Eq (3-5) with  = 3.0, 4.0 and 5.0, respectively

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❖Piecewise Linear Transformation Functions

➢ Contrast Stretching

where rmin and rmax denote

the minimum and maximum

intensity levels in the input

image, respectively

where m is the mean intensity

level in the image

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➢ Intensity-Level Slicing

Figure 1: (a) This transformation function highlights range [A, B] and

reduces all other intensities to a lower level (b) This function highlights

range [A, B] and leaves other intensities unchanged.

Figure 2: (a) Aortic angiogram (b) Result of using a slicing transformation

of the type illustrated in Fig 1(a) , with the range of intensities of interest selected in the upper end of the gray scale (c) Result of using the

transformation in Fig 1(b) , with the selected range set near black, so that the grays in the area of the blood vessels and kidneys were preserved

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➢ Bit-Plane Slicing

Bit-planes of an 8-bit image.

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image of size pixels (b) through (i) Bit planes 8 through 1, respectively, where plane 1 contains the least significant bit

Each bit plane is a binary image Figure (a) is an SEM image of a

trophozoite that causes a

disease called giardiasis

(Courtesy of Dr Stan Erlandsen, U.S Center for Disease Control and Prevention.)

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➢ Bit-Plane Slicing

Image reconstructed from bit planes: (a) 8 and 7; (b) 8, 7, and 6; (c) 8, 7, 6, and 5.

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1 Background

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❖Histogram

➢ The unnormalized histogram:

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

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

in f with intensity rk and the subdivisions of the

intensity scale are called histogram bins.

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❖Histogram

➢ The normalized histogram:

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

෍

𝑘=1 𝐿−1

𝑝 𝑟 𝑘 = 1

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❖Histogram

Four image types and their corresponding histograms (a) dark; (b) light; (c) low contrast; (d) high contrast

The horizontal axis of the histograms are values of rk and the vertical axis are values of p ( rk)

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❖Histogram Equalization

➢ Example: Illustration of the mechanics of histogram equalization.

• Suppose that a 3-bit image (L = 3) of size 64x64 pixels (MN = 4096) has the intensity distribution

in Table

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We round them to their nearest integer values in the range [0, 7]:

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Histogram equalization (a) Original histogram (b) Transformation function (c) Equalized histogram.

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➢ Algorithm for Histogram Equalization

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equalized images

Histogram-equalized images Source images Histogram

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(a) Image from Phoenix Lander (b) Result of histogram equalization (c) Histogram of image (a) (d) Histogram of image (b) (Original image courtesy of NASA.)

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1 Background

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❖The Mechanics of Linear Spatial Filtering

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

template, and window

➢ Linear spatial filtering

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❖Spatial Correlation and Convolution

➢ 2-D illustration

➢ Correlation

➢ Convolution

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❖Spatial Correlation and Convolution

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1 Background

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➢ Smoothing (also called averaging) spatial filters are used to reduce sharp

transitions in intensity.

➢ Application: noise reduction, reduce aliasing, reduce irrelevant detail in an image, smoothing the false contours, …

➢ Linear spatial filtering

➢ Nonlinear smoothing filters

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❖Box Filter Kernels

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❖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.

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❖Lowpass Gaussian Filter Kernels

➢ Gaussian kernels of the form

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(a) Sampling a Gaussian function to obtain a discrete Gaussian kernel

The values shown are for K = 1 and  = 1 (b) Resulting kernel.

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➢ Example: Lowpass filtering with a Gaussian kernel

(a)A test pattern of size 1024x1024 (b) Result of lowpass filtering the pattern with a Gaussian kernel of

size 21x21, with standard deviations  = 3.5 (c) Result of using a kernel of size 43x43, with  = 7 We

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➢ Example: Lowpass filtering with a Gaussian kernel

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

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

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➢ Example: Comparison of Gaussian and box filter smoothing characteristics.

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➢ Example: Using lowpass filtering and thresholding for region extraction.

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❖Order-Statistic (Nonlinear) Filters

values in the neighborhood of that pixel

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

→ The 50th percentile of a ranked set of numbers

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➢ Min filter:

→ used for the opposite purpose

→ The 0th percentile filter

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➢ Example: Median filtering

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1 Background

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❖Foundation

➢ First-order derivative

➢ Second-order derivative

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❖Image Sharpening —the Laplacian

➢ Laplacian

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➢ Laplacian kernel

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

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

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

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➢ Example: Image sharpening using the Laplacian

a) Blurred image of the North Pole of the moon (b) Laplacian image obtained using the kernel in Fig

3.51(a) (c) Image sharpened using Eq (3-63) with c = -1 (d) Image sharpened using the same procedure,

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❖Unsharp Masking and Highboost Filtering

➢ Unsharp masking

▪ Blur the original image

▪ Subtract the blurred image from the original (the resulting difference is called the mask)

▪ When k = 1 → unsharp masking

▪ When 0  k < 1 → reduces the contribution of the unsharp mask

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1-D illustration of the mechanics of unsharp masking (a) Original signal (b) Blurred signal with original

shown dashed for reference (c) Unsharp mask (d) Sharpened signal, obtained by adding (c) to (a).

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(a) Unretouched “soft-tone” digital image of size 469x600 pixels (b) Image blurred using a 31x31 Gaussian lowpass

filter with  = 5 (c) Mask (d) Result of unsharp masking using Eq (3-65) with k = 1 (e) and (f) Results of highboost

filtering with k = 2 and k = 3 respectively.

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❖Image Sharpening —the Gradient

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

➢ The magnitude (length) of vector f

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➢ Roberts cross-gradient operators

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➢ Sobel operators

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➢ Filter masks

(a) A 3x3 region of an image, where the zs are intensity values (b)–(c) Roberts cross-gradient operators

(d)–(e) Sobel operators All the kernel coefficients sum to zero, as expected of a derivative operator.

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➢ Example: Using the gradient for edge enhancement.

(a) Image of a contact lens (note defects on the boundary at 4 and 5 o’clock)

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1 Background

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❖Transfer functions of ideal 1-D filters

Transfer functions of ideal 1-D filters in the frequency domain (u denotes frequency) (a) Lowpass filter (b) Highpass filter (c) Bandreject filter (d) Bandpass filter (As before, we show only positive frequencies for simplicity.)

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❖Transfer functions of ideal 1-D filters

Tiêu đề	Intensity Transformations and Spatial Filtering
Người hướng dẫn	TS. Nguyễn Thành Hùng
Trường học	Trường Đại Học Bách Khoa Hà Nội
Chuyên ngành	Cơ Điện Tử
Thể loại	Thesis
Năm xuất bản	2021
Thành phố	Hà Nội

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Số trang	70
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