Tài liệu Xử lý ảnh Đại học bách khoa HN

Background ❖The Basics of Intensity Transformations and Spatial Filtering • The term spatial domain refers to the image plane itself, and image processing methods in this category are b

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XỬ LÝ ẢNH TRONG CƠ ĐIỆN TỬ

Machine Vision

1

TRƯỜNG ĐẠI HỌC BÁCH KHOA HÀ NỘI

Giảng viên: TS Mạc Thị Thoa Đơn vị: Bộ môn Cơ điện tử, Viện Cơ khí

Hà Nội, 2020

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Chapter 3 Intensity Transformations and Spatial Filtering

Rafael C Gonzalez, Richard E Woods, “Digital image processing,” Pearson (2018).

❖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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Chapter 3 Intensity Transformations and Spatial Filtering

1 Background

2 Some Basic Intensity Transformation Functions

3 Histogram Processing (xử lý Histogram-biểu đồ tần suất)

4 Fundamentals of Spatial Filtering (Nguyên lý lọc trên miền không

7 Highpass, Bandreject, and Bandpass Filters from Lowpass Filters

8 Combining Spatial Enhancement Methods (Các phương pháp cải

thiện chất lượng ảnh)

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1 Background

❖The Basics of Intensity Transformations and Spatial Filtering

• The term spatial domain refers to the image plane itself, and image processing methods

in this category are based on direct manipulation of pixels in an image.

• Understand the meaning of spatial domain processing, and how it differs from transform

domain processing.

• Be familiar with the principal techniques used for intensity transformations.

• Understand the physical meaning of image histograms and how they can be manipulated for

image enhancement.

• Understand the mechanics of spatial filtering, and how spatial filters are formed.

• Understand the principles of spatial convolution (tích chập) and correlation (Tương quan)

• Be familiar with the principal types of spatial filters, and how they are applied.

• Be aware of the relationships between spatial filters, and the fundamental role of lowpass

filters.

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1 Background

➢ 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.

hoặc trên các điểm ảnh của các ảnh các nhau

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1 Background

➢ intensity (also called a gray-level, or mapping) transformation function, s and r to

denote, respectively, the intensity of g and f at any point (x, y)

The result of applying the transformation to every pixel

in f to generate the corresponding pixels in g

would be to produce an image of higher contrast than

the original, by darkening the intensity levels below k and brightening the levels above k In this technique, sometimes called contrast stretching

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1 Background

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

T(r) produces a two-level (binary) image A

mapping of this form is

called a thresholding function

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❖Intensity transformations are among the simplest of all image processing techniques

❖ The values of pixels, before and after processing, by r and s

❖ With digital quantities, values of an intensity transformation function typically arestored in a table, and the mappings from r to s are implemented via table lookups For

an 8-bit image, a lookup table containing the values of T will have 256 entries

❖ Three basic types of functions used frequently in image processing: linear (negative and identity transformations), logarithmic (log and inverse-log transformations), and power-

law (nth power and nth root transformations).

❖ The identity function is the trivial case in which the input and output intensities areidentical

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Some basic intensity transformation functions Each curve was scaled independently

so that all curves would fit in the same graph Our

interest here is on the shapes of the curves, not on their relative values

Image Negatives

The negative of an image with intensity

levels in the range [0, L-1] is obtained by

using the negative transformation

function

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❖Image Negatives The negative of an image with intensity levels in the range is

obtained by using the negative transformation function

(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

• maps a narrow range of low intensity values in the input into a wider range of output

levels, higher values of input levels are mapped to a narrower range in the output

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

transformation in Eq (3-4) with c = 1 Both images are scaled to the range [0, 255].

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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) Each curve was scaled

independently so that all curves would fit in the same graph Our interest here is on the shapes of the curves,

not on their relative values.

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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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a) Magnetic resonance image (MRI- Hình ảnh cộng hưởng từ) of a fractured human spine- vùng xương sống bị gãy (the region of the fracture is enclosed by the circle) (b)–(d) Results of applying the transformation in Eq (3-5) with c =1 and γ= 0.6,0.4 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

(c = 1 in all cases.) (Original image courtesy of NASA.)

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❖Piecewise Linear Transformation Functions

Contrast stretching (a) Piecewise linear transformation function (b) A low-contrast electron microscope image of pollen, magnified

700 times (c) Result of contrast stretching (d) Result of thresholding (Original image courtesy

of Dr Roger Heady, Research School of Biological Sciences, Australian National University, Canberra, Australia.)

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 Cắt theo mức

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 (Original image courtesy of Dr Thomas R Gest, University of Michigan Medical School.)

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➢ Bit-Plane Slicing Trích chọn bít: Mục đích là để làm nổi bật các thành phần trên toàn

ảnh bởi việc sử dụng các bít đặc biệt

Bit-planes of an 8-bit image.

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➢ Bit bậc cao có độ bảo toàn thông tin tốt hơn bit bậc thấp

➢ Bit bậc thấp thường biểu diễn nhiễu hoặc nền

Để trích chọn bit có nghĩa nhất: bit thứ n và hiện thị chúng,

dùng biến đổi sau:

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➢ Bit-Plane Slicing

(a) An 8-bit gray-scale 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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3 Histogram Processing

❖Histogram

➢ The unnormalized histogram:

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

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

in f with intensity r k and the subdivisions of the

intensity scale are called histogram bins.

là biểu đồ tần xuất thống kê số lần xuất

hiện các mức sáng trong ảnh

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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

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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 r k and the vertical axis are values of p(r k)

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cân bằng, giá trị các điểm ảnh không bị co cụm tại một khoảng nhỏ mà được

"kéo dãn" ra Cân bằng histogram là một phương pháp tiền/hậu xử lí ảnh rất

mạnh mẽ Đặc biệt trong nhiều bài toán mình từng làm trong lĩnh vực compute

vision, phương pháp tiền xử lí ảnh này cho chất lượng dữ liệu rất cao, cải thiện

chất lượng model deep learning rất nhiều

a) T(r) is a monotonic increasing (tăng đơn điệu) function in the interval 0  r

 L-1; and

b) 0  T(r)  L-1 for 0  r  L-1

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➢ The inverse transformation

(a’) T(r) is a strictly monotonic increasing function in the interval 0  r  L-1

➔ The mappings from s back to r will be one-to-one,

thus preventing ambiguities

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First Program in OpenCV

Mat img = imread( "lena.jpg" );

namedWindow( "DisplayImage" , WINDOW_NORMAL ); imshow( "DisplayImage" , img);

waitKey(0);

}

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imwrite( "lena_800x400.jpg" , img_resize);

imshow( "Source image" , img);

imshow( "Resize Image" , img_resize);

waitKey(0);

return 0;

}

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• Mat img = imread( "lena.jpg" , cv:: IMREAD_COLOR ); // (512, 512, 3)

• //cout << "Width : " << img.size().width << endl;

• //cout << "Height: " << img.size().height << endl;

• //cout << "Width : " << img.cols << endl;

• //cout << "Height: " << img.rows << endl;

• int startX = 120, startY = 50, width = 280, height = 350;

• Mat ROI(img, Rect (startX, startY, width, height));

• Mat croppedImage;

• // Copy the data into new matrix

• ROI.copyTo(croppedImage);

• imshow( "Source image" , img);

• imshow( "Resize Image" , croppedImage);

• waitKey(0);

• return 0;

• }

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const float* histRange = { range };

Histogram 3 channel in OpenCV

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/// Compute the histograms:

calcHist(&bgr_planes [ 0 ] , 1, 0, Mat(), b_hist, 1, &histSize, &histRange, uniform, accumulate); calcHist(&bgr_planes [ 1 ] , 1, 0, Mat(), g_hist, 1, &histSize, &histRange, uniform, accumulate); calcHist(&bgr_planes [ 2 ] , 1, 0, Mat(), r_hist, 1, &histSize, &histRange, uniform, accumulate);

// Draw the histograms for B, G and R

int hist_w = 512; int hist_h = 400;

int bin_w = cvRound(( double )hist_w / histSize);

Mat histImage(hist_h, hist_w, CV_8UC3 , Scalar(0, 0, 0));

/// Normalize the result to [ 0, histImage.rows ]

normalize(b_hist, b_hist, 0, histImage.rows, NORM_MINMAX , -1, Mat());

normalize(g_hist, g_hist, 0, histImage.rows, NORM_MINMAX , -1, Mat());

normalize(r_hist, r_hist, 0, histImage.rows, NORM_MINMAX , -1, Mat());

/// Draw for each channel

for ( int i = 1; i < histSize; i++)

{line(histImage, Point(bin_w*(i - 1), hist_h - cvRound(b_hist.at< float >(i - 1))),

Point(bin_w*(i), hist_h - cvRound(b_hist.at< float >(i))),

Scalar(255, 0, 0), 2, 8, 0);

line(histImage, Point(bin_w*(i - 1), hist_h - cvRound(g_hist.at< float >(i - 1))),

Point(bin_w*(i), hist_h - cvRound(g_hist.at< float >(i))),

Scalar(0, 255, 0), 2, 8, 0);

line(histImage, Point(bin_w*(i - 1), hist_h - cvRound(r_hist.at< float >(i - 1))),

Point(bin_w*(i), hist_h - cvRound(r_hist.at< float >(i))),

Scalar(0, 0, 255), 2, 8, 0);

}

/// Display

imshow( "Source image" , src);

namedWindow( "calcHist Demo" , CV_WINDOW_AUTOSIZE );

imshow( "calcHist Demo" , histImage);

waitKey(0);

return 0;

}

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Mat gray = imread( "lena.jpg" , 0);

namedWindow( "Gray" , 1); imshow( "Gray" , gray);

calcHist(&gray, 1, 0, Mat (), hist, 1, &histSize, ranges, true , false );

// Show the calculated histogram in command window

double total;

total = gray.rows * gray.cols;

for ( int h = 0; h < histSize; h++)

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// Plot the histogram

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For example the original gray levels are [100,150] and the grey target levels are [0, 255]

g(f)=((f-100)/50)*255 of fk =100, fk+1=150, gk=0, gk+1=255

a=?, b=?

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❖Histogram Equalization

(a) Monotonic increasing function, showing how multiple values can map to a single value (b) Strictly monotonic increasing function This is a one-to-one mapping, both ways.

Tiêu đề	Xử Lý Ảnh Trong Cơ Điện Tử
Tác giả	Rafael C. Gonzalez, Richard E. Woods
Người hướng dẫn	TS. Mạc Thị Thoa
Trường học	Đại học Bách Khoa Hà Nội
Chuyên ngành	Cơ điện tử
Thể loại	thesis
Năm xuất bản	2020
Thành phố	Hà Nội

Định dạng
Số trang	96
Dung lượng	9,51 MB