Xử lý ảnh trong cơ điện tử: Machine Vision. Chapter 2: Digital Image Fundamentals92

Basic Mathematical Tools Used in Digital Image P... Basic Mathematical Tools Used in Digital Image P... Basic Mathematical Tools Used in Digital Image P... Basic Mathematical Tools Used

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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

Hà Nội, 2021

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Chapter 2 Digital Image Fundam

1 Image Sensing and Acquisition

2 Image Sampling and Quantization

3 Some Basic Relationships Between Pixels

4 Basic Mathematical Tools Used in Digital Image P

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1 Image Sensing and Acquisi

(a) Single sensing element

(b) Line sensor

(c) Array sensor

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Combining a single sensing element with mechanical motion to generate a

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2-1 Image Sensing and Acquisi

(a) Image acquisition using a linear sensor strip

(b) Image acquisition u

a circular sensor strip

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An example of digital imag (energy) source (b) A scen Projection of the scene ont Digitized image.

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➢ We denote images by two-dimensional functions of the form ( f x

f x y ( , ) = i x y r x ( , ) ( , y)

• i x y ( , ): the amount of source illumination incident on the scene

• r x y ( , ): the amount of illumination reflected by the objects in th

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2 Image Sampling and Quantiz

➢ Digitizing the coordinate values is called sampling Digitizing t values is called quantization

(a) Continuous image (b) A scan line

showing intensity variations along line

AB in the continuous image (c)

Sampling and quantization (d) Digital

scan line (The black border in (a) is

included for clarity It is not part of the

image).

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(a) Continuous image projected onto a sensor array

(b) Result of image samplin and quantization

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(a) Image plo Image displa array (c) Ima numerical arr and 1 represe white, respec

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➢ The number of intensity levels: L

where k is an integer.

➢ The discrete levels are equally spaced and that they are integers [0, - L 1]

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➢ The number, , of bits required to store a digital image is b

➢ When M = N :

Number of megabytes required to store

images for various values of N and k

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➢ coordinate indexing or subscript indexing (x, y) vs linear indexi

Illustration of column scanning for generating linear indices Shown are several

2-D coordinates (in parentheses) and their corresponding linear indices.

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➢ Spatial resolution is a measure of the

smallest discernible detail in an image.

➢ Dots per unit distance is a measure of

image resolution used in the printing and

publishing industry In the U.S., this

measure usually is expressed as dots per

inch (dpi)

➢ Intensity resolution is the number of bits

used to quantize intensity.

Effects of reducing spat are at: (a) 930 dpi, (b) 3

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(a) 256-level image (b)-(d) Image displayed in 128, 64, and 32 intensity levels, while k size constant (e)-(h) Image displayed in 16, 8, 4, and 2 intensity levels.

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(a) Image with a low level of detail (b) Image with a medium level of det relatively large amount of detail.

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➢ Observe that isopreference curves tend

to become more vertical as the detail in

the image increases

➢ This result suggests that for images with

a large amount of detail only a few

intensity levels may be needed.

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(a) Image reduced to 72 dpi and zoomed back to its original 930 dpi using interpolation (b) Image reduced to 72 dpi and zoomed using bilinear interp (b) but using bicubic interpolation.

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3 Some Basic Relationships Betwe

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➢ Let V be the set of intensity values used to define adjacency.

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➢ V = {1}

(a) An arrangement of pixels (b) Pixels that are 8-adjacent (adjacency is shown by dash adjacency (d) Two regions (of 1’s) that are 8-adjacent (e) The circled point is on the bo pixels only if 8-adjacency between the region and background is used (f) The inner bou region does not form a closed path, but its outer boundary does.

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Let represent a subset of pixels in an image S

➢ Two pixels p and q are said to be connected in if there exists a S them consisting entirely of pixels in S

➢ The set of pixels that are connected to in is called a p S connect S.

➢ If it only has one component, and that component is connected, connected set.

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Let represent a subset of pixels in an image R

➢ We call R a region of the image if is a connected set R

➢ Two regions, R i and R j are said to be adjacent if their union fo set.

➢ Regions that are not adjacent are said to be disjoint

➢ Foreground : the union of all the disjoint regions ( K R u )

➢ Background: the complement of the set R u : (R u ) c

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backg

foreground

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➢ The boundary (also called the border or contour ) of a region i R

in that are adjacent to pixels in the complement of R R

intensity discontinu closed paths

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➢ For pixels p, q , and , with coordinates ( s x, y ), ( u, v ), and ( , ), w z distance function or metric if:

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➢ The Euclidean distance between p and q is defined as:

The distance D 4, ( city-block distance ) The distance D 8,

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4 Basic Mathematical Tools Used in Digital

➢ An elementwise operation involving one or more images is carr by-pixel basis.

➢ The elementwise product of these two images is

➢ The matrix product of the images

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➢ Consider a general operator, H, that produces an output image, given input image, ( f x, y):

➢ H is said to be a linear operator if

➢ An operator that fails to satisfy above equation is said to be non

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➢ Arithmetic operations between two images ( f x, y ) and ( , ) g x y

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❖ Arithmetic Operations Using image addition (averaging) for noise

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(a) An 8-bit image (b) Intensity transformation function used to obtain the digital equiv negative of an 8-bit image The arrows show transformation of an arbitrary input intensi corresponding output value (c) Negative of (a), obtained using the transformation functi

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Local averaging using neig procedure is illustrated in neighborhood (c) An aorti using Eq (2) with m = m

790 x 686 pixels.

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(a) A 541 x Image rota interpolatio Image rota interpolatio bicubic int sections (e numbers sh

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(a) A digital image (b counterclockwise dire rotation) (c) Rotated area as the original im accommodate the ent

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Image registration (a) Ref (geometrically distorted im points are shown as small corners (c) Registered (ou

in the border) (d) Differen showing more registration

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Forming a vector from corresponding pixel values in three RGB component

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➢ 2-D linear transforms

➢ Inverse transform

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General approach for working in the linear transform dom

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(a) Imag interferen transform caused b were enl Mask use (d) Resu modified

Tiêu đề	Digital Image Fundamentals
Tác giả	Rafael C. Gonzalez, Richard E. Woods
Người hướng dẫn	TS. Nguyễn Thành Hùn
Trường học	Trường Đại Học Bách Khoa
Chuyên ngành	Cơ Điện Tử
Thể loại	Thesis
Năm xuất bản	2021
Thành phố	Hà Nội

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Số trang	56
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