Binary Images in Computer Vision
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Questions and Answers

What value does a pixel in a binary image represent for the background?

0

How is a binary image obtained from a gray level image?

By applying a threshold T to the gray level image.

What method can be used to determine an appropriate threshold T for a binary image?

Computing the histogram of the original gray-level image.

What is the best choice for the threshold T when computing binary images?

<p>A value that lies in the valley between the two peaks in the histogram.</p> Signup and view all the answers

What is one application of binary images in industrial settings?

<p>Detecting defects in printed circuit boards.</p> Signup and view all the answers

What pixel value in a binary image indicates an object or foreground?

<p>255</p> Signup and view all the answers

Why are binary images considered easy to process and store?

<p>Because they consist of only two possible pixel values.</p> Signup and view all the answers

In medical image analysis, how are binary images useful?

<p>They help in the detection and analysis of specific structures or abnormalities.</p> Signup and view all the answers

What does the characteristic function b(x,y) represent in a binary image?

<p>It represents 1 for points on the object and 0 for points in the background.</p> Signup and view all the answers

How is the area of an object calculated in binary images?

<p>The area is computed by integrating the characteristic function b(x,y) over the entire image or summing all pixel values in discrete binary images.</p> Signup and view all the answers

What is the significance of the center of the area in binary images?

<p>It represents the location of the object and is computed as the first moment.</p> Signup and view all the answers

Describe the concept of connected components in binary images.

<p>A connected component is a maximal set of connected points where the characteristic function is constant.</p> Signup and view all the answers

What is required for effective segmentation of binary images with multiple objects?

<p>Each object needs to be labeled with a unique label, assuming they do not overlap or touch each other.</p> Signup and view all the answers

How can the orientation of an object in a binary image be determined?

<p>The orientation can be analyzed through geometric properties derived from the pixel arrangement.</p> Signup and view all the answers

In what way can the translation or rotation of a 3D object be applied to binary images?

<p>An algorithm can be used to recognize the 2D shape in the binary image, enabling the identification of the corresponding 3D object.</p> Signup and view all the answers

What condition must be met for two points in a binary image to be considered 'connected'?

<p>There must exist a path from one point to the other along which the characteristic function is constant.</p> Signup and view all the answers

What is the significance of neighborhood class 𝑁0 in binary image processing?

<p>Neighborhood class 𝑁0 is important because it allows for conservative operations where the center pixel can be modified without introducing new bodies or holes into the image.</p> Signup and view all the answers

Explain the impact of changing a center pixel from 0 to 1 on the Euler number in the context provided.

<p>Changing the center pixel from 0 to 1 results in a decrease of one body, leading to an Euler number of -1 as two bodies become connected.</p> Signup and view all the answers

List the four possible neighborhood types identified in the content.

<p>The four neighborhood types are 𝑁+1, 𝑁0, 𝑁−1, and 𝑁−2.</p> Signup and view all the answers

What purpose does the thinning algorithm serve in binary image processing?

<p>The thinning algorithm reduces binary images to their skeletal structure, facilitating the analysis of shapes and features.</p> Signup and view all the answers

How does the concept of conservative operators relate to neighborhood patterns in binary images?

<p>Conservative operators maintain the integrity of the image by ensuring modifications do not create or eliminate bodies.</p> Signup and view all the answers

What are the steps involved in segmenting a binary image?

<p>The steps involve performing two raster scans of the image.</p> Signup and view all the answers

How can the skeleton of a binary image be beneficial?

<p>The skeleton helps in determining the pose of an object, like a human body, without compromising its overall structure.</p> Signup and view all the answers

Define the Euler number in the context of binary images.

<p>The Euler number is the number of bodies minus the number of holes in a binary image.</p> Signup and view all the answers

What does the Euler differential signify after an operation on an image?

<p>The Euler differential indicates the change in the Euler number due to an operation applied to the image.</p> Signup and view all the answers

How does the neighborhood classification relate to the Euler differential?

<p>Neighborhood classification organizes patterns of pixels based on the Euler differential generated when changing the center pixel from 0 to 1.</p> Signup and view all the answers

What is the significance of a hexagonal grid in the analysis of binary images?

<p>A hexagonal grid allows each pixel to have 6 neighbors, facilitating complex neighborhood pattern analysis.</p> Signup and view all the answers

What happens to the Euler number if no changes occur in an image region?

<p>If no changes occur, the Euler number of the complete image remains the same.</p> Signup and view all the answers

What purpose does the concept of 6-Connectedness serve in segmenting binary images?

<p>6-Connectedness introduces asymmetry in defining neighbors, which is crucial for accurately segmenting binary images.</p> Signup and view all the answers

What is the benefit of iterative modification of a binary image?

<p>Iterative modification allows for extracting useful information from the binary image, such as the object's skeletal structure.</p> Signup and view all the answers

How does Jordan's Curve Theorem relate to the outcomes of segmenting binary images?

<p>Jordan's Curve Theorem assures that the segmented outcomes will consist of distinct line segments and a single connected background.</p> Signup and view all the answers

Explain the sequential labeling process in segmentation of binary images.

<p>Sequential labeling involves raster scanning the image and assigning labels based on the values of neighboring pixels.</p> Signup and view all the answers

What happens when pixel A is labeled as 0 in the sequential labeling process?

<p>When pixel A is labeled as 0, it is considered part of the background, regardless of its neighbors' labels.</p> Signup and view all the answers

If pixels B and C are labeled differently, but pixel D is part of the background, how is pixel A treated?

<p>Pixel A is assigned the label of either B or C, and an equivalence is noted in the equivalence table.</p> Signup and view all the answers

What role does the equivalence table play in the sequential labeling process?

<p>The equivalence table stores information about equivalent labels assigned to adjacent pixels, consolidating segment relationships.</p> Signup and view all the answers

How does the choice of neighbors (top, diagonal, and left) contribute to the asymmetry in labeling?

<p>Using top, diagonal, and left neighbors introduces asymmetry, which is essential for meeting the conditions outlined in Jordan’s theorem.</p> Signup and view all the answers

What implications does the background labeling have on pixel segmentation?

<p>Labeling a pixel as part of the background restricts how neighboring pixels are labeled, influencing overall segmentation integrity.</p> Signup and view all the answers

What is the main goal of the algorithm described for segmenting binary images?

<p>The main goal is to identify and label connected regions of pixels with value b=1.</p> Signup and view all the answers

How does the algorithm determine when to stop searching for new seed points?

<p>The algorithm stops when no more unlabeled points with b=1 are found during the scanning process.</p> Signup and view all the answers

Define the concept of 4-Connectedness in the context of binary image segmentation.

<p>4-Connectedness considers a pixel's immediate neighbors: the pixels directly to the left, right, above, and below it.</p> Signup and view all the answers

What is the difference between 4-Connectedness and 8-Connectedness?

<p>8-Connectedness includes the diagonal neighbors in addition to the immediate vertical and horizontal neighbors.</p> Signup and view all the answers

What significant mathematical principle does the algorithm's method of segmentation violate?

<p>The algorithm violates Jordan's Curve Theorem.</p> Signup and view all the answers

What are the consequences of using 4-Connectedness in the segmentation of the example binary image?

<p>Using 4-Connectedness results in four disconnected objects and two separate backgrounds.</p> Signup and view all the answers

How does 8-Connectedness affect the identification of regions compared to 4-Connectedness?

<p>8-Connectedness tends to group nearby pixels into a single object, resulting in connected regions that 4-Connectedness might miss.</p> Signup and view all the answers

What issue arises when the algorithm connects the background pixels using 8-Connectedness?

<p>The background inside a ring can connect to the background outside it, violating the separation required by Jordan's theorem.</p> Signup and view all the answers

Flashcards

Binary Image

An image where each pixel has only two possible values: 0 (background) or 255 (foreground/object).

Thresholding

Converting a gray-scale image into a binary image by applying a threshold value (T) on the grayscale pixel values.

Gray-scale Image

An image where pixel intensities range from 0 to 255, representing different shades of gray.

Threshold Value (T)

The cutoff point used in thresholding to determine whether a pixel in a gray-scale image should be assigned to 0 or 255 (black or white).

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Histogram

A graphical representation of the distribution of pixel intensities in an image.

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Optimal Threshold Selection

Choosing the best threshold value (T) based on the histogram, often located at the valley between two peaks which correspond to background and object pixels.

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Binary Image Applications

Used in various computer vision tasks, including defect detection (e.g., on circuit boards), fingerprint analysis, visual code decoding (e.g., QR codes) and medical image analysis.

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Background

The part of an image that does not contain the object of interest in binary images. Its pixel intensities are set to 0.

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Area (of an object)

The total number of pixels belonging to an object in a binary image. Calculated by summing all pixel values (1s) in the image.

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Location/Center of an Object

The coordinates (x, y) of the geometric center of an object in the image. Computed from the first moment.

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Object Orientation

Describes the directionality of an object.

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Connected Points

Points in a binary image that are part of the same object (have value 1, are on the same connected component).

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Connected Component

The largest group of connected points representing a single identifiable object within a binary image.

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Characteristic Function (b(x,y))

A function that assigns a value of 1 to any pixel belonging to the object and 0 to any pixel in the background.

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Segmenting Binary Images

The process of isolating and labeling different objects within an image to determine the geometric properties of each object.

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Seed Point

The starting pixel in a binary image used to initiate region growing. It's typically an unlabeled point with a value of 1, representing an object.

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Region Growing

The process of expanding a region in a binary image by assigning the same label to neighboring pixels with a value of 1, iteratively.

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4-Connectedness

A neighborhood definition where a pixel's neighbors are only those directly above, below, left, and right of it.

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8-Connectedness

A neighborhood definition that includes diagonal pixels in addition to those directly above, below, left, and right.

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Jordan's Curve Theorem

States that a closed curve (like a loop) divides a region into two separate connected parts. In binary images, it can be used to check the validity of region growing algorithms.

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Violation of Jordan's Curve Theorem

When a binary image segmentation algorithm produces results that don't follow Jordan's Curve Theorem, like having a connected background and background inside a closed object.

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4-Connectedness Issues

Using 4-connectedness can lead to disconnected objects (multiple separate ones), but may also result in disconnected backgrounds (one background within another).

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8-Connectedness Issues

While 8-connectedness groups objects better, it can incorrectly connect the background inside a closed object to the background outside it.

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Neighborhood Class

A grouping of 3x3 pixel patterns based on the number of pixels that can be changed without creating new objects or holes in the image.

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N0 Class

A neighborhood class where the center pixel can be modified without affecting the number of objects or holes in the image.

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Euler Number

A topological property of a binary image that measures the difference between the number of objects and holes in the image.

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Euler Differential

The change in the Euler number caused by modifying a single pixel in the image.

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Thinning Algorithm

A process that iteratively removes pixels from an image while preserving the object's skeleton or shape.

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Skeletonization

A process of thinning a binary image by iteratively removing pixels while preserving the overall structure. This results in a skeletal representation of the object, highlighting its essential shape and connectivity.

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Neighborhood Pattern

Different combinations of pixel values (0s or 1s) surrounding a central pixel in a binary image.

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Neighborhood Class (N+1)

A category of neighborhood patterns where changing the central pixel from 0 to 1 results in an Euler differential of +1. This means adding a pixel adds a new object.

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Iterative Modification

A process that repeatedly alters a binary image using specific rules or operations to extract desired information or features.

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Object Recognition

The process of identifying and classifying objects within an image based on their geometric properties, such as area, center, and orientation.

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Image Segmentation

Dividing a binary image into distinct regions or objects. This separates different elements in the image and labels them.

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Sequential Labeling

A binary image segmentation algorithm that scans the image pixel by pixel. It labels pixels based on their value and the labels of their neighbors, associating connected pixels with the same label.

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Equivalence Table

A table used during sequential labeling to track and merge labels that belong to the same object, even if they were initially assigned different labels.

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Why is asymmetry needed?

Asymmetry in neighbor definitions helps prevent violations of Jordan's Curve Theorem, ensuring proper segmentation of closed objects. Without asymmetry, the algorithm might incorrectly connect background pixels within a closed object.

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What is the consequence of using 4-connectedness?

4-connectedness may lead to disconnected objects, but it can also result in disconnected backgrounds, where one background is contained within another.

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What is the consequence of using 8-connectedness?

8-connectedness tends to group objects together better than 4-connectedness, but it can lead to incorrect connections between the background inside a closed object and the background outside.

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Study Notes

Binary Images - Introduction

  • Binary images are the simplest type of images used in computer vision
  • Pixels have one of two values: 0 (background) or 255 (object/foreground)
  • Easy to process, store, and analyze
  • Useful in structured environments like factory assembly lines for efficient and robust tasks

How to Obtain a Binary Image

  • Threshold a gray-level image (0-255) with a value T.
  • Result is a function b(x,y)
  • Output value is 0 if the gray-level image value is less than the threshold, and 1 otherwise (or vice versa).

How to Obtain the Threshold

  • Calculate the histogram of the original gray-level image
  • Histogram has two peaks: one for background and one for foreground objects
  • Optimal threshold T lies in the valley between the peaks

Applications of Binary Images

  • Detecting defects in printed circuit boards
  • Fingerprint analysis
  • Detection & decoding of visual codes like QR codes
  • Medical image analysis

Applications of Binary Images - 3D Object Recognition

  • A stable 3D object produces a 2D shape that can be translated or rotated in an image
  • An algorithm can recognize the 2D shape to recognize the corresponding 3D object

Binary Images - Geometric Properties

  • The binary image is continuous with spatial coordinates x and y.
  • The characteristic function b(x,y) is 1 for points on the object and 0 for points in the background.

Geometric Property: Area

  • Area of the object is the zeroth moment
  • Computed by integrating the characteristic function b(x,y) over the entire image
  • Useful for distinguishing between objects

Geometric Property: Location (Center of Area)

  • Location of the object (center of the area) is the first moment
  • Computed using the formulas:
  • x̄ = (1/A) ∫∫ x * b(x,y) dx dy
  • ȳ = (1/A) ∫∫ y * b(x,y) dx dy

Geometric Property: Orientation

  • Orientation of the object is the computed as the wi

Discrete Binary Images - Geometric Properties

  • In discrete binary images, the area (zeroth moment) is the sum of all pixel values in the image
  • Formulas for area and center coordinates (first moments) use pixel values bij at (i, j).

Segmenting Binary Images

  • Segmenting binary images involves dividing them into regions corresponding to different objects.
  • Labeling each object with a unique label is necessary before computing geometric properties.
  • It is assumed that objects do not overlap or touch each other.

Connected Components

  • Two points A and B are connected if there exists a path from A to B where the binary image characteristic function remains constant.
  • A connected component is a maximal set of connected points.

Region Growing Algorithm

  • Algorithm for segmenting binary images based on connected components.
  • Iterative process that assigns a new label to a seed point (an unlabelled point with b=1).
  • Same label assigned to the neighbors with b=1 , and repeats until no unlabeled new neighbors with b = 1 are found
  • Scans the image row-by-row and column-by-column.

Two Kinds of Neighbors

  • 4-Connectedness: a pixel's neighbors are to the left, right, top, and bottom.
  • 8-Connectedness: includes the diagonal neighbors

Problems with 4- & 8- Connectedness & Solution

  • Jordan's Curve Theorem: A closed curve divides a region into two connected regions. 4- and 8-Connectedness violate this.
  • Solution: 6-Connectedness (drops diagonal neighbors). The 6-connectedness resolves this issue, by not considering diagonal neighbors as connected neighbors, to satisfy Jordan’s theorem

Sequential Labeling Algorithm

  • Raster scan of the image
  • Assigning pixel labels based on the values of neighboring pixels.
  • If pixel A is 1, B, C, and D are 0, use the labels of B or C or D as label of A if they are connected.
  • If B and C have the same label, then A is given that label.

Euler number - Iterative Modification

  • The Euler number is the difference between the number of bodies and the number of holes.
  • The Euler number of a full image is the sum of Euler numbers of non-overlapping regions.
  • An operation applied to a region does not change the complete image's Euler number.
  • The image’s Euler differential is measured and calculated

Skeleton of Images

  • A binary image can be iteratively modified to extract the skeleton (useful for information such as the object's shape)

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