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Edge Detection. Edge Detection. Edges characterize boundaries of objects in image A fundamental problem in image processing Edges are areas with strong intensity contrasts A jump in intensity from one pixel to the next Edge detected image Reduces significantly the amount of data,

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Edge detection2 l.jpg
Edge Detection

  • Edges characterize boundaries of objects in image

  • A fundamental problem in image processing

  • Edges are areas with strong intensity contrasts

  • A jump in intensity from one pixel to the next

  • Edge detected image

    • Reduces significantly the amount of data,

    • Filters out useless information,

    • Preserves the important structural properties


Slide3 l.jpg


Need of edge detection l.jpg
Need of Edge Detection from an image

  • Digital artists use it to create image outlines.

  • The output of an edge detector can be added back to an original image to enhance the edges

  • Edge detection is often the first step in image segmentation

  • Edge detection is also used in image registration by alignment of two images that may have been acquired at separate times or from different sensors



Thick edge l.jpg
Thick Edge from an image

  • The slope of the ramp is inversely proportional to the degree of blurring in the edge.

  • We no longer have a thin (one pixel thick) path.

  • Instead, an edge point now is any point contained in the ramp, and an edge would then be a set of such points that are connected.

  • The thickness of an edge is determined by the length of the ramp.

  • The length is determined by the slope, which is in turn determined by the degree of blurring.

  • Blurred edges tend to be thick and sharp edges tend to be thin


First and second derivatives l.jpg

the signs of the derivatives would be reversed for an edge that transitions from light to dark

First and Second Derivatives


Second derivatives l.jpg
Second Derivatives that transitions from light to dark

  • Produces 2 values for every edge in an image (an undesirable feature)

  • An imaginary straight line joining the extreme positive and negative values of the second derivative would cross zero near the midpoint of the edge. (zero-crossing property)

  • Quite useful for locating the centers of thick edges


Noise images l.jpg
Noise Images that transitions from light to dark

  • First column: images and gray-level profiles of a ramp edge corrupted by random Gaussian noise of mean 0 and  = 0.0, 0.1, 1.0 and 10.0, respectively.

  • Second column: first-derivative images and gray-level profiles.

  • Third column : second-derivative images and gray-level profiles.


Observation l.jpg
Observation that transitions from light to dark

  • Fairly little noise can have such a significant impact on the two key derivatives used for edge detection in images

  • Image smoothing should be serious consideration prior to the use of derivatives in applications where noise is likely to be present.


Edge point l.jpg
Edge Point that transitions from light to dark

  • To determine a point as an edge point

    • Determine the transition in grey level associated with the point which is significantly stronger than the background at that point.

    • Use threshold to determine whether a value is “significant” or not.

    • Note that the point’s two-dimensional first-order derivative must be greater than the specified threshold


Gradient operator l.jpg

commonly approx. that transitions from light to dark

the magnitude becomes nonlinear

Gradient Operator

  • first derivatives are implemented using the magnitude of the gradient.


Gradient direction l.jpg
Gradient Direction that transitions from light to dark

  • Let  (x,y) represent the direction angle of the vector f at (x,y)

     (x,y) = tan-1(Gy/Gx)


Gradient masks l.jpg
Gradient Masks that transitions from light to dark


Diagonal edges with prewitt and sobel masks l.jpg
Diagonal edges with Prewitt that transitions from light to darkand Sobel Masks

Sobel masks have slightly superior noise-suppression characteristics which is an important issue when dealing with derivatives.


Example l.jpg
Example that transitions from light to dark

  • Original Image

  • |Gx|, component of the gradient in the x-direction

  • |Gy|, component of the gradient in the y-direction

  • Gradient image,

  • Gx|+ |Gy|


Example17 l.jpg
Example that transitions from light to dark

Same sequence as previous figure, but with original image smoothed with a 5 x 5 averaging filter


Example18 l.jpg
Example that transitions from light to dark

  • Diagonal edge detection

  • Result of using the Prewitt masks

  • Result of using the Sobel masks


Laplacian l.jpg

Laplacian operator that transitions from light to dark

(linear operator)

Laplacian

Laplacian masks


Laplacian of gaussian log l.jpg

where r that transitions from light to dark2 = x2+y2, and

 is the standard deviation

Laplacian of Gaussian (LOG)

  • Laplacian combined with smoothing as a precursor to find edges via zero-crossing.


Mexican hat l.jpg

positive central term that transitions from light to dark

surrounded by an adjacent negative region (a function of distance)

zero outer region

Mexican Hat

  • Laplacian of a Gaussian

  • 3-D plot

  • Image (black is negative, gray is the zero plane, and white is positive)

  • Cross-section showing zero-crossings

  • 5x5 mask approximation to (a)

the coefficient must be sum to zero


Linear operation l.jpg
Linear Operation that transitions from light to dark

  • Second derivation is a linear operation

  • Thus, 2f is the same as convolving the image with Gaussian smoothing function first and then computing the Laplacian of the result


Example23 l.jpg
Example that transitions from light to dark

  • Original image

  • Sobel Gradient

  • Spatial Gaussian smoothing function

  • Laplacian mask

  • LoG

  • Threshold LoG

  • Zero crossings


Zero crossing log l.jpg
Zero Crossing & LoG that transitions from light to dark

  • Approximate the zero crossing from LoG image

  • Threshold the LoG image by setting all its positive values to white and all negative values to black.

  • Zero crossings occur between positive and negative values of the thresholded LoG.


Zero crossing vs gradient l.jpg
Zero Crossing vs. Gradient that transitions from light to dark

  • Attractive

    • Zero crossing produces thinner edges

    • Noise reduction

  • Drawbacks

    • sophisticated computation.

  • Gradient is more frequently used.


Edge linking and boundary detection l.jpg
Edge Linking and Boundary Detection that transitions from light to dark

  • Edge detection algorithm are followed by linking procedures to assemble edge pixels into meaningful edges.

  • Basic approaches

    • Local Processing

    • Global Processing via the Hough Transform

    • Global Processing via Graph-Theoretic Techniques


Slide27 l.jpg

Problems that transitions from light to darkwith Edge Detection Methods

  • Most of these partial derivative operators are sensitive to noise,

  • Use of these masks produces thick edges or boundaries,

  • Gives spurious edge pixels due to noise.

Input Image

Edge Detection

Edge Map

To overcome the effect of noise, smoothing operation is performed before edge detection

Input Image

Smoothing operation

Edge Detection

Edge Map


Smoothing based edge detection l.jpg
Smoothing based Edge Detection that transitions from light to dark

  • Two operators which use smoothing

  • Marr-Hildreth operator

    • Laplacian of Gaussian function (LOG)

    • Follows 2-Operations

      • Smoothing

      • Applying Laplacian operator

        Or generate the combined mask of LOG

  • Canny Edge Detector


Canny edge detection l.jpg
Canny Edge Detection that transitions from light to dark

  • Normally, edge operators use one threshold for whole image

Sobel

output

Sobel

output


Canny edge detector j canny 1986 l.jpg
Canny Edge Detector ( that transitions from light to darkJ. Canny’ 1986):

  • An "optimal" edge detector means:

    • Good detection - the algorithm should mark as many real edges in the image as possible.

    • Good localization - edges marked should be as close as possible to the edge in the real image.

  • Canny edge detector uses two threshold values to detect weak and strong edges


Canny edge detector l.jpg
Canny Edge Detector that transitions from light to dark

  • Stages of the Canny Algorithm:

    • Noise reduction

    • Finding the intensity gradient of the image

    • Non-maximum suppression

    • Tracing edges through the image and hysteresis thresholding


Stages of the canny algorithm l.jpg
Stages of the Canny algorithm that transitions from light to dark

  • Noise reduction: raw image is convolved with a Gaussian filter

  • Finding the intensity gradient of the image

    • Intensity gradient is estimated from the smoothed image using simple horizontal and vertical difference operators

    • Gradient direction together with the gradient magnitude then gives an estimated intensity gradient at each point in the image

    • Canny algorithm uses both gradient magnitude and direction in the edge detection


Stages of the canny algorithm33 l.jpg
Stages of the Canny algorithm that transitions from light to dark

  • Non-maximum suppression:

    • A search is carried out to determine if the gradient magnitude assumes a local maximum in the gradient direction

    • From this stage, referred to as non-maximum suppression, a set of edge points in the form of a binary image are obtained

    • Output of this stage is sometimes referred to as "thin edges"


Stages of the canny algorithm34 l.jpg
Stages of the Canny Algorithm that transitions from light to dark

  • Large threshold: gives true edges

  • Small threshold: gives false edges

  • Canny algorithm does not use same threshold for whole image

    • It does thresholding with hysteresis

  • Thresholding with hysteresis requires

    • two thresholds – high and low

    • Therefore we begin by applying a high threshold


  • Stages of the canny algorithm35 l.jpg
    Stages of the Canny Algorithm that transitions from light to dark

    • This marks out the edges we can be fairly sure are genuine.

    • Starting from these, using the directional information derived earlier, edges can be traced through the image.

    • While tracing an edge, we apply the lower threshold, allowing us to trace faint sections of edges as long as we find a starting point.


    Slide36 l.jpg

    Stages of the Canny algorithm that transitions from light to dark

    ….contd

    Original image

    Smoothing by Gaussian convolution

    Differential operators along x and y axis

    Non-maximum suppression

    finds peaks in the image gradient

    Hysteresis thresholding locates edge strings

    Edge map


    Slide37 l.jpg

    Sobel that transitions from light to dark

    Canny

    LOG


    Slide38 l.jpg

    Sobel that transitions from light to dark

    Canny

    LOG


    Slide39 l.jpg

    Sobel that transitions from light to dark

    Canny

    LOG


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