,10,10,11,11,11,99 CS223, Jana Kosecka **Image** Features Local, meaningful, **detectable** parts of the **image**. We will look at **edges** and corners CS223, Jana Kosecka **Image** Features – **Edges**, Corners Look for **detectable**, meaningful parts of the **image** **Edges** are **detected** at places where the **image** values exhibit sharp variation Gray value column column **Edge** **Edge** CS223, Jana Kosecka **Edge** **detection** (1D) F(x) **Edge**= sharp variation x F ’(x) Large first derivative x/

) Laplacian Of Gaussian The Laplacian of Gaussian (or Mexican hat) filter uses the Gaussian for noise removal and the Laplacian for **edge** **detection** **Images** taken from Gonzalez & Woods, Digital **Image** Processing (2002) Laplacian Of Gaussian Example **Images** taken from Gonzalez & Woods, Digital **Image** Processing (2002) **Edge** Linking and Boundary **Detection** Local Processing Global Processing Graph-Theoretic Techniques Local Processing **Edge** Linking using gradient and gradient direction. Graph-Theoretic Techniques

selection => feature extraction => feature vector. Challenging question: What details? Machinen Vision and Dig. **Image** Analysis Prof. Heikki Kälviäinen CT50A6100 4 **Detection** of discontinuities Point **detection**. Line **detection**. **Edge** **detection**. –Basic formulation. –Gradient operators. –Laplace operators. Corner **detection**. Combined **detection**. Machinen Vision and Dig. **Image** Analysis Prof. Heikki Kälviäinen CT50A6100 5 Point **detection** **Detection** of isolated points: a) Apply the mask -1 -1 -1 -1 8 -1 -1/

. By Dr. Xinwen Fu Laplacian Operator From the explanation above, we deduce that the second derivative can be used to **detect** **edges**. Since **images** are “2D”, we would need to take the derivative in both dimensions. Here, the Laplacian operator comes handy. The/ The Hough Line Transform is a transform used to **detect** straight lines. To apply the Transform, first an **edge** **detection** pre-processing is desirable. By Dr. Xinwen Fu How does it work? A line in the **image** space can be expressed with two variables. In the/

accomplish this. (1) where Y is the intensity value. 16 17 (a Fig. 2. Four color reference frames. 18 Fig. 3. Four grayscale reference **images**. Step 2: Execute the **edge** **detection**. The Canny **edge** detector is applied on each grayscale **image** yielding an **edge** map. A simple line deletion (horizontal and vertical) is followed if a line is too long. 19 20 Fig. 4. Four Canny/

variance of the background and the object pixels will be: The variance of the whole **image** is: 10.1- Fundamentals 10.2- Point, Line and **Edge** **Detection** 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using Morphological watersheds/Thresholds The following relationships hold: The optimum thresholds can be found by : The **image** is then segmented by 10.1- Fundamentals 10.2- Point, Line and **Edge** **Detection** 10.3- Thresholding 10.4- Region-Based Segmentation 10.5 - Segmentation Using /

is the number of pixels with the intensity rk.[4] Computer Vision search algorithms and techniques **Edge** feature **detection** The Sobel operator The Prewitt operators The Robert operator Laplacian/Laplacian of Gaussian operator Canny **edge** **detection** Fig(24). Reference object **image** [25] Fig(25). Object in scene **image** [25] **Edge** feature **detection** The Sobel operator (1.5) Where Gx is the vertical filter and Gy is the horizontal/

finding characteristic region size that is covariant with the **image** transformation A CHIEVING SCALE COVARIANCE R ECALL : E DGE **DETECTION** f Source: S. Seitz **Edge** Derivative of Gaussian **Edge** = maximum of derivative E DGE **DETECTION**, T AKE 2 f **Edge** Second derivative of Gaussian (Laplacian) **Edge** = zero crossing of second derivative Source: S. Seitz F ROM **EDGES** TO BLOBS **Edge** = ripple Blob = superposition of two ripples Spatial selection: the/

**Detection** **Image** features Global features –global properties of an **image**, including intensity histogram, frequency domain descriptors, covariance matrix and high order statistics, etc. Local features –local regions with special properties, including **edges**, corners, lines, curves, regions with special properties, etc Depending on applications, various features are useful. We will focus on **edges** and corners in this lecture **Edges** **Edge** points are pixels at or around which the **image**/

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. 13 Steps in **edge** **detection** 1.**Image** smoothing for noise reduction 2.**Detection** of **edge** points. Points on an **edge** 3.**Edge** localization 14 **Image** gradient Gradient is a vector The magnitude of the gradient The direction of the gradient vector/

example, the brickwork in the previous example. One way to overcome this is to smooth **images** prior to **edge** **detection**. Digital **Image** Processing – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k.mollazade 17 **Edge** **detection** example with smoothing Original **Image** Horizontal Gradient Component Vertical Gradient Component Combined **Edge** **Image** Digital **Image** Processing – Department of Biosystems Engineering – University of Kurdistan http://agri.uok.ac.ir/k/

-maximum suppression) Noise reduction: first derivatives are susceptible to noise present on raw unprocessed **image** data. Canny **edge** **detection** performs convolution of the original **image** with a Gaussian filter to remove noise. The result is a slightly blurred version of the original **image**. ‒Consider a single row or column of the **image** and plot intensity as a function of position. If pixels are disturbed with noise/

TALLAPALLY Problem statement Problem Description Some of the papers (**Edge** **Detection**) reviewed Canny **Edge** **Detection** **Detection** of **images** in speckle **images** Authentication of **edges** produced by zero crossings Adaptive Transform **edge** **detection** Summary Outline **Image** Segmentation in Ultrasound **imaging** Ultrasound **Imaging**: In Ultrasound **imaging**, high frequency sound waves are used to capture the **images**. Usually sound waves are directed towards object to be **imaged**. From the sound waves reflected from the object, 2/

or 3 Computer Vision : CISC 4/689 Example: Canny **Edge** **Detection** courtesy of G. Loy gap is gone Original **image** Strong **edges** only Strong + connected weak **edges** Weak **edges** Computer Vision : CISC 4/689 Example: Canny **Edge** **Detection** (Matlab automatically set thresholds) Computer Vision : CISC 4/689 **Image** Pyramids Observation: Fine-grained template matching expensive over a full **image** –Idea: Represent **image** at smaller scales, allowing efficient coarse- to-fine search/

mask to **detect** lines of a given direction 85 **Edge** **Detection** First derivative – **detect** if a point is on the **edge** Second derivative – **detect** the midpoint of the **edge** (zero-crossing property) 86 **Edge** **detection** in noisy **images** Examples of a ramp **edge** corrupted by random/Partitioning into regions done often by using gray values of the **image** pixels. Two general approaches : – Region-based segmentation – Boundary estimation using **edge** **detection** 103 Region-based Approach Pixels corresponding to an object grouped /

the discrete Gaussian mask shown before. If we need another standard deviation value we can create the corresponding integer-valued kernel. 20 MOTION **DETECTION** (cont’d) The following **images** show the original background frame and the corresponding **edge** map. This **image** will be saved so we can use it every time we need it. The next step will take care of two consecutive frames/

a number of these approaches and show that improvements in segmentation performance can be achieved by combining methods from distinct categories, such as techniques in which **edge** **detection** is combined with thresholding. Suppose the **Image** R using the **image** segmentation process, R will be partitioned into n sub regions: R 1, R 2,…,R n. In the segmentation process there are five possible conditions/

the theoretical analysis on optimization and performance analysis. 35 36 37 38 39 40 Isotropically Symmetrical? 41 42 43 44 F On Multi-**Edge** **Detection**, "CVGIP: Graphical Models And **Image** Processing", Vol.58, No.2, pp101-114, March 1996. F Multi-**Edge** **Detection** by Isotropical 2-D ISEF Cascade, “Pattern Recognition”, Vol.28, No.12, pp1871-1885, 1995. F Towards Unification of Band-Limited Differential/

7 Laplacian October 7, 2014Computer Vision Lecture 9: **Edge** **Detection** II 11 Laplacian Filters October 7, 2014Computer Vision Lecture 9: **Edge** **Detection** II 12 Gaussian **Edge** **Detection** As you know, one of the problems in **edge** **detection** is the noise in the input **image**. Noise creates lots of local intensity gradients that can trigger unwanted responses by **edge** **detection** filters. We can reduce noise through (Gaussian) smoothing, but there is a/

– Interpolation – Warping – Morphing – Compression Today – **Edge** **Detection** **Image** Manipulation and Enhancement **Image** Analysis **Image** Compression Recall: Digital **Image** Processing Digital **Image** Processing (DIP) – Is computer manipulation of pictures, or **images**, that have been converted into numeric form – Typical operations include **Image** Compression **Image** Warping Contrast Enhancement Blur Removal Feature Extraction Pattern Recognition **Image** Processing Goals Digital **image** processing is a subclass of signal/

Problem Statement Comparison of GCP selection algorithms Comparison of GCP selection algorithms Manual Manual Automated Automated Area-based Area-based Feature-based Feature-based Contour Mapping Contour Mapping Corner and **Edge** **Detection** Corner and **Edge** **Detection** Manual Registration Left: the reference **image** Right: the **image** to be registered Automated Registration Area-based algorithms Area-based algorithms A small window of points in the sensed/

is necessary for the sum or average of all elements of the kernel matrix to be zero. Digital **Image** ProcessingLecture 16 28 Summary Line **detection** **Edge** **detection** based on First derivative Provides gradient information 2 nd derivative using zero-crossing Indicates dark/bright side of an **edge** Line **detection** **Edge** **detection** based on First derivative Provides gradient information 2 nd derivative using zero-crossing Indicates dark/bright side/

Course 5 **Edge** **Detection** **Image** Features: local, meaningful, **detectable** parts of an **image**. **edge** corner texture … **Edges**: **Edges** points, or simply **edges**, are pixels at or around which the **image** values undergo a sharp variation. Usually, **edges** are classified as ： step **edge**, ridge **edge** roof **edge**. We will emphasize on step **edge** **detection** in our discussions. 1.**Edge** **detection**: 1)Goal: Given an **image** corrupted by acquisition noise, locate the **edges** most likely to be generated by scene elements not by/

that produces a set of **edges** from an **image** Contour –Is a list of **edges** or the mathematical curve that models the list of **edges**. **Edge** Linking –Is the process of forming an ordered list of **edges** from an unordered list **Edge** Following –Is the process of searching the **image** to determine contours Hema ENT 273 Lecture 6 6 **Edge** **Detection** **Edge** **detection** is an operation to **detect** significant local changes in the/

) filter uses the Gaussian for noise removal and the Laplacian for **edge** **detection** **Images** taken from Gonzalez & Woods, Digital **Image** Processing (2002) 23 of 20 Laplacian Of Gaussian Example **Images** taken from Gonzalez & Woods, Digital **Image** Processing (2002) 24 of 20 Summary In this lecture we have begun looking at segmentation, and in particular **edge** **detection** **Edge** **detection** is massively important as it is in many cases the first step/

13 Laplacian Filters 3 3 Laplacian 5 5 Laplacian zero **detection** 7 7 Laplacian September 26, 2013Computer Vision Lecture 8: **Edge** **Detection** II 14 Gaussian **Edge** **Detection** As you know, one of the problems in **edge** **detection** is the noise in the input **image**. Noise creates lots of local intensity gradients that can trigger unwanted responses by **edge** **detection** filters. We can reduce noise through (Gaussian) smoothing, but there is/

TALLAPALLY Problem statement Problem Description Some of the papers (**Edge** **Detection**) reviewed Canny **Edge** **Detection** **Detection** of **images** in speckle **images** Authentication of **edges** produced by zero crossings Adaptive Transform **edge** **detection** Summary Outline **Image** Segmentation in Ultrasound **imaging** Ultrasound **Imaging**: In Ultrasound **imaging**, high frequency sound waves are used to capture the **images**. Usually sound waves are directed towards object to be **imaged**. From the sound waves reflected from the object, 2/

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. 21 **Edge** point to determine a point as an **edge** point the transition in gray level associated with the point has to be significantly stronger/

and convolution Convluation and linear filter Gaussian filter, box filter, and median filter Application: Hybrid **images** **Edge** **detection** **Image** derivatives Gaussian derivative filters Canny **edge** detector O UTLINE **Image** filter and convolution Convolution and linear filter Gaussian filter, box filter, and median filter Application: Hybrid **images** **Edge** **detection** **Image** derivatives Gaussian derivative filters Canny **edge** detector M OTIVATION : I MAGE DENOISING How can we reduce noise in a photograph? M OVING/

J will point in the direction of the steepest ascent. Taking the derivative is prone to noise, so we normally apply smoothing first/or in combination by combining the **edge** detector with a Gaussian. INF 530048 **Edge** **detection** using Gaussian filters Gradient of a smoothed **image**: Derivative of Gaussian filter: Remember that the second derivative (Laplacian) carries information about the exact location of the/

gaussian filter matrix of 7 rows and 7 columns, with standard deviation of 5. Smoothing / Blurring Application of the same Gaussian filter to an intensity **image** (take the red layer of the previous **image**): **Edge** **Detection** The process of **edge** **detection** attenuates high fluctuations in color, i.e. dramatic change in intensity. In the frequency domain, this process refers to the attenuation of high frequencies. Matlab/

and Woods CS 484, Spring 2007©2007, Selim Aksoy20 Difference operators for 2D Adapted from Gonzales and Woods CS 484, Spring 2007©2007, Selim Aksoy21 Gaussian smoothing and **edge** **detection** We can smooth the **image** using a Gaussian filter and then compute the derivative. Two convolutions: one to smooth, then another one to differentiate? Actually, no - we can use a derivative of Gaussian/

looking for discontinuities in gradients. Linking these **edge** points in some way to produce descriptions of **edges** in terms of lines, curves etc. 22 I.Definitions & Concepts **Edges** 23 **Edges** are caused by a variety of factors surface normal discontinuity depth discontinuity surface color discontinuity illumination discontinuity II.**Edge** **Detection** Origin of **Edge** 24 II.**Edge** **Detection** **Images** and intensity gradients The **image** is a function mapping coordinates to intensity f/

and dissolves. By analyzing the spatial distribution of entering and exiting **edge** pixels, we can **detect** and classify wipes. **Edges**/contours (cont.) How to define the entering and exiting **edge** pixels Xnin and Xn-1out? Suppose we have 2 binary **images** en-1 and en. The entering **edge** pixels Xnin are the fraction of **edge** pixels in en which are more than a fixed distance r from/

transition. f (x) helps to identify the exact position of transition. f (x) helps to identify the exact position of transition. **Edge** **Detection** Gradient and Magnitude **Edge** **Detection** But an **image** is a two dimensional discretized gray level function f(x,y). But an **image** is a two dimensional discretized gray level function f(x,y). The norm of the gradient can be aproximated to reduce/

.gif in www.cis.temple.edu/~latecki/CIS601-04LecturesImages Compare the results. **Edge** **Detection** What are **edges** in an **image**? **Edge** **Detection** **Edge** **Detection** Methods **Edge** Operators Matlab Program Performance What are **edges** in an **image**? **Edges** are those places in an **image** that correspond to object boundaries. **Edges** are pixels where **image** brightness changes abruptly. Brightness vs. Spatial Coordinates More About **Edges** An **edge** is a property attached to an individual pixel and is calculated from/

in complex background 30/08/2006 IPCV 2006 Budapest Agenda (**Detection**) **Detecting** faces in gray scale **images** Knowledge-based Feature-based Template-based Appearance-based **Detecting** faces in color **images** **Detecting** faces in video Performance evaluation Research direction and concluding remarks 30/08/2006 IPCV 2006 Budapest Template Matching Methods Store a template Predefined: based on **edges** or regions Deformable: based on facial contours (e.g., Snakes/

blurring is minimized and **edges** stay sharp 41 **Edge** **Detection** Powerfull application of convolution! 42 **Edge** **detection** What are **edges**? Why are they interesting? How do we find them? –Prewitt –Sobel –Laplacian –Canny 43 What are **edges**? **Edge** **detection** Local intensity change Strong **edge** = the steep areas in a 3D plot (show: blobs) 44 Why are they interesting? **Edges** can (many times) represent the information in the **image** (the objects) A higher/

filter – can it be done with covolution 25 x 25 median filter 50 x 50 median filter **Edge** **detection** Goal: map **image** from 2d array of pixels to a set of curves or line segments or contours. Why? Main / noise Derivatives to locate contrast, gradient Templates, matched filters to find designated pattern. **Edge** **detection** processes the **image** gradient to find curves, or chains of **edges**. Binary **image** analysis useful to manipulate regions of interest Connected components Morphological operators (local operator, but/

segmentation A large group of methods based on information about previously **detected** **edges** in the **image** Preprocessing step: **edge** **detection** Motivation: **images** resulted from **edge** **detection** cannot be used as a segmentation result **Edges** have to be linked into chains which correspond better with boundaries in an **image** Final result: **detection** of boundaries of objects present in the **image** **Edge**-based segmentation is not about one algorithm, but involves a large group of/

: Gaussian filter The derivative of the Gaussian The 2 nd derivative (Laplacian of Gaussian) Digital **image** processing Chapter 8 **Image** analysis and pattern recognition **Edge** **detection** by different operators – comparison: Original **image** Sobel **edge** **detection** LoG **edge** **detection**; sigma=5 Digital **image** processing Chapter 8 **Image** analysis and pattern recognition Roberts **edge** **detection** LoG **edge** **detection**; Sigma=10 Objects representation by their boundaries: Contour extraction: Fig. 8.8 4-connectivity; 8/

of Gibbs) **Edge** **Detection** with Gibbs Original **Image** (512x512) Canny **Edge** **Detection** **Edge** **Detection** with Gibbs **Edge** **Detection** with Gibbs Original **Image** (200x200) Canny **Edge** **Detection** **Edge** **Detection** with Gibbs **Edge** **Detection** with Gibbs Original **Image** (2048x2048) Canny **Edge** **Detection** **Edge** **Detection** with Gibbs **Edge** **Detection** with Gibbs Original **Image** (800x800) Canny **Edge** **Detection** **Edge** **Detection** with Gibbs **Image** Enlargement, Canny **Edge** Detector **Image** Used **Image** Enlargement, Gibbs Enhanced **Edge** Detector **Image** Used/

thresholding step T, that is, on effectively locating the shadow **edges**. As we will see, our shadow **edge** **detection** is not yet perfect ECCV 2002 Shadow **Edge** **Detection** The Shadow **Edge** **Detection** consists of the following steps: 1. **Edge** **detect** a smoothed version of the original (by channel) and the invariant **images** 2. Threshold to keep strong **edges** in both **images** 3. Shadow **Edge** = **Edge** in Original & NOT in Invariant 4. Applying a suitable/

| for all ji – the point is within line i. Use one mask to **detect** lines of a given direction 10/50 **Edge** **Detection** First derivative – **detect** if a point is on the **edge** Second derivative – **detect** the midpoint of the **edge** (zero-crossing property) 11/50 **Edge** **detection** in noisy **images** Examples of a ramp **edge** corrupted by random Gaussian noise of mean 0 and = 0.0, 0.1, 1/

the texture –Reflections depends on view point and illumination 7 Contrast **detection** process **Image** processing **Image** analysis **image** intermediate **image** representation **image** description 8 Contrast **detection** methods Search for extremum in 1 st derivative Search for zero crossing in 2 nd derivative 9 Contrast **detection** Step **edge** Smoothed step **edge** First derivative Second derivative (white pos, yellow negative) 10 **Image** processing tools Let s(i), f(i) be two real discrete/

. Feature selection => feature extraction => feature vector. Challenging question: What details? Machinen Vision and Dig. **Image** Analysis Prof. Heikki Kälviäinen CT50A6100 4 **Detection** of discontinuities Point **detection**. Line **detection**. **Edge** **detection**. –Basic formulation. –Gradient operators. –Laplace operators. Combined **detection**. Machinen Vision and Dig. **Image** Analysis Prof. Heikki Kälviäinen CT50A6100 5 Point **detection** **Detection** of isolated points: a) Apply the mask -1 -1 -1 -1 8 -1 -1/

in surface material properties) Illumination discontinuity (e.g., shadow) **Edge** **Detection** **Edge** Types –Step **edge** (ramp) –Line **edge** (roof) Searching for **Edges**: –Filter: Smooth **image** –Enhance: Apply numerical derivative approximation –**Detect**: Threshold to find strong **edges** –Localize/analyze: Reject spurious **edges**, include weak but justified **edges** Step **edge** **detection** First derivative **edge** detectors: Look for extrema –Sobel operator (Matlab: **edge**(I, ‘sobel’) ) –Prewitt, Roberts cross –Derivative of Gaussian/

gradient per point Look at the gradient behavior over a small window Categories **image** windows based on gradient statistics Constant: Little or no brightness change **Edge**: Strong brightness change in single direction Flow: Parallel stripes Corner/spot: Strong brightness changes in orthogonal directions Computer Vision : CISC 4/689 Corner **Detection**: Analyzing Gradient Covariance Intuitively, in corner windows both Ix and Iy should be/

does median filtering have over Gaussian filtering? Source: K. Grauman Salt & pepper noise – median filtering = 1 pixel = 2 pixels = 5 pixels 3x3 window 5x5 window 7x7 window Questions? **Edge** **detection** Convert a 2D **image** into a set of curves Extracts salient features of the scene More compact than pixels TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box/

(upper right), sum for two masks (bottom). **Edge** **detection**. Sobel (left), Prewitt (right) **Edge** **detection**. Marr **edge** **detection** (Laplacian of Gaussian). After convolution with a smoothing filter h(r) of =1.5 (left) and =5 (right). **Edge** **detection** is given in next slide. **Edge** **detection**. Marr **edge** **detection**. Zero crossing from above (presented in previous slide) **image** (right) and the same for left **image**. **Edge** **detection**. Original **image** (grains). **Edge** **detection**. Sobel (upper left), Prewitt (upper right), Roberts/

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