13/22 4. The Canny **edge** detector The Canny **edge** detector is an **edge** **detection** operator that uses a multi-stage **algorithm** to **detect** a wide range of **edges** in images. It was developed by John F. Canny in 1986. Cannys aim was to discover the optimal **edge** **detection** **algorithm**. In this situation, an "optimal" **edge** detector means: good **detection** – the **algorithm** should mark as many real **edges** in the image as possible. good/

Constructed a machine-file bipartite graph (0.2 TB+) 1 billion nodes (machines and files) 37 billion **edges** As of today, has grown to more than three times Taiwan12 Faloutsos, Prakash, Chau, Koutra, Akoglu Faloutsos/ Koutra, Akoglu Faloutsos, Prakash, Chau, Koutra, Akoglu Outline Part 1: anomaly **detection** Part 2: influence propagation Motivation Epidemics: what happens? (Theory) Action: Who to immunize? (**Algorithms**) Taiwan12 Faloutsos, Prakash, Chau, Koutra, Akoglu A fundamental question Strong Virus Epidemic/

–Random walks stay longer in dense clusters LC, [Ahn et al. 2010] –Link Community **Detection** –A community is redefined as a set of closely interrelated **edges** –Overlapping and hierarchical clustering Community **Detection** **Algorithms** An Evaluation of Community **Detection** **Algorithms** on Large-Scale Email Traffic 10 Used to assess the quality of the **algorithms** when the true community structure of the network is not known. There is no/

something missing… What are we ignoring in the following **edge** **detection** processes? Gaussian filter Sobel **edge** **detection** Threshold based binarization of Sobel magnitude And Laplacian-Gaussian filter Zero crossing **detection** We need a smarter **algorithm** We merely selected each **edge** based on its magnitude and zero-crossing We completely ignored its immediate surroundings Why is this bad? **Detects** **edges** we don’t want Prone to noise Prone to clutter/

calculations using damage vector sensitivity –Optimize sensor placement –Optimize interrogation frequency –Implementation of strain-based approach –Investigate alternate **detection** and extent **algorithms** non-linear time series feature extraction (Todd et al, 2001) Remarks –Damage **detection** in helicopter main rotor using active interrogation with trailing **edge** flap is promising –Damage extent using frequency domain AMRPT is difficult due to sensitivity to errors in damage vectors/

graph Can use pre/post visit numbers to **detect** properties of graphs Account for all **edges**: Tree **edges** (solid) and back **edges** (dashed) Back **edges** **detect** cycles Properties still there even if explored in a different order (i.e. start with F, then J) Depth-First Search in Directed Graphs Can use the same DFS **algorithm** as before, but only traverse **edges** in the prescribed direction – Thus, each/

for the message or MPI_Test() -- establish whether message has actually been received at that point. 27 Distributed Termination **Detection** **Algorithms** Termination Conditions At time t requires the following conditions to be satisfied: Application-specific local termination conditions exist throughout the/ by a graph. The nodes are called vertices, and the links are called **edges**. If the **edges** have implied directions (that is, an **edge** can only be traversed in one direction, the graph is a directed graph. 42/

process. Eventually all processes turn white, and no message is in transit -- this signals termination. How to develop a signaling mechanism to **detect** termination? passive active initiator Dijkstra-Scholten **algorithm** An initiator initiates termination **detection** by sending signals (messages) down the **edges** via which it engages other nodes. At a “suitable time,” the recipient sends an ack back. When the initiator receives ack from/

Serializability A schedule is conflict serializable if and only if its precedence graph is acyclic. Cycle-**detection** **algorithms** exist which take order n 2 time, where n is the number of vertices in the graph. (Better **algorithms** take order n + e where e is the number of **edges**.) If precedence graph is acyclic, the serializability order can be obtained by a topological sorting of/

Rz 0) ab )1 Ry y )1 (1 )2 (2 Rz z Static Race **Detection** for C136 Two Observations We are doing constraint copying –Notice the **edge** from c to a got “copied” to Ry to y We didn’t draw the transitive **edge**, but we could have This **algorithm** can be made demand-driven –We only need to worry about paths from constant/

PROGRAM THE COMPUTER? Let’s think about typical example which is already becoming popular in cameras: We would like to implement **algorithms** which will mark faces in pictures, recognize familiar faces. This may of course extended to other objects and complete scenes, /How to produce the ”good enough” representation is the essential problem to solve Next we will show example of representation by **edges** **EDGE** **DETECTION** LINEAR FILTERING: AREA AROUND EVERY POINT IN THE IMAGE MATRIX IS MULTIPLIED z l m u x v n p q /

Spanning Trees: Summary Model: –Transient adversarial network dynamics **Algorithmic** techniques: –Symmetry-breaking through ids and/or a distinguished root –Cycle-breaking through sequence numbers or local **detection** Analysis techniques: –Self-stabilization paradigm Other network structures: / d j mini-vertices for each j Construct a random perfect matching Graph obtained by adding an **edge** for every **edge** between mini-vertices Adapting for Internet: –Prune 1- and 2-degree vertices repeatedly –Reattach them using/

Rz 0) ab )1 Ry y )1 (1 )2 (2 Rz z Static Race **Detection** for C136 Two Observations We are doing constraint copying –Notice the **edge** from c to a got “copied” to Ry to y We didn’t draw the transitive **edge**, but we could have This **algorithm** can be made demand-driven –We only need to worry about paths from constant/

: In automated analysis of digital images, a sub-problem often arises of **detecting** simple shapes, such as straight lines, circles or ellipses introduction Applications and **Algorithms** in CV Tutorial 3: Grouping & Fitting Primitives **detection** Solution? **Edge** **detection** introduction Applications and **Algorithms** in CV Tutorial 3: Grouping & Fitting Finding straight lines An **edge** detector can be used as a pre-processing stage to obtain points (pixels) that are/

L3 Thread1 Invalid! L3 Thread1 L4 Thread1 L4 Thread4 L3 Thread4 L3 Thread1 Valid 12 /44 **Detection** of Potential Deadlocks (Cont.) Due to Locks (Cont.) Modified Depth-First Search **algorithm** Traverses only valid paths, because it extends the current path (on the search stack) only with **edges** satisfying both criteria for validity a node all of whose neighbors have been explored may be/

boundary (position 3). At this point, the routine should stop Groucho from moving and return. 3. Write align with **edge**( ), which should drive Groucho forward for a second or two (dumping any collected balls over to the opponent’s side/attempt the unified program and describe the results. Copyright Prentice Hall, 200121 Exit Conditions Problem with simple **algorithmic** approach: there is no provision for **detecting**, no less correcting for, problem situations –Consider Groucho’s program: most of the time, it /

Laboratory Slide-10 Power Law Graphs Target Identification Social Network Analysis Anomaly **Detection** Many graph **algorithms** must operate on power law graphs Most nodes have a few **edges** A few nodes have many **edges** Many graph **algorithms** must operate on power law graphs Most nodes have a few **edges** A few nodes have many **edges** MIT Lincoln Laboratory Slide-11 Modeling of Power Law Graphs Adjacency Matrix/

is convolution, and convolution is associative: This saves us one operation: Associative property of convolution f Source: S. Seitz 2D **edge** **detection** filters Gaussian derivative of Gaussian ( x ) Derivative of Gaussian filter x-direction y-direction The Sobel operator Common approximation of / 4 3.set r = node with minimum cost on the ACTIVE list 4.repeat Step 2 for p = r Dijkstra’s shortest path **algorithm** **Algorithm** 1.init node costs to , set p = seed point, cost(p) = 0 2.expand p as follows: for each of p/

Routing by rumor." Ex. RIP, Xerox XNS RIP, Novells IPX RIP, Ciscos IGRP, DECs DNA Phase IV, AppleTalks RTMP. Caveat. **Edge** costs may change during **algorithm** (or fail completely). t v 1 s 1 1 deleted "counting to infinity" 2 1 65 Path Vector Protocols Link state routing./ rates between pairs of currencies, is there an arbitrage opportunity? Remark. Fastest **algorithm** very valuable! F$ £ ¥ DM 1/7 3/10 2/3 2 17056 3/50 4/3 8 IBM 1/10000 800 70 **Detecting** Negative Cycles: Summary Bellman-Ford. O(mn) time, O(m + n/

2 2 2 3 Main steps: Find smallest neighbors Compute connected components of graph H induced by selected **edges** Contract each component into a single vertex Call the procedure recursively Copy label of every vertex v G/does not guarantee complete fault coverage; expensive; system halt upon **detection** of uncorrectable errors; service disruption; etc… etc… 67 Impact of Memory Errors 68 Resilient **Algorithms** and Data Structures Resilient **Algorithms** and Data Structures: Capable of tolerating memory errors on data /

operator: **Edge** **Detection** Using the Gradient Main steps in **edge** **detection** using masks: **Edge** **Detection** Using the Gradient (an example using the Prewitt **edge** detector - don’t divide by 2) **Edge** **Detection** Using the Gradient Example: **Edge** **Detection** Using the Gradient Example – cont.: **Edge** **Detection** Using the Gradient Example – cont.: **Edge** **Detection** Using / m 2 ),…,(r m nm, m nm ) jjjj rjrjrjrj jjjj H.T. table Generalized H.T. **Algorithm**: x c = x i + r i cos( i ) y c = y i + r i sin( i ) Finds a /

to b) and c) Described problem statement In medical field ( ex : Ultrasound imaging), **edge** **detection** plays a role in aiding the physician Described some of the existing **edge** **detection** **algorithms** Would like to use LOG **edge** detector to identify the **edges** between berves and any other surrounding regions Summary 1. “A computational approach to **edge** **detection** by John Canny”, IEEE Transactions on Pattern Analysis and Machine Intelligence, November 1986/

up-to-the moment survey on community **detection**: S. Fortunato, “Community **Detection** in Graphs.“ arXiv 0906.0612v2. S. Fortunato, “Community **Detection** in Graphs.“ arXiv 0906.0612v2. In graph clustering, look for a quantitative defi of community. No definition is universally accepted. Intuitively, community has more **edges** “ inside” than linked to the outside. **Algorithmically** defined (final product of an **algorithm**, without a precise a priori def.) Let/

of keywords in a rooted labeled tree Each **edge** labeled with a letter from an alphabet Each **edge** labeled with a letter from an alphabet Any two **edges** coming out of the same vertex have distinct labels Any two **edges** coming out of the same vertex have /by extending it to the left and right, until (k + 1) mismatches are found An Introduction to Bioinformatics **Algorithms** (Jones and Pevzner) www.bioalgorithms.info Filtration: Match **Detection** Theorem: If x 1 …x n and y 1 …y n match with at most k mismatches, they /

resource R j - represented by a dashed line. Claim **edge** converts to request **edge** when a process requests a resource. When a resource is released by a process, assignment **edge** reconverts to a claim **edge**. Resources must be claimed when a process first starts in / resources to fulfill other processes requests. Deadlock exists, consisting of processes P 1, P 2, P 3, and P 4. **Detection**-**Algorithm** Usage When, and how often, to invoke depends on: How often a deadlock is likely to occur? How many processes will need/

to b) and c) Described problem statement In medical field ( ex : Ultrasound imaging), **edge** **detection** plays a role in aiding the physician Described some of the existing **edge** **detection** **algorithms** Would like to use LOG **edge** detector to identify the **edges** between berves and any other surrounding regions Summary 1. “A computational approach to **edge** **detection** by John Canny”, IEEE Transactions on Pattern Analysis and Machine Intelligence, November 1986/

HMT **Algorithm** Step 1. Converting the input image to a binary image: The splitting technique converts the input image to the binary image X. Step 2. Implementing the hit-filter: X is correlated hexagonally with a hit filter that **detects** the horizontal and vertical **edges** to /or region growing code to be verified as a filament region. Solar Image Recognition Workshop, Brussels, 23 & 24 Oct. The **detection** **algorithm** **detects** the filaments in a 1024 × 1024 image in about 0.8 seconds using P4-2.0 G Hz PC with 512 M/

(V is the number of vertices) over all **edges** relaxing, or updating, the distance to the destination of each **edge**. Finally it checks each **edge** again to **detect** negative weight cycles, in which case it returns false. The time complexity is O(VE), where E is the number of **edges**. The **algorithm** has to iterate over the **edges** several times to make sure that the effect of/

: Canny Assume: – Linear filtering – Additive iid Gaussian noise An "optimal" **edge** detector should have: – Good **Detection** Filter responds to **edge**, not noise. – Good Localization **detected** **edge** near true **edge**. – Single Response one per **edge**. Optimal **Edge** **Detection**: Canny Based on the first derivative of a Gaussian **Detection**/Localization trade-off – More smoothing improves **detection** – And hurts localization. Stages of the Canny **algorithm** Noise reduction Size of Gaussian filter Finding the intensity gradient/

? String Barcoding Uncovering Optimal Virus Signatures Sam Rash, Dan Gusfield University of California, Davis. Motivation Need for rapid virus **detection** –Given unknown virus database known viruses –Problem identify unknown virus quickly based on a small set of substrings. Motivation –/ sequences in M[C]), and connect each network correctly to the **edges** in T, the resulting network is a fully-decomposed blobbed-tree that generates M. **Algorithmically**, T is easy to find and is the tree resulting from contracting/

graph partitioning Heuristics for load balancing and termination **detection** K. Madduri, D.A. Bader, J.W. Berry, and J.R. Crobak, “An Experimental Study of A Parallel Shortest Path **Algorithm** for Solving Large-Scale Graph Instances,” Workshop on **Algorithm** Engineering and Experiments (ALENEX), New Orleans, LA, January 6, 2007. ∆ - stepping **algorithm** [MS03] Label-correcting **algorithm**: Can relax **edges** from unsettled vertices also ∆ - stepping: “approximate bucket implementation/

has 4 cells with a basically uniform intensity” to search for candidates Level 2: local histogram equalization followed by **edge** **detection** Level 3: search for eye and mouth features for validation 30/08/2006 IPCV 2006 Budapest Knowledge-Based Method: / spaces CIELab, HSV, HS, Normalized RGB and YCrCb Four different metrics are used to evaluate the results of the skin **detection** **algorithms** C %– Skin and Non Skin pixels identified correctly S %– Skin pixels identified correctly SE – Skin error – skin pixels/

Results Conclusion/Future Work References **Edge** **Detection** **Detecting** **Edges** in images is a complex task, but it useful in other image processing problems Feature **detection**/extraction Segmentation Picture enlargement Many **algorithms** exist for **edge** **detection** Used Canny **Algorithm** for its robustness (when set correctly, hard to find a better performing **algorithm**) However, issues in image enhancement still exist when using Canny **Edge** Detector Gibbs Sampler in **Edge** **Detection** Gibbs Sampler is a Markov/

**algorithm** Resource-Allocation Graph Scheme Claim **edge** Pi → Rj indicated that process Pj may request resource Rj in the future; represented by a dashed line. Claim **edge** converts to request **edge** when a process requests a resource. Request **edge** converted to an assignment **edge**/ Request [i j ] = k, then process Pi is requesting k more instances of resource type Rj. **Detection** **Algorithm** **Detection** Example **Detection** **Algorithm** Usage When, and how often, to invoke depends on: 1. How often a deadlock is likely to occur/

all processes turn white, and no message is in transit -- this signals termination. How to develop a signaling mechanism to **detect** termination? Dijkstra-Scholten **algorithm** The basic scheme Node j engages node k. An initiator initiates termination **detection** by sending signals (messages) down the **edges** via which it engages other nodes. At a “suitable time,” the recipient sends an ack back. When the initiator/

R4 Use a wait-for graph: Collapse resources An **edge** P i P k exists only if RAG has P i R j & R j P k Cycle in wait-for graph deadlock! 2 nd **Detection** **Algorithm** What if there are multiple resource instances? Data structures:/R1R1 R2R2 R3R3 P1P1 111 P2P2 212 P3P3 110 P4P4 111 R1R1 R2R2 R3R3 P1P1 321 P2P2 P3P3 P4P4 Allocation Request When to run **Detection** **Algorithm**? For every resource request? For every request that cannot be immediately satisfied? Once every hour? When CPU utilization drops below 40%? /

Robust Parallel Processing Resilient **Algorithms** Feb. 2015Part V – Malfunctions: Architectural AnomaliesSlide 43 19.1 Malfunction **Detection** No amount of spare resources is useful if the malfunctioning of the active module is not **detected** quickly **Detection** options Periodic testing: / D: measure of cost-effectiveness Node symmetry: all nodes have the same view of the network **Edge** symmetry: **edges** are interchangeable via relabeling Hamiltonicity: the p-node ring (cycle) can be embedded in the graph Given/

at-1 fault at the output of the AND gate. n Using the parallel fault simulation **algorithm**, determine which of the four primary input faults are **detectable** by the test derived above. s-a-1 Copyright 2001 Agrawal & BushnellHyderabad, July 27-29/ 2001 Agrawal & BushnellHyderabad, July 27-29, 2006 (Day 2)95 Single threshold IDDQ Excessive yield loss is observed at wafer **edge** due to single threshold IDDQ limits Copyright 2001 Agrawal & BushnellHyderabad, July 27-29, 2006 (Day 2)96 Distribution variance: (/

41Yishai BeeriSimilarity Flooding SDBI – Winter 2001 Example: Change **Detection** **Algorithm** Script: Product = SFJoin(T2, T1); Result = SelectLeft(product); 42Yishai BeeriSimilarity Flooding SDBI – Winter 2001 Example: Change **Detection** No initial mapping SelectLeft operator selects best absolute match/the actual values do 52Yishai BeeriSimilarity Flooding SDBI – Winter 2001 Complexity Usually 5-30 iterations Each iteration is O(|E|) (**edges** in propagation graph) |E| = O(|E1||E2|) |E1| = O(|V1| 2 ) – if G1 is /

systems Important for Social networks Ad-hoc networks Protein interaction networks Genetic networks Motivation: Why to **detect** communities? Predict how much someone going to love a movie based on their movie preferences Grand / Multilevel graph partitioning Experimental results Conclusions Previous Work Two main classes **Algorithms** based on Agglomerative Methods (addition of **edges**) Divisive Methods (removal of **edges**) **Algorithms** based on Laplacian Matrix Centrality measures Flow models Random walks Resistor /

: the bottleneck is larger than r. Now, contract all **edges** with weight at most r, and recurse. T(m) = O(m) + T(m/2) **Algorithms** and Networks: Shortest paths **Algorithms** and Networks: Shortest paths 5 Conclusions **Algorithms** and Networks: Shortest paths **Algorithms** and Networks: Shortest paths Conclusions Applications Several **algorithms** for shortest paths Variants of the problem **Detection** of negative cycles Reweighting technique Scaling technique A*, bidirectional/

all the vertices of the graph. Has no loops. The weight of a Spanning Tree is the sum of weights of its **edges**. A Minimum Spanning Tree (MST) of G is a spanning tree with minimum weight (when all w e ’s are / remain unaltered. Remarks: The parameters ε and q influence significantly the performance of DBSCAN. These should selected such that the **algorithm** is able to **detect** the least “dense” cluster (experimentation with several values for ε and q should be carried out). Implementation of DBSCAN using R/

**edge**? operator Where is the **edge**? Zero-crossings of bottom graph 2D **edge** **detection** filters Laplacian of Gaussian Gaussian derivative of Gaussian is the Laplacian operator: Optimal **Edge** **Detection**: Canny Assume: Linear filtering Additive iid Gaussian noise **Edge** detector should have: Good **Detection**. Filter responds to **edge**, not noise. Good Localization: **detected** **edge** near true **edge**. Single Response: one per **edge**. Optimal **Edge** **Detection**/H.T. table Generalized H.T. **Algorithm**: Finds a rotated, scaled, and /

path l Path tracking l Reference point calculation does not have obstacle vicinity knowledge. l Computationally and Memory intensive **algorithm**. HPF with Motion controller l Region to point Reference array for the whole workspace. l Goal seeking l/network based integrated navigation system. NC STATE UNIVERSITY ADAC, NC State University32 Future Research l Improvement on **edge** **detection** as reliable **edge** **detection** is the backbone of the new structure of iSpace. l Considering the dimensions of the robot before /

STANDARD PETRI NET Regular Place Place Delay Place Trigger Link Place Directed Arc Trigger Token Directed Arc Not **Edge** Primary **Edge** Token [Jackman88] © IEEE 1988 Copyright 1995-1999 SCRA6 Methodology Reinventing Electronic Design Architecture Infrastructure DARPA/RASSP ETC **Algorithm** Description l Back-end Processing (**detection** and classification) m Single Ping Cluster Filtering (SPF)- weed out some of the echo returns from clutter m Automatic **Detection** and Tracking (ADT)- automates the **detection** of /

on graph partitioning Heuristics for load balancing and termination **detection** K. Madduri, D.A. Bader, J.W. Berry, and J.R. Crobak, “An Experimental Study of A Parallel Shortest Path **Algorithm** for Solving Large-Scale Graph Instances,” Workshop on **Algorithm** Engineering and Experiments (ALENEX), New Orleans, LA, January 6, 2007. ∆ - stepping **algorithm** Label-correcting **algorithm**: Can relax **edges** from unsettled vertices also “approximate bucket implementation of/

around each keypoint 3. Compare regions Different region appearance for matching keypoints Tutorial 9: Descriptors **Detection**:: General Approach Problem Applications and **Algorithms** in CV Visual Descriptors What to look at? (Keypoints) Introduction Tutorial 9: Descriptors / descriptors **Edge** points are poorly located **Edge** points have a much larger principal curvature across the **edge** than along the **edge** Finding Principal curvatures amounts to finding the eigenvalues of the Hessien Applications and **Algorithms** in /

extent 1-D Gaussian kernel written as: 2-D Gaussian kernel: Separable Gaussian Smoothing (example) **Algorithm** 2: Canny **Edge** **Detection** **Edge** **detection** a commonly operation in image processing **Edges** are discontinuities in image gray levels, have strong intensity contrast. Canny **Edge** **Detection** is an optimal **edge**-detector **algorithm**. Illustrated ahead with an example. Canny **Edge** **Detection** (example) **Algorithm** 3: KLT Tracking First proposed by Lucas and Kanade. Extended by Tomasi and Kanade and/

{ e = ExtractCheapestEdge( q ); } while ( !Cycle( e, T ) ); AddEdge( T, e ); } return T; } Add to a heap here Extract from a heap here Kruskal’s **Algorithm** Cycle **detection** Forest MinimumSpanningTree( Graph g, int n, double **costs ) { Forest T; Queue q; **Edge** e; T = ConsForest( g ); q = ConsEdgeQueue( g, costs ); for(i=0;i<(n-1);i++) { do { e = ExtractCheapestEdge( q ); } while ( !Cycle( e, T/

or gradient direction n 3D model feature space (2D location + orientation) n Extract 3D (**edge**) features from image as well. n Requires 3D distance transform of image features weight orientation versus location fast forward-backward pass **algorithm** applies n Increases **detection** robustness and speeds up matching better able to discriminate object from clutter better able to eliminate cells in branch and bound search/

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