Cutting complete weighted graphs Jameson Cahill Ido Heskia Math/CSC 870 Spring 2007.

Slides:



Advertisements
Similar presentations
Liang Shan Clustering Techniques and Applications to Image Segmentation.
Advertisements

Top-Down & Bottom-Up Segmentation
Normalized Cuts and Image Segmentation
Lecture 07 Segmentation Lecture 07 Segmentation Mata kuliah: T Computer Vision Tahun: 2010.
Graph-Based Image Segmentation
10/11/2001Random walks and spectral segmentation1 CSE 291 Fall 2001 Marina Meila and Jianbo Shi: Learning Segmentation by Random Walks/A Random Walks View.
The Visual Recognition Machine Jitendra Malik University of California at Berkeley Jitendra Malik University of California at Berkeley.
Lecture 6 Image Segmentation
CS 376b Introduction to Computer Vision 04 / 08 / 2008 Instructor: Michael Eckmann.
Normalized Cuts and Image Segmentation Jianbo Shi and Jitendra Malik, Presented by: Alireza Tavakkoli.
© 2003 by Davi GeigerComputer Vision October 2003 L1.1 Image Segmentation Based on the work of Shi and Malik, Carnegie Mellon and Berkley and based on.
Fast, Multiscale Image Segmentation: From Pixels to Semantics Ronen Basri The Weizmann Institute of Science Joint work with Achi Brandt, Meirav Galun,
Region Segmentation. Find sets of pixels, such that All pixels in region i satisfy some constraint of similarity.
Image Segmentation Chapter 14, David A. Forsyth and Jean Ponce, “Computer Vision: A Modern Approach”.
Announcements Project 2 more signup slots questions Picture taking at end of class.
CS 376b Introduction to Computer Vision 04 / 04 / 2008 Instructor: Michael Eckmann.
1 Cutting complete weighted graphs Jameson Cahill Ido Heskia Math/CSC 870 Spring 2007.
Segmentation and Perceptual Grouping. The image of this cube contradicts the optical image.
Image Segmentation A Graph Theoretic Approach. Factors for Visual Grouping Similarity (gray level difference) Similarity (gray level difference) Proximity.
Announcements Project 3 questions Photos after class.
Thresholding Thresholding is usually the first step in any segmentation approach We have talked about simple single value thresholding already Single value.
Segmentation and Boundary Detection Using Multiscale Measurements Ronen Basri Achi Brandt Meirav Galun Eitan Sharon.
Computer Vision - A Modern Approach Set: Segmentation Slides by D.A. Forsyth Segmentation and Grouping Motivation: not information is evidence Obtain a.
Segmentation via Graph Cuts
Clustering Unsupervised learning Generating “classes”
Image Segmentation Image segmentation is the operation of partitioning an image into a collection of connected sets of pixels. 1. into regions, which usually.
Domain decomposition in parallel computing Ashok Srinivasan Florida State University COT 5410 – Spring 2004.
Image Segmentation Rob Atlas Nick Bridle Evan Radkoff.
CS 376b Introduction to Computer Vision 04 / 02 / 2008 Instructor: Michael Eckmann.
Linked Edges as Stable Region Boundaries* Michael Donoser, Hayko Riemenschneider and Horst Bischof This work introduces an unsupervised method to detect.
Presenter : Kuang-Jui Hsu Date : 2011/5/3(Tues.).
Segmentation using eigenvectors
CSSE463: Image Recognition Day 34 This week This week Today: Today: Graph-theoretic approach to segmentation Graph-theoretic approach to segmentation Tuesday:
Segmentation using eigenvectors Papers: “Normalized Cuts and Image Segmentation”. Jianbo Shi and Jitendra Malik, IEEE, 2000 “Segmentation using eigenvectors:
Region Segmentation Readings: Chapter 10: 10.1 Additional Materials Provided K-means Clustering (text) EM Clustering (paper) Graph Partitioning (text)
Image Segmentation February 27, Implicit Scheme is considerably better with topological change. Transition from Active Contours: –contour v(t) 
Chapter 14: SEGMENTATION BY CLUSTERING 1. 2 Outline Introduction Human Vision & Gestalt Properties Applications – Background Subtraction – Shot Boundary.
Random Walk with Restart (RWR) for Image Segmentation
A Clustering Algorithm based on Graph Connectivity Balakrishna Thiagarajan Computer Science and Engineering State University of New York at Buffalo.
G52IVG, School of Computer Science, University of Nottingham 1 Edge Detection and Image Segmentation.
Segmentation and Boundary Detection Using Multiscale Intensity Measurements Eitan Sharon, Meirav Galun, Ronen Basri, Achi Brandt Dept. of Computer Science.
Jad silbak -University of Haifa. What we have, and what we want: Most segmentations until now focusing on local features (K-Means). We would like to extract.
The Implementation of Markerless Image-based 3D Features Tracking System Lu Zhang Feb. 15, 2005.
Presenter : Kuang-Jui Hsu Date : 2011/3/24(Thur.).
Image Segmentation Dr. Abdul Basit Siddiqui. Contents Today we will continue to look at the problem of segmentation, this time though in terms of thresholding.
Image Segmentation Superpixel methods Speaker: Hsuan-Yi Ko.
Domain decomposition in parallel computing Ashok Srinivasan Florida State University.
CS654: Digital Image Analysis Lecture 28: Advanced topics in Image Segmentation Image courtesy: IEEE, IJCV.
 In the previews parts we have seen some kind of segmentation method.  In this lecture we will see graph cut, which is a another segmentation method.
Mestrado em Ciência de Computadores Mestrado Integrado em Engenharia de Redes e Sistemas Informáticos VC 15/16 – TP10 Advanced Segmentation Miguel Tavares.
Example Apply hierarchical clustering with d min to below data where c=3. Nearest neighbor clustering d min d max will form elongated clusters!
Network Partition –Finding modules of the network. Graph Clustering –Partition graphs according to the connectivity. –Nodes within a cluster is highly.
Color Image Segmentation Mentor : Dr. Rajeev Srivastava Students: Achit Kumar Ojha Aseem Kumar Akshay Tyagi.
Normalized Cuts and Image Segmentation Patrick Denis COSC 6121 York University Jianbo Shi and Jitendra Malik.
Document Clustering with Prior Knowledge Xiang Ji et al. Document Clustering with Prior Knowledge. SIGIR 2006 Presenter: Suhan Yu.
Machine Vision ENT 273 Lecture 4 Hema C.R.
Miguel Tavares Coimbra
Image Segmentation Today’s Readings Szesliski Chapter 5
Region Segmentation Readings: Chapter 10: 10
CSSE463: Image Recognition Day 34
CSSE463: Image Recognition Day 23
Lecture 31: Graph-Based Image Segmentation
Announcements Photos right now Project 3 questions
Seam Carving Project 1a due at midnight tonight.
Segmentation (continued)
Announcements Project 4 out today (due Wed March 10)
Announcements Project 1 is out today help session at the end of class.
Region-Based Segmentation
CSSE463: Image Recognition Day 34
Presentation transcript:

Cutting complete weighted graphs Jameson Cahill Ido Heskia Math/CSC 870 Spring 2007

Cutting Complete Weighted Graphs In image segmentation in computer vision the goal is to divide the image into regions which are similar in the properties of the pixels. Image is a weighted graph Nodes are the pixels. Each pixel has a vector associated to it Containing the data about the properties of the pixel (texture, color, intensity, etc).

Image segmentation: basic model We start with a complete graph (an edge between every 2 nodes) The weight of the edge w(i,j) corresponds to the similarity between nodes i,j. The more the nodes are “similar” the higher the weight that is associated to the edge joining them.

Goal: Partition V into disjoint sets of nodes V 1,…, V m In such a way that the similarity between the nodes in each set V i is high and across different sets Vi,Vj is low. We partition the nodes, so that However, we are about to lose edges, since we are cutting our graph.

Cutting graphs A B C3 51 X Y Z We could cut this graph by removing the edges (A,X) and (C,Y) whose weights are 7 and 4 respectively. The In this case it is T1T1 T2T2 + =11

So we can partition by removing edges that connect 2 components. To make sure the regions are indeed different we’re looking for edges whose weight is low, so we wish to minimize the total weight of the edges that have been removed. Minimize the cut Unfortunately, it is not that simple. Example:

Imagine that there are weighted edges between each pair of nodes. Assume that the similarity between nodes in this case is simply their Euclidean distance from each other so the weights of the edges between close nodes is high. We want to bipartition this graph. Best cut Bad cut Since we are simply minimizing the cut, we will actually pick the bad cut in this case since any edge we add on to the cut increases it. We must Normalize this cut!

Normalized cuts Calculate the cut as a fraction of the total edge connections from the set to the rest of the graph to exclude cuts of small isolated Components, called the Ncut.  disassociation measure. Now the previous cut which favors small isolated sets won’t have low Ncut value since it will be a large percentage of the total connections From that set to all other nodes (in the previous example it will be 100%).

Normalized association The measure for similarity between sets of nodes (Nassoc): Where This gives us the measure of how closely related (on average) nodes within the set A are, relatively to their similarity to the rest of the nodes in the graph.

We have this relationship between these measures: Thus, when we try to minimize the Ncut we also maximize the Nassoc and we indeed make sure that the two requirements we imposed on our partition of the nodes will be satisfied. Now we could apply this to our complete graph, and continue recursively on each component until we get Our desired m components.

What’s the plan We plan to study an algorithm inspired by algabraic multi-grid which involves the normalized cuts. Basics of the segmentation by weighted aggregation (SWA) algorithm: We are treating our graph as a grid graph, starting from the most Refined grid, and we coarsen it at each step. First choose ½ your nodes as representatives (called seeds). Choose those so that each node in your graph is “strongly” connected to at-least one seed adjacent to it.

Aggregation Now we will aggregate all the nodes which are strongly coupled to a seed, to that respective seed, so that we eliminate a big amount of the nodes. Now each node Corresponds to an aggregate of pixels, not just a single one. Recalculate the aggregate properties. Recalculate the edges weight accordingly. Now apply the same to the seeds.

This process only keeps tracks of what are the different regions. In order to find the actual boundaries, we will have to retrace our steps. So what do we want to do?

Similarly to image segmentation, we want to partition the forest into regions which our similar in the species of plants which they consist of. Segment a Forest First we want to understand the SWA algorithm and write a Matlab Code which performs it. We will test our code trying to segment images. If we can make that happen then we would really like to Each node corresponds to a square of land, and the vector Associated with it records which species of plants are in this square.

Refrences: IEEE Transactions on patterns analysis and machine intelligence vol. 22 no. 8 Normalized cuts and Image Segmentation. By Jianbo Shi and Jitendra Malik Fast Multiscale Image Segmentation. By Eitan Sharon, Achi Brandt and Ronen Basri. Nature Hierarchy and adaptivity in segmenting visual scenes. By Eitan Sharon, Meirav Galun, Dahlia Sharon, Ronen Basri and Achi Brandt