Download presentation
Presentation is loading. Please wait.
Published byAudrey Hodges Modified over 9 years ago
1
Image Segmentation Rob Atlas Nick Bridle Evan Radkoff
2
Image Segmentation Separate an image into sets of pixels which represent some structure in the image Main application is object and boundary detection
3
High Level Overview of Papers
Image Segmentation Local approaches Graph cuts Mean Shift Normalized Cuts Comaniciu et al., 1999 Shi and Malik, 2000 Interactive Cuts Rother et al., 2004 Li et al., 2004
4
Mean Shift Analysis Rutgers University, ICCV 1999
Dorin Comaniciu, Peter Meer Rutgers University, ICCV 1999
5
{ x / ∂s , y / ∂s , R / ∂r , G / ∂r , B / ∂r }
Spatial-Range Domain Spatial domain: pixel locations Range domain: intensity values Spatial-Range domain: concatenation of the two { x, y, R, G, B } Parameters: ∂s: Spatial domain normalization ∂r: Range domain normalization { x / ∂s , y / ∂s , R / ∂r , G / ∂r , B / ∂r } 5 dimensions for RGB, 3 for grayscale
6
Kernel Density Estimate
For n points {xi}i=1..n in a d-dimensional Euclidean space with kernel function K(x) and window radius h:
7
Epanechnikov Kernel cd : volume of the unit d-dimensional sphere
8
Estimating the Density Gradient
Goal: where Sh is a hypersphere containing nx data points
9
Mean Shift Vector Vector with a direction towards the largest increase in density, thus leading to a local density maximum.
10
Mean Shift Procedure 1) Compute the mean shift vector Mh(x)
2) Translate the window Sh(x) by Mh(x) 3) If not converged, go to step 1. Mathematically guaranteed to converge
11
Applying Mean Shift to Images
Spatial-Range Domain: { x / ∂s , y / ∂s , R / ∂r , G / ∂r , B / ∂r } The authors apply the mean shift procedure to all points in the spatial-range domain. Two applications: Filtering, Segmentation Two parameters: spatial resolution and range resolution
12
Mean Shift Filtering xi: source pixel zi: filtered pixel for each xi
apply the mean shift procedure on xi to find the convergence point yi spacial domain of zi = spacial domain of xi range domain of zi = range domain of yi
13
Results
14
Results
15
Results
16
Segmentation Instead of changing pixels ranges (colors), group them by which point their mean shift procedure converges to.
17
Advantages: Disadvantages: No oversight required
Preserves detail when appropriate Disadvantages: Cannot choose how many segments are made
18
Normalized Cuts and Image Segmentation
Shi and Malik, 2000 ...
19
Basic Idea Big Questions:
Treat image segmentation as a graph-partitioning problem Big Questions: Advantage over older methods: fast and global 1. How do we define a good partitioning? 2. How do we do partition efficiently?
20
Images as a graph G=(V,E) Vertices: pixels Edges: similarity
21
Graph cuts Assumes: Graph is fully connected Given: G=(V,E) Do:
Create disjoint vertex sets A, B s.t. and
22
Similarity metric Weight between edges in graph: X(i): Location of pixel i F(i): Feature vector describing pixel i Simple case - F(i)=1 for segmenting points Intensity, color, texture Like mean shift, we take into account distance in space and intensity difference , : Parameters
23
2-way graph cut Minimize:
Existing efficient methods for optimal 2-way cut
24
Recursive minimum cuts
Iteratively bipartition graph according to minimum cut (Wu and Leahy, 1993) The problem: favors small clusters
25
Intuition for normalized cuts
Want to minimize cut score But, we also want to partition out larger areas with more connections So, what we're really interested in is the proportion of total weights that we are cutting for each segment
26
Normalized cuts Goal: partition into disassociated groups
27
Minimizing association between groups ~ maximizing association within groups
28
Computational complexity
Minimizing normalized cut: NP-complete Can compute approximate solution by solving a generalized eigenvalue problem Proof - see paper
29
Eigenvalue system D - diagonal matrix of the total weight from each node to every other W - matrix of weights between nodes y - eigenvectors lambda - eigenvalues However, this is not in standard form for solving
30
A solvable representation
First eigenvector (eigenvalue=0):
31
Second smallest eigenvalue describes solution
Remember, the smallest eigenvalue is 0
32
Recursive two-way Ncut
Third, fourth, etc eigenvalues correspond to eigenvectors that subdivide the existing graphs However, error accumulates with each Better to recompute partitioning on each subgraph iteratively
33
Segmentation Algorithm
1. Create weighted graph G=(V,E) 2. Solve and take the eigenvector with the second smallest eigenvalue 3. Bipartition the graph with this eigenvector 4. If Ncut is below threshold value, recursively partition each segment
34
Partitioning by an eigenvector
The partitioning eigenvector contains one continuous value per pixel Since these are continuous, not discrete, they don't directly tell us which points are in which segment Instead, we try different cutoffs, and select the one that produces the minimal NCut value
35
Partitioning by an eigenvector
36
Examples - segmenting point sets
37
Examples - segmenting noisy data
38
Examples - images
39
Example - image with texture metric
40
Interactive Graph Cuts
User can provide hints about where the objects are in the scene Ideally, the less work the user has to do, the better
41
Foreground Extraction
Goal is to partition the pixels into two sets: foreground and background
42
Foreground Extraction
Given pixel intensity values Output set of alphas which determine how much each pixel belongs to the foreground "Hard segmentation": "Soft segmentation":
43
GrabCut Rother et al., SIGGRAPH 2004
44
GrabCut: Handling Color Images
Previous work: histogram of gray values for foreground and background GrabCut: - histograms are intractable for color - instead use Gaussian Mixture Model (GMM) to represent the distribution of color
45
GrabCut: Algorithm
46
GrabCut: Border Matting
Perform hard segmentation on image, and then relax alpha values on the border of the object
48
Lazy Snapping Li et al., SIGGRAPH 2004
49
Lazy Snapping: Energy Function
Minimize the Gibbs energy function Run k-means clustering on foreground and background points E1 defined in terms of these mean colors:
50
Lazy Snapping: Speeding it up
Speed is crucial for a responsive user experience Use the watershed algorithm to divide the image into small approximately constant patches, then do graph cut using these as the nodes
51
Lazy Snapping: Boundary Editing
Want boundary to "snap" to the user-defined polygon Energy term E2 becomes
52
Lazy Snapping: Results
53
Thanks for listening. Questions?
Similar presentations
© 2024 SlidePlayer.com. Inc.
All rights reserved.