1 1 EE 6882 Statistical Methods for Video Indexing and Analysis Fall 2004 Prof. Shih-Fu Chang http://www.ee.columbia.edu/~sfchang Lecture 2 Part A (9/15/04) 2 EE6882-Chang EE E6882 SVIA Lecture 2 Review: Image features, color feature, similarity metrics Additional distance metrics Texture feature Performance evaluation metrics Review of statistic techniques Probability, Distribution Functions and Matlab demos Entropy and mutual information Discriminant Classifiers Bayesian Classifiers, GMM estimation by Expectation Maximization Readings Readings on the class web site about content based image search Vittorio Castteli, Probability Refresher, notes for EE E6880, Statistical Pattern Recognition, Spring 2002. A. Jain et al, "Statistical Pattern Recognition: A Review," IEEE Tran. on Pattern Analysis and Machine Intelligence, vol 22, No 1, Jan. 2000. Digital Image Processing Textbooks: Image classification Gonzalez and Woods Chap 12, Anil Jain Chap 9.14
12
Embed
EE 6882 Statistical Methods for Video Indexing and Analysissfchang/course/svia-F04/slides/lecture2-A.pdf · EE E6882 SVIA Lecture 2 Review: Image features, color feature, ... Content-based
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
1
1
EE 6882 Statistical Methods for Video Indexing and Analysis
Fall 2004Prof. Shih-Fu Chang
http://www.ee.columbia.edu/~sfchang
Lecture 2 Part A (9/15/04)
2EE6882-Chang
EE E6882 SVIA Lecture 2Review: Image features, color feature, similarity metricsAdditional distance metricsTexture featurePerformance evaluation metricsReview of statistic techniques
Probability, Distribution Functions and Matlab demos Entropy and mutual informationDiscriminant ClassifiersBayesian Classifiers, GMM estimation by Expectation Maximization
ReadingsReadings on the class web site about content based image searchVittorio Castteli, Probability Refresher, notes for EE E6880, Statistical PatternRecognition, Spring 2002.A. Jain et al, "Statistical Pattern Recognition: A Review," IEEE Tran. on Pattern Analysis and Machine Intelligence, vol 22, No 1, Jan. 2000.Digital Image Processing Textbooks: Image classification
I: set of suppliersJ: set of consumerscij : cost of shipping a unit of supply from i to j
Problem: find the optimal set of flows fij to
0, ,
,
,
i j iji I i I
ij
ij ji I
ij ij J
j ij J
minimize c f s.t.
f i I j J (No reverse shipping)
f y j J (satisfy each consumer need /cacacity)
f x i I (bounded by each supplier's limit)
y x (
∈ ∈
∈
∈
∈
≥ ∈ ∈
= ∈
≤ ∈
≤
∑∑
∑∑
∑i I
feasibility)∈∑
4
7EE6882-Chang
Advantage of EMDEfficient implementations exist (Simplex Method)Also support partial matching (||I|| >< ||J||, e.g., histogram defined in different color spaces, or scales)If the mass of two distributions equal, then EMD is a true metricAllow flexible structures, e.g., matching multiple regions in each image
Multiple region in one image, each region represented by individual feature vector
Region set: {R1, R2, R3} Region set: {R1’, R2’, R3’, R4’}
Cij = dist(Ri, Rj’), which can be based on EMD also
8EE6882-Chang
EMD of Color Histogram( ) ( ) ( ) ( ) ( ) ( )
( ) 1 1
1 1
, ,..., , , ,..., , ( ) ( )
,
j i
M N
ij iji j
M N
iji j
h h 1 h 2 h M g= g 1 g 2 h N assume g j h i
C f
EMD h gf
= =
= =
= ≤
=
∑ ∑
∑∑
∑∑ Earth Hole
1 1 1
/M N N
ij ij ji j j
ij
ij ij
= C f g Fill up each hole
C : distance between color i in color space h and color j in color space g
f : move f units of mass from color i in h to color j in g
= = =∑∑ ∑
Normalization by the denominator termAvoid bias toward low mass distributions (i.e., small images)what’s the difference if both h and g are normalized first?
exact matching of sub-parts is changed.
5
9EE6882-Chang
TextureWhat is texture?
Has structure or repetitious pattern, i.e., checkeredHas statistical pattern, i.e., grass, sand, rocks
Why texture?Application to satellite images, medical images Describes contents of real world images, i.e., clouds, fabrics, surfaces, wood, stone
Challenging issuesRotation and scale invariance (3D)Segmentation/extraction of texture regions from imagesTexture in noise
10EE6882-Chang
6
11EE6882-Chang
Some approaches for texture featuresFourier Domain Energy Distribution