Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Visual Hacks Henrik I. Christensen Robotics and Intelligent Machines @ GT College of Computing Georgia Institute of Technology Atlanta, GA hic@cc.gatech.edu February 12, 2008 H. I. Christensen (RIM@GT) Vision February 12, 2008 1 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Outline Introduction 1 Imaging Geometry 2 Features 3 Feature Description 4 Recognition 5 6 Wrap-up H. I. Christensen (RIM@GT) Vision February 12, 2008 2 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Camera Most flexible sensory modality Complex sensory processing Not discussed in any detail Offers wide range Diverse tasking of sensor Relatively inexpensive Computationally demanding H. I. Christensen (RIM@GT) Vision February 12, 2008 3 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Image processing chain image Image image Image Recognition/ optics enhancement/ Description acquisition segmentation Estimation processing (features) H. I. Christensen (RIM@GT) Vision February 12, 2008 4 / 37
Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Color Models There are quite a few image color models RGB Red, Green, Blue HSI Hue, Saturation, Intensity CMY Cyan, Magenta, Yellow For this course RGB is adequate Check carefully on the selected / available color models H. I. Christensen (RIM@GT) Vision February 12, 2008 5 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Color combinations B Cyan Magenta Black G Yellow R H. I. Christensen (RIM@GT) Vision February 12, 2008 6 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Outline Introduction 1 Imaging Geometry 2 Features 3 Feature Description 4 Recognition 5 Wrap-up 6 H. I. Christensen (RIM@GT) Vision February 12, 2008 7 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Pin-Hole Model H. I. Christensen (RIM@GT) Vision February 12, 2008 8 / 37
Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Pin-Hole Model The relations are then: x X = λ Z y Y = λ Z ⇒ λ X x = Z λ Y = y Z H. I. Christensen (RIM@GT) Vision February 12, 2008 9 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Pin-Hole Model Remember Homogeneous Coordinates? X Y � P = Z 1 Define the Perspective transform as 1 0 0 0 0 1 0 0 T = 0 0 1 0 1 0 0 0 λ H. I. Christensen (RIM@GT) Vision February 12, 2008 10 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Camera models The pin-hole model is a fair approximation for medium focal lengths For extreme values of the focal length various kinds of distortion should be taken into account Calibration is usually required to ensure use of the camera for real-world tasks MATLAB has a great toolbox for image calibration http://www.vision.caltech.edu/bouguetj/calib_doc/ H. I. Christensen (RIM@GT) Vision February 12, 2008 11 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Outline Introduction 1 Imaging Geometry 2 Features 3 Feature Description 4 Recognition 5 6 Wrap-up H. I. Christensen (RIM@GT) Vision February 12, 2008 12 / 37
Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Image Features Computer Vision has been studied for 4 decades. It might offer the biggest potential. Robustness is the major challenge SLAM is termed “Structure from motion” (SFM) in the vision literature. H. I. Christensen (RIM@GT) Vision February 12, 2008 13 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Harris Features Detection of high curvature corner/edge points Standard in several image processing packages. Noise sensitive � I 2 � I x I y x M = I 2 I x I y y R = det M − k ( trace M ) 2 Lukas-Tomasi-Kanade (condition number of M) H. I. Christensen (RIM@GT) Vision February 12, 2008 14 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Harris H. I. Christensen (RIM@GT) Vision February 12, 2008 15 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Harris example H. I. Christensen (RIM@GT) Vision February 12, 2008 16 / 37
Introduction Imaging Geometry Features Feature Description Recognition Wrap-up SIFT features (Lowe, 2004) Scale-space top-points Coding of local orientation at top-points Example code is available (linux) and several Matlab versions. H. I. Christensen (RIM@GT) Vision February 12, 2008 17 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up SIFT Example H. I. Christensen (RIM@GT) Vision February 12, 2008 18 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Harris Example H. I. Christensen (RIM@GT) Vision February 12, 2008 19 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Outline Introduction 1 Imaging Geometry 2 Features 3 Feature Description 4 Recognition 5 6 Wrap-up H. I. Christensen (RIM@GT) Vision February 12, 2008 20 / 37
Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Feature Detection Covered in more detail in future lectures Basics of feature detection to get started The idea is to condense regions into a compact representation. H. I. Christensen (RIM@GT) Vision February 12, 2008 21 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Example features Euler Number / #holes in a region Ellipse approximation (major/minor axes) Line parameters Compactness Perimeter length H. I. Christensen (RIM@GT) Vision February 12, 2008 22 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Feature / Region Description Description of two different types of regions Contour based 1 Region based 2 Advantages / Disadvantages? H. I. Christensen (RIM@GT) Vision February 12, 2008 23 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Contour descriptors Chain codes Signatures (polar) Polygonal approximation H. I. Christensen (RIM@GT) Vision February 12, 2008 24 / 37
Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Moments Statistical moments are in general defined as: L − 1 � x n m n = i g ( x i ) i =0 The mean is then L − 1 � m 1 = x i g ( x i ) i =0 Central moments are defined as L − 1 � ( x i − m 1 ) n g ( x i ) µ n = i =0 In two dimensions L − 1 K − 1 � � ( x i − m 10 ) m ( y j − m 01 ) n g ( x i , y j ) µ mn i =0 j =0 H. I. Christensen (RIM@GT) Vision February 12, 2008 25 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Well-known moments Standard deviation � L − 1 � σ = √ µ 2 = � � ( x i − m 1 ) 2 g ( x i ) � i =0 Skewness - µ 3 - indicates the symmetry of the distribution, value 0 = perfect symmetry Normalized central moments of order (p+q) ν pq = µ pq m γ pq where γ = p + q + 1 2 Moments are widely used for characterization of regions and for standard tasks H. I. Christensen (RIM@GT) Vision February 12, 2008 26 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Least Square Line Fitting Assume g(x,y) = 1 where we have the line elements If we have computed µ 20 , µ 11 , µ 02 , µ 10 , µ 01 , µ 00 We want to estimate a line of the form y = a + bx The regressions can be computed as b = µ 11 µ 20 a = µ 01 − b µ 10 Quality of fit defined as r 2 µ 2 r 2 = 11 µ 02 µ 20 H. I. Christensen (RIM@GT) Vision February 12, 2008 27 / 37 Introduction Imaging Geometry Features Feature Description Recognition Wrap-up Other use of moments Characterization of image texture Variance, Cross correlation, ... allow pattern matching Ellipse matching - major / minor axes of a region A rich and easy to use descriptor H. I. Christensen (RIM@GT) Vision February 12, 2008 28 / 37
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