Computer Vision Lecture 1: Course Overview and Convolution - Prof. Marshall Tappen, Study Guides, Projects, Research of Computer Science

Download Computer Vision Lecture 1: Course Overview and Convolution - Prof. Marshall Tappen and more Study Guides, Projects, Research Computer Science in PDF only on Docsity! CAP 5415 – Computer Vision Marshall Tappen Fall 2009 Lecture 1 Welcome!  About Me − (Relatively) New Faculty Member (Three Years) − Interested in Machine Vision and Machine Learning − Happy to chat with you at almost any time  May want to e-mail me first − Office Hours:  Tuesday-Thursday after class Environments  MATLAB − Pro:Well-established package. You can find many tutorials on the net. − Con: Not free. If your lab does not already have it, talk to me about getting access.  Octave − Free MATLAB look-alike − Pro: Should be able to handle anything you will do in this class − Con: “Should be”. I'm not sure about support in Windows Environments  Numerical Python − All the capabilities of MATLAB − Free! − Real programming language − Used for lots of stuff besides numerical computing − Cons: Documentation is a bit sparse and can be outdated  I can get you started – I am working on a tutorial Math  We will use it  We will be talking about mathematical models of images and image formation  This class is not about proving theorems  My goal is to have you build intuitions about the models  Try and visualize the computation that each equation is expressing  Basic Calculus and Basic Linear Algebra should be sufficient Image Processing  For now, we won't worry about the physical aspects of getting images  View image as an array of continuous values Simple Modification  What if we wanted to blur this image?  We could take a local average − Replace each pixel with the mean of an NxN pixel neighborhood surrounding that pixel. 3x3 Neighborhood Original Averaged Let's represent this more generally 16 46 oO} Oo}; ol1}o Oo] Oo] DAI Ww NO) NI] —|}o 43  Let's represent this more generally 43200 46200 16160 0030 1/91/91/9 1/91/91/9 1/91/91/9 Input Image Kernel Let's represent this more generally  Multiply corresponding numbers and add 43200 46200 16160 0030 1/91/91/9 1/91/91/9 1/91/91/9 Input Image ???? ???? ??1.33? ???? Take out a piece of paper  Let’s say i= 10 and j=10  Which location in K is multiplied by I(5,5)?  I(5,4) Resulting Image Input Image Convolution Kernel Resulting Image Input Image Convolution Kernel Notation  Also denoted as  R = I * K  We “convolve” I with K − Not convolute! Sliding Template View  Take the template K  Flip it  Slide across image 987 654 321 123 456 789 Predict the Image Input 000 100 000 Kernel Output ? Predict the Image 000 100 000 Input Kernel Output Predict the Image Predict the Image 000 000 001 Input Kernel Output Predict the Image Predict the Image Predict the kernel  What if I wanted to compute R(i,j) = I(i+1,j) – I(i,j) at every pixel?  What would the kernel be?  This is one discrete approximation to the derivative What’s the problem with this derivative? [1 -1 0] − Where’s the center of the derivative?  An alternative − [-1 0 1] Your Convolution filter toolbox  In my experience, 90% of the filtering that you will do will be either − Smoothing (or Blurring) − High-Pass Filtering (I’ll explain this later)  Most common filters: − Smoothing: Gaussian − High Pass Filtering: Derivative of Gaussian Effect of Changing σ  With σ set to 1  With σ set to 3 Input Practical Aspects of Computing Convolutions  Let's blur this flat, gray image:  What should it look like? Practical Aspects of Computing Convolutions  Depending on how you do the convolution in MATLAB, you could end up with 3 different images 266x266 Image 256x256 Image 246x246 Image Practical Aspects of Computing Convolutions Filled in borders with zeros, computed everywhere the kernel touches Called “full” in MATLAB 266x266 Image Border Handling 1/9 |1/9 |1/9 1/9 |1/9 |1/9 119 |1/9 |1 }/3 0 0 (6 16 0 {0 46 0 |0 43  Practical Aspects of Computing Convolutions  Fill in border with zeros, only compute at “original pixels”  Called “same” in MATLAB 256x256 Image There are other options  The first two methods that I described fill missing values in by substituting zero  Can fill in values with different methods − Reflect image along border − Pull values from other side  Not supported in MATLAB's convolution − Eero Simoncelli has a package that supports that kind of convolution Going Non-Linear  Convolution is a linear operation − What does that mean?  A simple non-linear operation is the median filter − Will explore that filter in the first problem set. Practical Use of These Properties – Image Sharpening  Take this image and blur it Let's make the image sharper  We know + = Let's boost the sharp stuff a little +2× Let's boost the sharp stuff a little +2× = Rewrite this This is an identity filter or unit impulse Basic Convolution Properties  Can derive all of these with the definition of convolution  Comes from linearity of convolution Rewrite this Tx f+2(2—-Txf) Tx f+2(Z*xd—-—TZx f) T x (f +206 —2f)