COMP 558 lecture 16
Oct. 27, 2009
Linear shape from shading (continued)
Recall the linear shading model from last class, where the lZ component of the light source was
small in comparison to |(lX , lY )|. In order to estimate shape from shading using this
COMP 558 lecture 17
Oct. 29, 2009
Slant and tilt
One familiar perceptual property of an overall surface shape is its depth gradient, or more intuitively,
how it slopes away from you. Does it slope to the right, or to the left, or downward (a ceiling) or
u
COMP 558 lecture 18
Nov. 3, 2009
The last several lectures we have looked at image properties such as local intensity gradients
and how these are can be directly tied to scene structure. The remaining lectures will be concerned
mostly with geometry (as op
COMP 558 lecture 13
Oct. 15, 2009
We have spent several lectures on how to process images and detect features such as edges and
blobs, and estimate image transformations such as translations. Throughout the rest of this course,
we will use these image mea
COMP 558 lecture 9
Sept. 29, 2009
2D Edge Detection
Last lecture I introduced the Cannys basic criteria for edge detection. Lets now look at the 2D
case, and the particular lter that he uses.
Recall from your probability background the denition of a Gauss
COMP 558 lecture 15
Oct. 22, 2009
We are gradually moving into the third part of the course, which deals with estimation of 3D
properties of scenes. Last lecture we discussed how to estimate vanishing points, which directly
relate 2D image properties to a
COMP 558 lecture 14
Oct. 20, 2009
Vanishing points
One of the more interesting and familiar phenomena in perspective geometry is that parallel lines
in the 3D world typically project to non-parallel lines in the image and in particular these projected
lin
COMP 558 lecture 12
Oct. 13, 2009
Today we will look at a few important topics in scale space in computer vision, in particular, coarseto-ne approaches, and the SIFT feature descriptor. I will present only the main ideas here to give
you a sense of the pr
COMP 558 lecture 11
Oct. 8, 2009 (modied Oct. 10)
Today we will look more closely at an important issue scale. Scale has come up indirectly in our
discussions. For example, in the Canny edge analysis, we considered what happens when we stretch
the size of
COMP 558 lecture 10
Sept. 29, 2009
Image registration
Suppose we have two images I (x, y ) and J (x, y ) that are almost the same. We may have two
neighboring image frames in a video, or we may have two images taken by two cameras (stereo)
that have the s
COMP 558 lecture 8
Sept. 24, 2009
Edge detection
Today we will see key ideas about edge detection which were introduced in a very well known article
1
by John Canny. The edge detection method he proposed is now called the Canny edge detector.
We begin wit
COMP 558 lecture 4
Sept. 10, 2009
Up to now, we have taken the projection plane to be in front of the center of projection. Of
course, the physical projection planes that are found in cameras (and eyes) are behind the center
of the projection. For this re
COMP 558 lecture 6
Sept. 17, 2009
Illumination and reectance spectra
Digital color images have three intensity values per pixel (RGB) which dene a color at each
pixel. We would like to understand better what these intensities mean. A good place to start o
COMP 558 lecture 5
Sept. 15, 2009
Lighting and reectance
All of discussion up to now has been about geometry. Today we will talk about radiometry which
concerns measures of light.1 We will begin by talking informally about light sources, then we
will disc
COMP 558 lecture 3
Sept. 8, 2009
Last class we considered smooth translations and rotations of the camera coordinate system
and the resulting motions of points in the image projection plane. These two transformations
were expressed mathematically in a sli
COMP 558 lecture 7
Sept. 22, 2009
Introduction to Linear Systems
Today we begin the second part of the course, which addresses image analysis. We will start o
with the basic elements of linear system theory. The main application that we will start with is
COMP 558 Exercises 1
Oct 2, 2009
Questions
1. Show that if three 3D points X1 , X2 , X3 lie on a line in the scene, then their 2D image
projections lie on a line also.
2. Consider a wall at depth Z0 . What is the region of this wall that contributes to th
Midterm Exam
COMP 558
Fundamentals of Computer Vision
Oct. 6, 2009
Prof. M. Langer
Answer all questions in the exam booklet. You may keep this exam sheet.
Use the equations on page 3. There are a total of 15 points. GOOD LUCK!
1. (1 points)
Explain why, i
COMP 558 Linear Algebra Exercises
Sept, 2009
Rotations
Questions
1. Given a 3-vector a, what is the 3 3 matrix A such that, for any other 3-vector b,
Ab = a b ?
Hint: just compute a b and construct a matrix A that does the job.
2. Consider a rotation by d
Assignment 1
Instructor:
Teaching Assistant:
Posted:
Due:
COMP 558
Prof. Michael Langer
Fahim Mannan
Monday, Sept. 14, 2009.
Tuesday, Sept. 30, 2009 (midnight).
Instructions
For each question, you should explain how you arrived at your answer. Zero point