Computer vision involves the development of algorithms and software that have the potential to mimic a biological organism's ability to ``see''. Though the sense of vision is immediate for most people, the complexity of the task that the human visual system accomplishes is in fact enormous. The field of computer vision has grown steadily over the past few decades, and has advanced to the point where a set of core algorithms and techniques now exist for solving specific vision problems in constrained settings. Several international research laboratories now exist and applications of computer vision techniques in industry, robotics, and bio-medicine abound. This course seeks to present the fundamentals of computer vision at an advanced undergraduate/beginning graduate level.   Students will become familiar with the basic theoretical and practical tools of computer vision, which would be needed to carry out research or to find employment in this field.

• image projection with a pinhole camera
• motion field seen by a moving observer  (translation and rotation)
• camera model  (homogeneous coordinates, extrinsic and intrinsic parameters)
• thin lens model  (aperture, f-stop, blur, depth of field)
• lighting and reflectance  (light and shade, specularities, radiance, BRDF)
• image capture  (color, RGB, image irradiance, exposure, dynamic range, noise, sampling)

• basic linear systems (convolution, filtering, noise, derivatives, smoothing)
• edge detection (Canny),  corner detection (2nd moment matrix, Harris vs. Laplacian)
• features and affine invariance (SIFT)
• motion estimation (aperture problem, Kanade-Lucas-Tomasi, Horn & Schunk)
• linear algebra tools (matrix decompositions, QR, SVD)
• least squares minimization (pseudoinverse, non-linear methods)
• line fitting (least squares, Hough transform,  RANSAC)
• finding a vanishing point

• shape from shading (sunny vs. cloudy days)
• shape from texture, defocus 
• geometric camera calibration
• homographies and planar rectification 
• egomotion (Rieger Lawton)
• affine structure (factorization, Basri-Ullman, bas relief ambiguity)
• epipolar geometry, estimating the fundamental matrix
• dense stereo correspondence (dynamic programming, graph cuts)

• Three assignments (40 %)
• Midterm exam  (15 %)
• Final Exam  (30 %)
• Term Paper (15 %)

• Assignments (40 %)
• There will be three assignments, of roughly equal weight.
• The assignments will involve taking digital photographs, writing MATLAB programs to analyze them, and answering questions related to the lecture material.  Students are not required to know about digital photography or MATLAB prior to the course.  The principles of digital photography will be covered in class.  Examples of starter MATLAB code will be given, and students will asked to extend these examples.  
• Assignments must be submitted in electronic form via WebCT.   
• Policy on lateness and other specific instructions will be specified on each assignment.  


• Exams (midterm 15% + final 30% = 45 %)

• Term Paper  (15 %)
• The student must summarize three original research articles on a specific topic. These articles must have appeared in one of the three main computer vision conferences, namely CVPR, ECCV, ICCV. (links are to most recent conference only). At least one of these papers must be recent (since 2005). The usual way to choose the three papers is to find one recent paper which uses or replaces techniques developed in two earlier papers.
• Three potential articles must be chosen by the end of October. Students should submit URL to these articles (no attachments please) along with a brief (say 100 word) description that justifies the choice of each article. Feedback on the choice of articles will be given within one week of submission. The choice of articles must be finalized by Friday Nov. 13.
• A hard copy of the Term Paper is due on the last official lecture day. Late submissions will be given a maximum grade of 10/15. NOTE: if the Final Exam is scheduled very early in the Final Exam period, then this Term Paper deadline will be extended beyond the Final Exam period in order to give you time to study for the Final Exam.

[ADDED Oct. 23, 2009] Because the Final Exam is being held early in the Final Exam period, I am extending the dates associated with the Term Paper as follows: Initial submission of URLs and justification of articles (FRI. NOV. 13), Finalization of 3 articles (FRIDAY NOV. 27), Term Paper due (TUESDAY, DEC. 22 5 pm).


• Further specifications:
  • The submitted Term Paper must be between 1300 and 1500 words according to the UNIX/LINUX command wc. The instructor will verify the word count. If the word count is not between 1300-1500 words, the student will be asked to resubmit and if the resubmission is beyond the due date then the late penalty will be applied (see below). This word count does not include the Bibliography.
  • The Term Paper must be written in the student's own words. It is forbidden to copy phrases or sentences directly from the articles unless the exact wording is crucial (for example, in a definition). In this case, quotation marks and a proper citation must be used. See Student's Guide to Avoiding Plagarism mentioned below. It is also considered bad style to paraphrase, and marks will be deducted if students merely re-ordered or slightly changed the author's wording.
  • Neither equations nor figures may be included in the Term Paper. Instead the equations and figures must be cited from the article being summarized. e.g. see Eq. (5) in reference [3].
  • The paper must be typeset -- either Latex or Word -- and run through a spell checker. Marks will be taken off for spelling mistakes.
  • The student must submit:
  • one hard copy of the Term Paper, including a Bibliography
  • one hard copy of each of the three articles being summarized
  • one electronic ASCII version of the Term Paper, which the instructor will use to determine the word count. The electronic version must not include the Bibliography.
• The Grading Scheme for the term paper is as follows (15 points total)
  • Organization (5 points)
  • The Term Paper must have a one paragraph Introduction outlining what the topic is. The article summaries should then follow. The key idea(s) of each article should be explained in simple terms, and references to particular equations and figures should be given to help the reader follow the summary. Roughly equal weight should be given to the three articles. Given the tight word constraints, a Conclusion section is optional and should only be included if it includes ideas that were not covered in the Introduction.
  • Possible ways of organizing the Term Paper include:
  • the development of a particular computational method or theory
  • the development of one particular author's work
  • a comparison of different experimental or computational methods for solving a particular problem
  • Clarity/Readability (5 points)
  • The Instructor should be able to understand the main ideas of the summarized articles by reading only the Term Paper. For details that are not fully explained in the summaries, the Instructor should be able to easily index from the statements in the Term Paper to relevant locations in the articles. For example, give pointers to page/paragraphs where ideas are elaborated.
  • Choice of Detail (5 points)
  • Because the word count is severely limited, it is not possible to cover all the details in each article. Students must therefore decide which details to include and which to leave out. Students will be penalized for including details that are not central to the main ideas of the article(s).
  • The paper should be written at a level appropriate for the instructor, as only he will read the paper. The student should not re-explain concepts covered in class, nor explain standard methods that are used (but not introduced) by the authors.

In accord with McGill University's Charter of Students' Rights, students in this course have the right to submit in English or in French any written work that is to be graded.

• 40 hours for attending lectures
• 40 hours for reviewing lecture material to study for exams and to review material needed to do the assignments.
• 10 hours for the Term Paper
• 10 hours for each of the three Assignments (30 total), note: this does not include the time needed to review lecture material that the assigment is based on

• COMP 557 Fundamentals of Computer Graphics (Fall 2009)
• COMP 646 Machine Learning (Fall 2009)
• COMP 599 Computer Animation (Winter 2010)
• COMP 755 Mobile Robotics (Winter 2010)
• COMP 766 Shape Analysis in Computer Vision (Winter 2010)