Computational Vision

1. Computational Vision Jitendra Malik University of California at Berkeley

2. Taxonomy of Vision Problems • Reconstruction: • estimate parameters of external 3D world. • Visual Control: • visually guided locomotion and manipulation. • Segmentation: • partition I(x,y,t) into subsets of separate objects. • Recognition: • classes: face vs. non-face, • activities: gesture, expression.

3. Reconstruction • Computer graphics is the forward problem: given scene geometry, reflectances and lighting, synthesize an image. • Computer vision must address the inverse problem: given an image/multiple images, reconstruct the scene geometry, reflectacnes and illumination.

4. Recovering geometry • Historical roots in photogrammetry and analysis of 3D cues in human vision • Single images adequate given knowledge of object class • Multiple images make the problem easier, but not trivial as corresponding points must be identified.

5. Arc de Triomphe

6. Taj Mahal modeled from one photograph by G. Borshukov

7. Recovered Campus Model Campanile + 40 Buildings (Debevec et al)

10. Inverse Global Illumination (Yu et al) Reflectance Properties Radiance Maps Light Sources Geometry

11. Real vs. Synthetic

12. Real vs. Synthetic

13. Challenges in Reconstruction • Finding correspondences automatically • Optimal estimation of structure from n views under perspective projection • Models of reflectance and texture for natural materials and objects

14. Control • Visual feedback signal for control of manipulation tasks such as grasping, moving and assembly • Visual feedback for guiding locomotion • Obstacle avoidance for a moving robot • Lateral and longitudinal control of driving

15. Challenges in control • Delay in feedback loop due to visual processing • Hierarchies in sensory motor control • Open loop or closed loop • Discrete planning or continuous control

16. Image Segmentation

17. Boundaries of image regions defined by a number of attributes • Brightness/color • Texture • Motion • Stereoscopic depth • Familiar configuration

18. Approaches • Fitting a piecewise smooth surface to the image e.g. Mumford and Shah • Probabilistic Inference using Markov Random Field model of image e.g. Geman and Geman • Graph partitioning using spectral techniques e.g. Shi and Malik

19. Image Segmentation as Graph Partitioning Build a weighted graph G=(V,E) from image V: image pixels E: connections between pairs of nearby pixels Partition graph so that similarity within group is large and similarity between groups is small -- Normalized Cuts [Shi&Malik 97]

20. Temporal Segmentation: Tracking

21. Challenges in Segmentation • Interaction of multiple cues • Local measurements to global percepts • Interplay of image-driven and object model driven processing

22. Possible for both instances or object classes (Mona Lisa vs. faces or Beetle vs. cars) • Tolerant to changes in pose and illumination, and occlusion Recognition

23. Recognition of Gait and Gesture run measurement recognition animation

24. Challenges in recognition • Unified framework for segmentation and recognition • Representing shape variability in a category • Interplay of discriminative vs generative models

25. Core disciplines • Geometry • Differential geometry • Projective geometry • Probability and Statistics • Reconstruction = estimation • Control = decision theory • Segmentation = clustering • Recognition = classification