Oct 21/23 Silhouettes/carving (Fall break) Oct 28/30 - Structure from motion Project update
Proj. SfM Nov 11/13 Camera calibration Segmentation Nov 18/20 Fitting Prob. segm.&fit.
Nov 25/27 Matching templates (Thanksgiving) Matching relations Range data Sep 2/4 Sep 9/11 Sep30/Oct2
Oct 7/9 Nov 4/6 Dec 2/4 Computer Vision Discussion assignment 2 Simple stereo using SSD on 11x11 windows and a disparity range of [0,150] without histogram equalization
with histogram equalization Computer Vision Assignment 3 Use Hough, RANSAC and EM to estimate noisy line embedded in noise (details on the web by tonight) Computer Vision
Reminder EM (Expectation Maximization) Alternate Expectation Px i | i 1, P i 1 (determine feature appearance) P 1| , x i i Px i | i 1, P i 1 Px i | i 0, P i 0
Px i | i 1, P i 1 2 P i 1| , x i 1 exp x cos y sin
c P i 2 Px i | i 1, Pi i 1i Px i | i 0, 2 2 exp 1 2 xi cos y1i sin2 xi ccos yexp
k 12 exp sin n c i 2 2 2
exp 1 2 xi cos yi sin c exp kn 2
Maximization (determine ML model parameters) , , c optimization (weighted with i) counting Computer Vision
Last class: Recognition by matching templates Classifiers decision boundaries, not prob.dens. PCA LDA dimensionality reduction maximize discrimination
Computer Vision Last class: Recognition by matching templates Neural Networks Universal approximation property Support Vector Machines Convex problem! also for non-linear boundaries support vectors
2 w Optimal separating hyperplane (OSH) Computer Vision Matching by relations Idea: find bits, then say object is present if bits are ok Advantage:
objects with complex configuration spaces dont make good templates internal degrees of freedom aspect changes (possibly) shading variations in texture etc.
Computer Vision Simplest Define a set of local feature templates could find these with filters, etc. corner detector+filters Think of objects as patterns Each template votes for all patterns that contain it Pattern with the most votes wins Computer Vision
Figure from Local grayvalue invariants for image retrieval, by C. Schmid and R. Mohr, IEEE Trans. Pattern Analysis and Machine Intelligence, 1997 copyright 1997, IEEE Computer Vision Probabilistic interpretation Write Assume Likelihood of image given pattern
Computer Vision Possible alternative strategies Notice: different patterns may yield different templates with different probabilities different templates may be found in noise with different probabilities Computer Vision
Employ spatial relations Figure from Local grayvalue invariants for image retrieval, by C. Schmid and R. Mohr, IEEE Trans. Pattern Analysis and Machine Intelligence, 1997 copyright 1997, IEEE Computer Vision Figure from Local grayvalue invariants for image retrieval, by C. Schmid and R. Mohr, IEEE Trans. Pattern Analysis and Machine Intelligence, 1997 copyright 1997, IEEE Computer Vision
Example Training examples Test image Computer Vision Computer Vision Computer Vision
Finding faces using relations Strategy: Face is eyes, nose, mouth, etc. with appropriate relations between them build a specialized detector for each of these (template matching) and look for groups with the right internal structure Once weve found enough of a face, there is little uncertainty about where the other bits could be Computer Vision Finding faces using relations
Strategy: compare Notice that once some facial features have been found, the position of the rest is quite strongly constrained Figure from, Finding faces in cluttered scenes using random labelled graph matching, by Leung, T., Burl, M., and Perona, P., Proc. 5th Int. Conf. on Computer Vision, 1995 Computer Vision
Detection This means we compare Computer Vision Issues Plugging in values for position of nose, eyes, etc. search for next one given what weve found when to stop searching when nothing that is added to the group could change the decision
i.e. its not a face, whatever features are added or its a face, and anything you cant find is occluded what to do next look for another eye? or a nose? probably look for the easiest to find What if theres no nose response marginalize Computer Vision Figure from, Finding faces in cluttered scenes using random labelled graph matching,
Leung, T., Burl, M., and Perona, P., Proc. 5th Int. Conf. on Computer Vision, 1995 Computer Vision Pruning Prune using a classifier crude criterion: if this small assembly doesnt work, there is no need to build on it. Example: finding people without clothes on
find skin find extended skin regions construct groups that pass local classifiers (i.e. lower arm, upper arm) give these to broader scale classifiers (e.g. girdle) Computer Vision
Pruning Prune using a classifier better criterion: if there is nothing that can be added to this assembly to make it acceptable, stop equivalent to projecting classifier boundaries. Computer Vision
Horses Computer Vision Hidden Markov Models Elements of sign language understanding the speaker makes a sequence of signs Some signs are more common than others the next sign depends (roughly, and probabilistically) only on the current sign there are measurements, which may be inaccurate; different signs tend to generate different probability densities on measurement
values Many problems share these properties tracking is like this, for example Computer Vision Hidden Markov Models Now in each state we could emit a measurement, with probability depending
on the state and the measurement We observe these measurements Computer Vision HMMs - dynamics Computer Vision HMMs - the Joint and Inference
Computer Vision Trellises Each column corresponds to a measurement in the sequence Trellis makes the collection of legal paths obvious Now we would like to get the path with the
largest negative logposterior Trellis makes this easy, as follows Computer Vision Computer Vision Fitting an HMM I have: sequence of measurements collection of states
topology I want state transition probabilities measurement emission probabilities Straightforward application of EM discrete vars give state for each measurement M step is just averaging, etc. Computer Vision
HMMs for sign language understanding-1 Build an HMM for each word Computer Vision HMMs for sign language understanding-2 Build an HMM for each word Then build a language model
Computer Vision User gesturing For both isolated word recognition tasks and for recognition using a language model that has five word sentences (words always appearing in the order pronoun verb noun adjective pronoun), Starner and Pentlands displays a word accuracy of the order of 90%. Values are slightly larger or
smaller, depending on the features and the task, etc. Figure from Real time American sign language recognition using desk and wearable computer based video, T. Starner et al., Proc. Int. Symp. on Computer Vision, 1995 Computer Vision HMMs can be spatial rather than temporal; for example, we have a simple model where the position of the arm depends on the position of the torso, and the position of the leg depends on the position of the
torso. We can build a trellis, where each node represents correspondence between an image token and a body part, and do DP on this trellis. Computer Vision Computer Vision Figure from Efficient Matching of Pictorial Structures, P. Felzenszwalb and D. Huttenlocher, Proc. Computer Vision and Pattern Recognition Conf., 2000
Computer Vision Recognition using local affine and photometric invariant features Tuytelaars and Van Gool, BMVC2000 Hybrid approach that aims to deal with large variations in Viewpoint Computer
Vision Recognition using local affine and photometric invariant features Hybrid approach that aims to deal with large variations in Viewpoint Illumination Computer Vision Recognition using local affine and photometric invariant features
Hybrid approach that aims to deal with large variations in Viewpoint Illumination Background Computer Vision Recognition using local affine and photometric invariant features Hybrid approach that aims to deal with large variations in
Viewpoint Illumination Background and Occlusions Computer Vision Recognition using local affine and photometric invariant features
Hybrid approach that aims to deal with large variations in Viewpoint Illumination Background and Occlusions Use local invariant features
Invariant features = features that are preserved under a specific group of transformations Robust to changes in viewpoint and illumination Robust to occlusions and changes in background Computer Vision
Transformations for planar objects Affine geometric deformations x' a b x e y ' c d y f Linear photometric changes R' sR G ' 0 B' 0 0
sG 0 0 R oR 0 G oG s B B oB Computer Vision Local invariant features Affine invariant neighborhood
Computer Vision Local invariant features Computer Vision Local invariant features Geometry-based region extraction Curved edges Straight edges Intensity-based region extraction
Geometry-based method (curved edges) 2. Canny edge detection Computer Vision Geometry-based method (curved edges) 3. Evaluation relative affine invariant parameter along two edges (1) i
li abs(| p ( si ) p pi ( si ) |)ds i Computer Vision Geometry-based method (curved edges) 4. Construct 1-dimensional family of parallelogram shaped regions Computer
Vision Geometry-based method (curved edges) 5. Select parallelograms based on local extrema of invariant function f ( ) | p1 p g p2 p g | | p p1
p p2 | 1 M 101 M 01 p g ( 1 , 1 ) M 00 M 00 M a pq 1 M 00
1 1 M 002 M 000 M 00 M 00 f a I ( x, y ) x p y q dxdy (l ) Computer Vision
Geometry-based method (curved edges) 5. Select parallelograms based on local extrema of invariant function Computer Vision Geometry-based method (straight edges) Relative affine invariant parameters are identically zero! Computer
Geometry-based method (straight edges) 3. Fit lines to edges Computer Vision Geometry-based method (straight edges) 4. Select parallelograms based on local extrema of invariant functions Computer Vision
Geometry-based method (straight edges) 4. Select parallelograms based on local extrema of invariant functions Computer Vision Intensity based method 1. Search intensity extrema 2. Observe intensity profile along rays 3. Search maximum of invariant function f(t)
along each ray 4. Connect local maxima 5. Fit ellipse 6. Double ellipse size f (t ) abs( I 0 I ) abs( I max( 0
t I )dt ,d) Computer Vision Intensity based method Computer Vision
Comparison Intensity-based method More robust Geometry-based method Less computations More environments Computer Vision Robustness Correct detection of single
environment cannot be guaranteed Non-planar region Noise, quantization errors Non-linear photometric distortion Perspective-distortion All regions of an object / image
should be considered simultaneously Computer Vision Search for corresponding regions 1. Extract affine invariant regions 2. Describe region with feature vector of moment invariants abc M pq R a G b B c x p y q dxdy
M e.g. M 200 00 M 000 00
110 00 M M 000 00 M 100
00 M 100 2 00 M 020 00 010 2 00
M 000 00 M 010 2 00
Computer Vision Search for corresponding regions 1. Extract affine invariant regions 2. Describe region with feature vector of moment invariants 3. Search for corresponding regions based on Mahalanobis distance 4. Check cross-correlation (after normalization)
5. Check consistency of correspondences Computer Vision Semi-local constraints = check consistency of correspondences Epipolar constraint (RANSAC) based on 7 points Geometric constraints Photometric constraints a23 b23 det a22 b22 a21 b21
b13 a13 b12 a12 b11 a11 based on a combination of only 2 regions a13b23 b13a23 a12b23 b13a22 a13b22 b12 a23 a11b23 b13a21 a13b21 b11a23 Computer
Vision Number of matches Experimental validation symmetric correct degrees Experimental validation Number of matches Computer Vision
error symmetric correct scale Computer Vision Number of matches Experimental validation
= objects are modeled by a set of reference images Voting principle based on number of similar regions More invariance = requires less reference images Computer Vision Object recognition and localization
Wide-baseline stereo Computer Vision Wide-baseline stereo Computer Vision Content-based image retrieval from database = Searching of similar images in a
database based on image content Local features Similarity = images contain the same object or the same scene Voting principle Based on the number of similar regions Computer Vision Content-based image retrieval
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