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Introduction Introduction Which are the similar geometrical features between these images ?
Introduction
Introduction
Which are the similar geometrical features between these images ?
Introduction
Introduction
Which are the similar geometrical features between these images ?
Introduction
Introduction
Is there any similar geometrical features between these images ?
Introduction
Introduction
Introduction
Motivation and requirements
Problem: finding correspondences between images.
Applicationscomparison of images content;research in a database;object detection/recognition;image stiching;3D reconstruction, stereo...
Usual requirement: invariance or robustness toillumination (contrast changes),scale and viewpoint (local similarity, affine or projective transformations),occlusion,noise
Introduction
Motivation and requirements
Introduction
Methodology
Four steps1 Extraction of local features: invariance or robustness requirements;2 Feature comparison: distance between features;3 Decision: thresholds on the distance and matching;4 Grouping of previous matching in coherent rigid transformations.
A B
Introduction
Methodology
Four steps1 Extraction of local features: invariance or robustness requirements;2 Feature comparison: distance between features;3 Decision: thresholds on the distance and matching;4 Grouping of previous matching in coherent rigid transformations.
A B
Introduction
Methodology
Four steps1 Extraction of local features: invariance or robustness requirements;2 Feature comparison: distance between features;3 Decision: thresholds on the distance and matching;4 Grouping of previous matching in coherent rigid transformations.
A B
Introduction
Methodology
Four steps1 Extraction of local features: invariance or robustness requirements;2 Feature comparison: distance between features;3 Decision: thresholds on the distance and matching;4 Grouping of previous matching in coherent rigid transformations.
A B
Local feature extraction SIFT
Part I
Local descriptors
Local feature extraction SIFT
Local representation choice
Many local features have been proposed in the literature:level lines pieces: [Lisani 2001], [Muse et al 2006];local descriptors: SIFT [Lowe, 1999], GLOH [Mikolajczyk, Schmid,2005], PCA-SIFT [Ke, Sukthankar, 2004], SURF [Bay et al, 2006], ShapeContext [Belongie, Malik, 2000] etc...region descriptors: shapes [Monasse, Guichard, 2000], MSER [Mataset al, 2002].
Local feature extraction SIFT
Local feature extraction
1 Discrete image u2 Linear scale-space representation8�, u� = g� ⇤ u
3 Local extrema (~x , �) in space andscale of �2�u�
4 Harris criterion to eliminate edgepoints! interest points (~x , �).
5 Main orientations (direction ofru�) assigned at each point!interest points (~x , �, ✓).
Local feature extraction SIFT
Local feature extraction
1 Discrete image u2 Linear scale-space representation8�, u� = g� ⇤ u
3 Local extrema (~x , �) in space andscale of �2�u�
4 Harris criterion to eliminate edgepoints! interest points (~x , �).
5 Main orientations (direction ofru�) assigned at each point!interest points (~x , �, ✓).
Local feature extraction SIFT
Local feature extraction
1 Discrete image u2 Linear scale-space representation8�, u� = g� ⇤ u
3 Local extrema (~x , �) in space andscale of �2�u�
4 Harris criterion to eliminate edgepoints! interest points (~x , �).
5 Main orientations (direction ofru�) assigned at each point!interest points (~x , �, ✓).
Local feature extraction SIFT
Local feature extraction
1 Discrete image u2 Linear scale-space representation8�, u� = g� ⇤ u
3 Local extrema (~x , �) in space andscale of �2�u�
4 Harris criterion to eliminate edgepoints! interest points (~x , �).
5 Main orientations (direction ofru�) assigned at each point!interest points (~x , �, ✓).
Local feature extraction SIFT
Local feature extraction
1 Discrete image u2 Linear scale-space representation8�, u� = g� ⇤ u
3 Local extrema (~x , �) in space andscale of �2�u�
4 Harris criterion to eliminate edgepoints! interest points (~x , �).
5 Main orientations (direction ofru�) assigned at each point!interest points (~x , �, ✓).
Local feature extraction SIFT
Local feature representation: example of SIFT descriptors [Lowe, 1999]
Construction of a local descriptor a at each interest point (~x , �, ✓).
Mask (e.g. a square, a disk) around ~x :M sectors,size proportional to �.orientation given by ✓
Descriptor a = (a1, . . . aM)
am = normalized histogram of the gradientorientation (*), weighted by the gradientmagnitude, in the mth sector.(*) Orientations defined with respect to the referencedirection ✓.
