Handling Geometric Distortion • As pointed out in seminal work by Berg and Malik (CVPR’01) the effectiveness of SSD will degrade with significant viewpoint and/or illumination change. • Two options to match patches:- 1. simultaneously estimate the distortion and position of matching patch. 2. to “blur” the template window performing matching coarse-to-fine. 0 “1D Patch” 0 “Distorted 1D Patch” 31
Handling Geometric Distortion • As pointed out in seminal work by Berg and Malik (CVPR’01) the effectiveness of SSD will degrade with significant viewpoint and/or illumination change. • Two options to match patches:- 1. simultaneously estimate the distortion and position of matching patch. 2. to “blur” the template window performing matching coarse-to-fine. 0 “1D Patch” “blur” 0 “Distorted 1D Patch” 31
Handling Geometric Distortion • As pointed out in seminal work by Berg and Malik (CVPR’01) the effectiveness of SSD will degrade with significant viewpoint and/or illumination change. • Two options to match patches:- 1. simultaneously estimate the distortion and position of matching patch. 2. to “blur” the template window performing matching coarse-to-fine. 0 “1D Patch” “match” “blur” 0 “Distorted 1D Patch” 31
Handling Geometric Distortion • As pointed out in seminal work by Berg and Malik (CVPR’01) the effectiveness of SSD will degrade with significant viewpoint and/or illumination change. • Two options to match patches:- 1. simultaneously estimate the distortion and position of matching patch. 2. to “blur” the template window performing matching coarse-to-fine. 0 “1D Patch” “match” “blur” 0 “Distorted 1D Patch” Option 2 is attractive, low computational cost! 31
x
x
Not Always Zero Always Zero P x
Not Always Zero Always Zero Px P x
x
φ { x } = Px x
φ { x } = Px x
φ { x } = Px x
φ { x } = Px P ∈ G x
“Similarity” “Rotation” P ∈ G “Translation” “Circular Shift”
“Similarity” “Rotation” P ∈ G “Translation” “Circular Shift”
“Similarity” “Rotation” 1 X φ { x } = Px | G | P ∈ G “Translation” “Circular Shift”
“Similarity” “Rotation” 1 X φ { x } = Px | G | P ∈ G “Translation” “Circular Shift”
“Similarity” “Rotation” X φ { x } = Px P ∈ G “Translation” “Circular Shift”
“Similarity” “Rotation” X φ { x } = Px P ∈ G “throws away information” “Translation” “Circular Shift”
What About Blurring? “Edge Filter” “Blur Kernel” “Edge Blur Filter” ∗ 37
What About Blurring? “Edge Filter” “Blur Kernel” “Edge Blur Filter” ∗ 37
What About Blurring? “Edge Filter” “Blur Kernel” “Edge Blur Filter” ∗ “Power Normalized” 38
What About Blurring? “Edge Filter” “Blur Kernel” “Edge Blur Filter” ∗ “Power Normalized” 38
What About Blurring • Clearly, blurring a high-frequency edge filter simply lowers the centre frequency (not what we want). λ b > λ e “Blurred Edge Wavelength” “High Frequency Edge Wavelength” 39
Sparseness and Positiveness • Blurring only works if the signals being matched are sparse and positive. • Unfortunately natural images are neither. • Combination of oriented filter banks and rectification can remedy this problem with little loss in performance. ... ... ... y x “Rectification” ∗ ... ... ... y x 40
Sparseness and Positiveness • Blurring only works if the signals being matched are sparse and positive. • Unfortunately natural images are neither. • Combination of oriented filter banks and rectification can remedy this problem with little loss in performance. r “Rectification” “Non-Linearly sets Centre r · r Frequency to Zero” 41
Sensitivity to Shift Edge Energy D ( p ) ( p ) Warp Pixel Coordinates No Blurring 42
Sensitivity to Shift Edge Energy D ( p ) ( p ) Warp Pixel Coordinates No Blurring 42
Sensitivity to Shift Rectified Edge D ( p ) ( p ) Warp Pixel Coordinates Gaussian Blur 43
Sensitivity to Shift Rectified Edge D ( p ) ( p ) Warp Pixel Coordinates Gaussian Blur 43
Sensitivity to Shift Rectified Edge D ( p ) ( p ) Warp Pixel Coordinates Histogram Blur 44
Sensitivity to Shift Rectified Edge D ( p ) ( p ) Warp Pixel Coordinates Histogram Blur 44
Sparseness and Positiveness • Comes at additional computational cost, as new representation is F times larger (where F is the number of filters employed). I ( p ) φ { I ( p ) } φ {} = image descriptor function 45
Reminder - SIFT Descriptor 1. Compute image gradients 2. Pool into local histograms 3. Concatenate histograms 4. Normalize histograms 46
Relationship to Deep Learning 47
Relationship to Deep Learning 47
Sensitivity of VGG to Geometric Variation image patch 3@ conv1 conv2 conv3 conv4 conv5 fc-6 fc-7 (224x224) 64@ 256@ 384@ 384@ 256@ (4096) (4096) (54x54) (27x27) (13x13) (13x13) (13x13) SNR (dB) conv1 conv2 conv3 conv4 conv5 fc-6 fc-7 48
Sensitivity of VGG to Geometric Variation image patch 3@ conv1 conv2 conv3 conv4 conv5 fc-6 fc-7 (224x224) 64@ 256@ 384@ 384@ 256@ (4096) (4096) (54x54) (27x27) (13x13) (13x13) (13x13) SNR (dB) conv1 conv2 conv3 conv4 conv5 fc-6 fc-7 48
Sensitivity of VGG to Geometric Variation image patch 3@ conv1 conv2 conv3 conv4 conv5 fc-6 fc-7 (224x224) 64@ 256@ 384@ 384@ 256@ (4096) (4096) (54x54) (27x27) (13x13) (13x13) (13x13) SNR (dB) conv1 conv2 conv3 conv4 conv5 fc-6 fc-7 48
Today • Exhaustive Search & Sampling • Motivation for Descriptors • Overcoming the Curse of Dimensionality in Search 49
Exhaustive Search p ||I ( p ) − T ( 0 ) || 2 arg min 2 p = 0 p 2 p 6 = 0 p 1 “Possible Source Warps” where: p = { p 1 , p 2 } d = dim( p )
Exhaustive Search p ||I ( p ) − T ( 0 ) || 2 arg min 2 p = 0 ∆ p p 2 p 6 = 0 || ∆ p || 2 = ✏ p 1 “Possible Source Warps” where: p = { p 1 , p 2 } d = dim( p )
Exhaustive Search • One can see that as accuracy linearly increases the number 1 / ✏ of required training samples increases exponentially as a function of . d ��������� ����������������� ��������� ������������ ����������������� where: O (1 / ϵ d ) ��������������������� ������������ d = dim( p ) O ( C d log 1 / ϵ ) ���������� Tian & O ( C d 1 + C 2 log 1 / ϵ ) ��������� 1 / ϵ ����
Can we do better? ��������� ����������������� ��������� ������������ ����������������� O (1 / ϵ d ) ��������������������� ������������ O ( C d log 1 / ϵ ) ���������� Tian & Narasimhan [ICCV 2013] O ( C d 1 + C 2 log 1 / ϵ ) ��������� 1 / ϵ ����
Can we do better? ��������� ����������������� ��������� ������������ ����������������� O (1 / ϵ d ) ��������������������� ������������ O ( C d log 1 / ϵ ) ���������� Tian & Narasimhan [ICCV 2013] O ( C d 1 + C 2 log 1 / ϵ ) ��������� 1 / ϵ ����
Data Driven Descent Tian & Narasimhan 2012
Data Driven Descent {T ( ∆ p k ) } K k =1 Tian & Narasimhan 2012
Data Driven Descent {T ( ∆ p k ) } K k =1 T ( 0 ) Tian & Narasimhan 2012
Data Driven Descent Tian & Narasimhan 2012
Data Driven Descent T ( ∆ p i ) T ( 0 ) I ( p ) Tian & Narasimhan 2012
Data Driven Descent Tian & Narasimhan 2012
Data Driven Descent p ! p � − 1 ∆ p i “inverse composition” Tian & Narasimhan 2012
Data Driven Descent Tian & Narasimhan 2012
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