CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an...
Transcript of CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an...
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Lecture 9: Template Matching (cont.) and Scaled Representations
CPSC 425: Computer Vision
( unless otherwise stated slides are taken or adopted from Bob Woodham, Jim Little and Fred Tung )
Image Credit: https://docs.adaptive-vision.com/4.7/studio/machine_vision_guide/TemplateMatching.html
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Menu for Today (September 28, 2020)Topics:
— Template Matching — Normalized Correlation
Redings:
— Today’s Lecture: Forsyth & Ponce (2nd ed.) 4.5 - 4.7 — Next Lecture: Forsyth & Ponce (2nd ed.) 5.1 - 5.2
Reminders:
— Assignment 1: Image Filtering and Hybrid Images is due Wednsday — Assignment 2: Scaled Representations, Face Detection and Image Blending
— Scaled Representations — Image Derivatives
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Today’s “fun” Example: Rainbow Illusion
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Today’s “fun” Example: Lilac Chaser (a.k.a. Pac-Man) Illusion
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Today’s “fun” Example: Lilac Chaser (a.k.a. Pac-Man) Illusion
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Lecture 8: Re-cap
“Color” is not an objective physical property of light (electromagnetic radiation).
Instead, light is characterized by its wavelength.
Color Filter Arrays (CFAs) allow capturing of mosaiced color information; the layout of the mosaic is called Bayer pattern.
Demosaicing is the process of taking the RAW image and interpolating missing color pixels per channel
!5
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How can we find a part of one image that matches another?
or,
How can we find instances of a pattern in an image?
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Lecture 8: Re-cap
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How can we find a part of one image that matches another?
or,
How can we find instances of a pattern in an image?
Key Idea: Use the pattern as a template
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Lecture 8: Re-cap
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!8
Template Matching
Slide Credit: Kristen Grauman
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We can think of correlation as comparing a template (the filter) with each local image patch. — Consider the filter and image patch as vectors. — Applying a filter at an image location can be interpreted as computing the dot product between the filter and the local image patch.
!9
Template Matching
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Template Matching
0 0
0 0 0
0
1
1 1
Template
We can think of correlation as comparing a template (the filter) with each local image patch. — Consider the filter and image patch as vectors. — Applying a filter at an image location can be interpreted as computing the dot product between the filter and the local image patch.
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Template Matching
0 0
0 0 0
0
1
1 1
Template0
0
0
0
0
0
1
1
1
Vector
We can think of correlation as comparing a template (the filter) with each local image patch. — Consider the filter and image patch as vectors. — Applying a filter at an image location can be interpreted as computing the dot product between the filter and the local image patch.
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Template Matching
0 0
0 0 0
0
1
1 10 0
0 0 0
0
1
1 1
0 0
0
0
00
1
1 1
TemplateImage Patch 1
Image Patch 2
We can think of correlation as comparing a template (the filter) with each local image patch. — Consider the filter and image patch as vectors. — Applying a filter at an image location can be interpreted as computing the dot product between the filter and the local image patch.
![Page 14: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/14.jpg)
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Template Matching
0 0
0 0 0
0
1
1 10 0
0 0 0
0
1
1 1
0 0
0 0 0
0
1
1 1
0 0
0
0
00
1
1 1
TemplateImage Patch 1
Image Patch 2
element
multiply
0 0
0 0 0
0
1
0 0
We can think of correlation as comparing a template (the filter) with each local image patch. — Consider the filter and image patch as vectors. — Applying a filter at an image location can be interpreted as computing the dot product between the filter and the local image patch.
![Page 15: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/15.jpg)
!14
Template Matching
0 0
0 0 0
0
1
1 10 0
0 0 0
0
1
1 1
0 0
0 0 0
0
1
1 1
0 0
0
0
00
1
1 1
TemplateImage Patch 1
Image Patch 2
element
multiply
0 0
0 0 0
0
1
0 0
= 3
= 1
We can think of correlation as comparing a template (the filter) with each local image patch. — Consider the filter and image patch as vectors. — Applying a filter at an image location can be interpreted as computing the dot product between the filter and the local image patch.
![Page 16: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/16.jpg)
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Template Matching
0 0
0 0 0
0
1
1 10 0
0 0 0
0
1
1 1
0 0
0 0 0
0
1
1 1
0 0
0
0
00
1
1 1
TemplateImage Patch 1
Image Patch 2
element
multiply
0 0
0 0 0
0
1
0 0
= 3
= 1 ⇥255⇥255
We can think of correlation as comparing a template (the filter) with each local image patch. — Consider the filter and image patch as vectors. — Applying a filter at an image location can be interpreted as computing the dot product between the filter and the local image patch.
![Page 17: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/17.jpg)
!16
Template Matching
0 0
0 0 0
0
1
1 10 0
0 0 0
0
1
1 1
0 0
0 0 0
0
1
1 1
0 0
0
0
00
1
1 1
TemplateImage Patch 1
Image Patch 2
element
multiply
0 0
0 0 0
0
1
0 0
= 3
= 1 ⇥255⇥255
The dot product may be large simply because the image region is bright. We need to normalize the result in some way.
We can think of correlation as comparing a template (the filter) with each local image patch. — Consider the filter and image patch as vectors. — Applying a filter at an image location can be interpreted as computing the dot product between the filter and the local image patch.
![Page 18: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/18.jpg)
Let and be vectors. Let be the angle between them. We know
where · is dot product and | | is vector magnitude
Correlation is a dot product
Correlation measures similarity between the filter and each local image region
Normalized correlation varies between −1 and 1
Normalized correlation attains the value 1 when the filter and image region are identical (up to a scale factor)
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Template Matching
cos ✓ =
a · b|a||b| =
a · bp(a · a)(b · b)
=
a
|a|b
|b|
a b ✓
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!18
Template Matching
Slide Credit: Kristen Grauman
Assuming template is all positive, what does this tell us about correlation map?
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!19
Template Matching
Slide Credit: Kristen Grauman
cos ✓ =
a · b|a||b| =
a · bp(a · a)(b · b)
=
a
|a|b
|b| =?
Assuming template is all positive, what does this tell us about correlation map?
![Page 21: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/21.jpg)
!20
Template Matching
Slide Credit: Kristen Grauman
cos ✓ =
a · b|a||b| =
a · bp(a · a)(b · b)
=
a
|a|b
|b| =?
Assuming template is all positive, what does this tell us about correlation map?
![Page 22: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/22.jpg)
!21
Template Matching
Slide Credit: Kristen Grauman
cos ✓ =
a · b|a||b| =
a · bp(a · a)(b · b)
=
a
|a|b
|b| =?
Assuming template is all positive, what does this tell us about correlation map?
![Page 23: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/23.jpg)
!22
Template Matching
Slide Credit: Kristen Grauman
cos ✓ =
a · b|a||b| =
a · bp(a · a)(b · b)
=
a
|a|b
|b| =?
Assuming template is all positive, what does this tell us about correlation map?
![Page 24: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/24.jpg)
!23
Template Matching
Slide Credit: Kristen Grauman
Detection can be done by comparing correlation map score to a threshold
What happens if the threshold is relatively low?
![Page 25: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/25.jpg)
!24
Template Matching
Slide Credit: Kristen Grauman
Detection can be done by comparing correlation map score to a threshold
What happens if the threshold is relatively low?
![Page 26: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/26.jpg)
!25
Template Matching
Slide Credit: Kristen Grauman
Detection can be done by comparing correlation map score to a threshold
What happens if the threshold is very high (e.g., 0.99)?
![Page 27: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/27.jpg)
!26
Template Matching
Slide Credit: Kristen Grauman
Detection can be done by comparing correlation map score to a threshold
What happens if the threshold is very high (e.g., 0.99)?
![Page 28: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/28.jpg)
Linear filtering the entire image computes the entire set of dot products, one for each possible alignment of filter and image
Important Insight: — filters look like the pattern they are intended to find — filters find patterns they look like
Linear filtering is sometimes referred to as template matching
!27
Template Matching
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Template Matching
!28
Let and be vectors. Let be the angle between them. We know
where · is dot product and | | is vector magnitude
cos ✓ =
a · b|a||b| =
a · bp(a · a)(b · b)
=
a
|a|b
|b|
a b ✓
![Page 30: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/30.jpg)
Template Matching
!29
Let and be vectors. Let be the angle between them. We know
where · is dot product and | | is vector magnitude
cos ✓ =
a · b|a||b| =
a · bp(a · a)(b · b)
=
a
|a|b
|b|
a b ✓
1. Normalize the template / filter ( ) in the beginning 2. Compute norm of | | by convolving squared image with a filter of all 1’s of
equal size to the the template and squarooting the response 3. We can compute the dot product by convolution of image ( ) with
normalized filter ( ) 4. We can finally compute the normalized correlation by dividing element-wise
result in Step 3 by result ins Step 2
a
b
ab
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Example 1:
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Credit: W. Freeman et al., “Computer Vision for Interactive Computer Graphics,” IEEE Computer Graphics and Applications, 1998
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Example 1:
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Credit: W. Freeman et al., “Computer Vision for Interactive Computer Graphics,” IEEE Computer Graphics and Applications, 1998
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Example 1:
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Credit: W. Freeman et al., “Computer Vision for Interactive Computer Graphics,” IEEE Computer Graphics and Applications, 1998
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Example 1:
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Credit: W. Freeman et al., “Computer Vision for Interactive Computer Graphics,” IEEE Computer Graphics and Applications, 1998
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Example 1:
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Credit: W. Freeman et al., “Computer Vision for Interactive Computer Graphics,” IEEE Computer Graphics and Applications, 1998
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Example 1:
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Credit: W. Freeman et al., “Computer Vision for Interactive Computer Graphics,” IEEE Computer Graphics and Applications, 1998
Template (left), image (middle), normalized correlation (right)
Note peak value at the true position of the hand
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When might template matching fail?
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Template Matching
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When might template matching fail?
!37
— Different scales
Template Matching
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When might template matching fail?
!38
— Different scales
— Different orientation
Template Matching
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When might template matching fail?
!39
— Different scales
— Different orientation
— Lighting conditions
Template Matching
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When might template matching fail?
!40
— Different scales
— Different orientation
— Lighting conditions
— Left vs. Right hand
Template Matching
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When might template matching fail?
!41
— Different scales
— Different orientation
— Lighting conditions
— Left vs. Right hand
— Partial Occlusions
Template Matching
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When might template matching fail?
!42
— Different scales
— Different orientation
— Lighting conditions
— Left vs. Right hand
— Partial Occlusions
— Different Perspective
— Motion / blur
Template Matching
![Page 44: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/44.jpg)
Good News: — works well in presence of noise — relatively easy to compute
Bad News: — sensitive to (spatial) scale change — sensitive to 2D rotation
More Bad News: When imaging 3D worlds: — sensitive to viewing direction and pose — sensitive to conditions of illumination
!43
Template Matching Summary
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Scaled Representations
Problem: Make template matching robust to changes in 2D (spatial) scale.
Key Idea(s): Build a scaled representation: the Gaussian image pyramid
Alternatives: — use multiple sizes for each given template — ignore the issue of 2D (spatial) scale
Theory: Sampling theory allows us to build image pyramids in a principled way
“Gotchas:” — template matching remains sensitive to 2D orientation, 3D pose and illumination
!44
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Scaled Representations
Why build a scaled representation of the image instead of scaled
representation of the template?
!45
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Scaled Representations: Goals
to find template matches at all scales — template size constant, image scale varies — finding hands or faces when we don’t know what size they are in the image
!46
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Scaled Representations: Goals
to find template matches at all scales — template size constant, image scale varies — finding hands or faces when we don’t know what size they are in the image
efficient search for image–to–image correspondences — look first at coarse scales, refine at finer scales — much less cost (but may miss best match)
!47
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Scaled Representations: Goals
to find template matches at all scales — template size constant, image scale varies — finding hands or faces when we don’t know what size they are in the image
efficient search for image–to–image correspondences — look first at coarse scales, refine at finer scales — much less cost (but may miss best match)
to examine all levels of detail — find edges with different amounts of blur — find textures with different spatial frequencies (i.e., different levels of detail)
!48
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Shrinking the Image
We can’t shrink an image simply by taking every second pixel
!49
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Shrinking the Image
We can’t shrink an image simply by taking every second pixel
!49
Why?
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Shrinking the Image
We can’t shrink an image simply by taking every second pixel
If we do, characteristic artifacts appear: — small phenomena can look bigger — fast phenomena can look slower
Common examples include: — checkerboard patterns misrepresented in video games — striped shirts look funny on colour television — wagon wheels roll the wrong way in movies
!50
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!51
Shrinking the Image
Forsyth & Ponce (2nd ed.) Figure 4.12-4.14 (top rows)
![Page 54: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/54.jpg)
Template Matching: Sub-sample with Gaussian Pre-filtering
!52
Gaussian filter delete even rows
delete even columns
1/2
1/4
1/8
Apply a smoothing filter first, then throw away half the rows and columns
Gaussian filter delete even rows
delete even columns
Slide Credit: Ioannis (Yannis) Gkioulekas (CMU)
![Page 55: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/55.jpg)
!53
1/2 1/4 (2x zoom) 1/8 (4x zoom)
Template Matching: Sub-sample with Gaussian Pre-filtering
Slide Credit: Ioannis (Yannis) Gkioulekas (CMU)
![Page 56: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/56.jpg)
!54
Template Matching: Sub-sample with NO Pre-filtering
1/2 1/4 (2x zoom) 1/8 (4x zoom)
Slide Credit: Ioannis (Yannis) Gkioulekas (CMU)
![Page 57: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/57.jpg)
Gaussian Pre-filtering
!55
Question: How much smoothing is needed to avoid aliasing?
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Gaussian Pre-filtering
!56
Question: How much smoothing is needed to avoid aliasing?
Answer: Smoothing should be sufficient to ensure that the resulting image
is band limited “enough” to ensure we can sample every other pixel.
Practically: For every image reduction of 0.5, smooth by � = 1
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Image Pyramid
An image pyramid is a collection of representations of an image. Typically, each layer of the pyramid is half the width and half the height of the previous layer.
In a Gaussian pyramid, each layer is smoothed by a Gaussian filter and resampled to get the next layer
!57
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Again, let denote convolution Create each level from previous one — smooth and (re)sample
Smooth with Gaussian, taking advantage of the fact that
!58
Gaussian Pyramid
⌦
G�1(x)⌦G�2(x) = G
p�21+�2
2(x)
![Page 61: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/61.jpg)
Example 2: Gaussian Pyramid
!59Forsyth & Ponce (2nd ed.) Figure 4.17
Slide Credit: Ioannis (Yannis) Gkioulekas (CMU)
![Page 62: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/62.jpg)
Example 2: Gaussian Pyramid
!60
What happens to the details?
— They get smoothed out as we move to higher levels
Forsyth & Ponce (2nd ed.) Figure 4.17Slide Credit: Ioannis (Yannis) Gkioulekas (CMU)
![Page 63: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/63.jpg)
Example 2: Gaussian Pyramid
!61Forsyth & Ponce (2nd ed.) Figure 4.17
What happens to the details?
— They get smoothed out as we move to higher levels
What is preserved at the higher levels?
— Mostly large uniform regions in the original image
Slide Credit: Ioannis (Yannis) Gkioulekas (CMU)
![Page 64: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/64.jpg)
Example 2: Gaussian Pyramid
!62
What happens to the details?
— They get smoothed out as we move to higher levels
What is preserved at the higher levels?
— Mostly large uniform regions in the original image
How would you reconstruct the original image from the image at the upper level?
— That’s not possibleForsyth & Ponce (2nd ed.) Figure 4.17
Slide Credit: Ioannis (Yannis) Gkioulekas (CMU)
![Page 65: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/65.jpg)
Example 2: Gaussian Pyramid
!63
What happens to the details?
— They get smoothed out as we move to higher levels
What is preserved at the higher levels?
— Mostly large uniform regions in the original image
How would you reconstruct the original image from the image at the upper level?
— That’s not possibleForsyth & Ponce (2nd ed.) Figure 4.17
Slide Credit: Ioannis (Yannis) Gkioulekas (CMU)
![Page 66: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/66.jpg)
From Template Matching to Local Feature Detection
We’ll now shift from global template matching to local feature detection
Consider the problem of finding images of an elephant using a template
!64
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From Template Matching to Local Feature Detection
We’ll now shift from global template matching to local feature detection
Consider the problem of finding images of an elephant using a template
An elephant looks different from different viewpoints — from above (as in an aerial photograph or satellite image) — head on — sideways (i.e., in profile) — rear on
What happens if parts of an elephant are obscured from view by trees, rocks, other elephants?
!65
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!66Slide Credit: Li Fei-Fei, Rob Fergus, and Antonio Torralba
From Template Matching to Local Feature Detection
![Page 69: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/69.jpg)
!67
From Template Matching to Local Feature Detection
Slide Credit: Li Fei-Fei, Rob Fergus, and Antonio Torralba
![Page 70: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/70.jpg)
— Move from global template matching to local template matching
— Local template matching also called local feature detection
— Obvious local features to detect are edges and corners
!68
From Template Matching to Local Feature Detection
![Page 71: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/71.jpg)
Human vision …
* slide from Fei-Dei Li, Justin Johnson, Serena Yeung, cs231n Stanford
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David Marr, 1970s
* slide from Fei-Dei Li, Justin Johnson, Serena Yeung, cs231n Stanford
![Page 73: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/73.jpg)
David Marr, 1970s
[ Stages of Visual Representation, David Marr ] * slide from Fei-Dei Li, Justin Johnson, Serena Yeung, cs231n Stanford
![Page 74: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/74.jpg)
— Move from global template matching to local template matching
— Local template matching also called local feature detection
— Obvious local features to detect are edges and corners
!72
From Template Matching to Local Feature Detection
![Page 75: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/75.jpg)
Recall, for a 2D (continuous) function, f(x,y)
Differentiation is linear and shift invariant, and therefore can be implemented as a convolution
!73
Estimating Derivatives
@f
@x
= lim✏!0
f(x+ ✏, y)� f(x, y)
✏
@f
@x
⇡ F (X + 1, y)� F (x, y)
�x
![Page 76: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/76.jpg)
Recall, for a 2D (continuous) function, f(x,y)
Differentiation is linear and shift invariant, and therefore can be implemented as a convolution
A (discrete) approximation is
!74
@f
@x
= lim✏!0
f(x+ ✏, y)� f(x, y)
✏
@f
@x
⇡ F (X + 1, y)� F (x, y)
�x
Estimating Derivatives
@f
@x
= lim✏!0
f(x+ ✏, y)� f(x, y)
✏
@f
@x
⇡ F (X + 1, y)� F (x, y)
�x
![Page 77: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/77.jpg)
Recall, for a 2D (continuous) function, f(x,y)
Differentiation is linear and shift invariant, and therefore can be implemented as a convolution
A (discrete) approximation is
!75
@f
@x
= lim✏!0
f(x+ ✏, y)� f(x, y)
✏
@f
@x
⇡ F (X + 1, y)� F (x, y)
�x
Estimating Derivatives
@f
@x
= lim✏!0
f(x+ ✏, y)� f(x, y)
✏
@f
@x
⇡ F (X + 1, y)� F (x, y)
�x
�1 1
![Page 78: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/78.jpg)
A similar definition (and approximation) holds for
Image noise tends to result in pixels not looking exactly like their neighbours, so simple “finite differences” are sensitive to noise.
The usual way to deal with this problem is to smooth the image prior to derivative estimation.
!76
@f
@y
Estimating Derivatives
![Page 79: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/79.jpg)
Example 1D
!77
0.5
0.4
0.3
0.2
![Page 80: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/80.jpg)
Example 1D
!78
0.5
0.4
0.3
0.2
0.5 0.5 0.5 0.4 0.3 0.2 0.2 0.2 0.35 0.5 0.5Signal
![Page 81: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/81.jpg)
Example 1D
!79
0.5
0.4
0.3
0.2
0.5 0.5 0.5 0.4 0.3 0.2 0.2 0.2 0.35 0.5 0.5Signal
Derivative
![Page 82: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/82.jpg)
Example 1D
!80
0.5
0.4
0.3
0.2
0.5 0.5 0.5 0.4 0.3 0.2 0.2 0.2 0.35 0.5 0.5
0.0
Signal
Derivative
![Page 83: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/83.jpg)
Example 1D
!81
0.5
0.4
0.3
0.2
0.5 0.5 0.5 0.4 0.3 0.2 0.2 0.2 0.35 0.5 0.5
0.0
Signal
Derivative
![Page 84: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/84.jpg)
Example 1D
!82
0.5
0.4
0.3
0.2
0.5 0.5 0.5 0.4 0.3 0.2 0.2 0.2 0.35 0.5 0.5
0.0 0.0
Signal
Derivative
![Page 85: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/85.jpg)
Example 1D
!83
0.5
0.4
0.3
0.2
0.5 0.5 0.5 0.4 0.3 0.2 0.2 0.2 0.35 0.5 0.5
0.0 0.0
Signal
Derivative
![Page 86: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/86.jpg)
Example 1D
!84
0.5
0.4
0.3
0.2
0.5 0.5 0.5 0.4 0.3 0.2 0.2 0.2 0.35 0.5 0.5
0.0 0.0 -0.1
Signal
Derivative
![Page 87: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/87.jpg)
Example 1D
!85
0.5
0.4
0.3
0.2
0.5 0.5 0.5 0.4 0.3 0.2 0.2 0.2 0.35 0.5 0.5Signal
Derivative 0.0 0.0 -0.1 -0.1 -0.1 0.0 0.0 0.15 0.15 0.0 X
![Page 88: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/88.jpg)
!86
Estimating DerivativesDerivative in Y (i.e., vertical) direction
Forsyth & Ponce (1st ed.) Figure 7.4 (top left & top middle)
![Page 89: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/89.jpg)
!87
Estimating DerivativesDerivative in Y (i.e., vertical) direction
Forsyth & Ponce (1st ed.) Figure 7.4 (top left & top middle)
Note: visualized by adding 0.5/128
![Page 90: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/90.jpg)
!88
Estimating DerivativesDerivative in X (i.e., horizontal) direction
Forsyth & Ponce (1st ed.) Figure 7.4 (top left & top right)
![Page 91: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/91.jpg)
!89
Derivative in Y (i.e., vertical) direction
Forsyth & Ponce (1st ed.) Figure 7.4 (top left & top middle)
Estimating Derivatives
![Page 92: CPSC 425: Computer Visionlsigal/425_2020W1/Lecture9.pdfLecture 8: Re-cap “Color” is not an objective physical property of light (electromagnetic radiation).Instead, light is characterized](https://reader036.fdocuments.us/reader036/viewer/2022071412/6109f234682f3921646e77bb/html5/thumbnails/92.jpg)
!90
Derivative in X (i.e., horizontal) direction
Forsyth & Ponce (1st ed.) Figure 7.4 (top left & top right)
Estimating Derivatives