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 Recognizing Objects: Feature Matching
•<= /span>Problem: Match when viewing conditions change a lot.
–<= /span>Lighting changes: brightness constancy false. =
–<= /span>Viewpoint changes: appearance changes, many viewpoints.
•<= /span>One Solution: Match using edge-based features. = ;
–<= /span>Edges less variable to lighting, viewpoint. 
–<= /span>More compact representation can lead to efficiency= .
•<= /span>Match image or object to image
–<= /span>If object, matching may be asymmetric <= /span>
–<= /span>Object may be 3D.
•<= /span>Line finding was an example: line=3Dobject; points= =3Dimage.
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Lighting affects appearance
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km2Q3qxltkZ+TyJWxgqV+8Ac4z2zimapqV7bW6PDNsYzKhPlxNlSkhIw8bDqoOcZ469a/9l= ------=_NextPart_01C4383C.6E28D720 Content-Location: file:///C:/A2CBB24E/Recognition_files/slide0153.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" CMSC 426: Image Processing (Computer Vision)
Problem Definition
•<= /span>An Image is a set of 2D geometric features, along with positions.
•<= /span>An Object is a set of 2D/3D geometric = features, along with positions. =
•<= /span>A pose positions the object relative to the image.
–<= /span>2D Translation; 2D translation + rotation; 2D translation, rotation and scale; planar or 3D obje= ct positioned in 3D with perspective or scaled orth.&= #13;
•<= /span>The best pose places the object features nearest the image features
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Strategy
B= uild feature descriptions
S= earch possible poses.  =
C= an search space of poses  <= /span>
Or search feature matches, which produce pose
T= ransform model by pose.
C= ompare transformed model and image.
P= ick best pose.
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Presentation Strategy
Already discussed finding features.= 3;
First discuss picking = best pose since this defines the problem.
Second discuss search methods appropriate for 2D.
Third discuss transfor= ming model in 2D and 3D.
Fourth discuss search = for 3D objects.
•<= /span>
•<= /span>
•<= /span>
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Example
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Evaluate Pose
= 226;We look at this first, since it defines the problem.
&#= 8226;Again, no perfect measure;
= 211;Trade-offs between veracity of measure and computational considerations.
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Chamfer Matching
<= span style=3D'font-family:Arial;color:#FF9900;mso-color-index:4;mso-special-for= mat: lastCR;display:none'>
For every edge point in the transformed object, compute the distance to the nearest image edge point.  Sum distances.
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Main Feature:
 Every model point matc= hes an image point.
 An image point can mat= ch 0, 1, or more model points.
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 Variations
•<= /span>Sum a different distance
–<= /span>f(d) =3D d2  =
–<= /span>or Manhatt= an distance.
–<= /span>f(d) =3D 1 if d < threshold, 0 otherwise.
This is called bounded error.
•<= /span>Use maximum distance instead of sum.
–<= /span>This is called: directed Hausdorff distance.
•<= /span>Use other features
–<= /span> Corners.
–<= /span>Lines.  Then position and angles of lines must be similar.
•<= /span>Model line may be subset of image line.
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Other comparisons
Enforce each image f= eature can match only one model feature. Enforce continuity, ordering along curves.
<= span class=3DBB style=3D'position:absolute;left:-4.26%'>•These are= more complex to optimize.
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Presentation Strategy
Already discussed finding features.= 3;
First discuss picking = best pose since this defines the problem.
Second discuss search methods appropriate for 2D.
Third discuss transfor= ming model in 2D and 3D.
Fourth discuss search = for 3D objects.
•<= /span>
•<= /span>
•<= /span>
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Pose Search
<= span class=3DBB style=3D'position:absolute;left:-4.07%'>•Simplest = approach is to try every pose.
Two probl= ems: many poses, costly to evaluate each. We can re= duce the second problem with:
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Pose: Chamfer Matching with the Distance Transform
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= Example: Each pixel has (Manhat= tan) distance to nearest edge pixel.=
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D.T. Adds Efficiency
Compute once.
Fast algo= rithms to compute it.
Makes Cha= mfer Matching simple.
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Then, try all translations of model edges.  Add distances under each edge pixel.=
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Computing Distance Transform
•<= /span>It’s only done once, per problem, not once <= /span>per pose.
•<= /span>Basically a shortest path problem.
•<= /span>Simple solution passing through image once = for each distance.
–<= /span>First pass mark edges 0. 
–<= /span>Second, mark 1 anything next to 0, unless it’= ;s already marked.&n= bsp; Etc….
•<= /span>Actually, a more clever method requires 2 <= /span>= passes. 
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Pose: Ransac
Match enough features = in model to features in image to determine pose. 
Examples: <= /div>
match a point and deter= mine translation.
match a corner and determine translation and rotation.
Points and translation, rotation, scaling?
Lines and rotation and translation?
•<= /span>
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Pose: Generalized Hough Transfo= rm
Like Hough Transform= , but for general shapes. Example: match one p= oint to one point, and for every rotation of the object its translation is determined.
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Presentation Strategy
Already discussed finding features.= 3;
First discuss picking = best pose since this defines the problem.
Second discuss search methods appropriate for 2D.
Third discuss transforming model in 2D and 3D.
Fourth discuss search = for 3D objects.
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Computing Pose: Points
&#= 8226;Solve I =3D S*P.
&= #8211;In Structure-from-Motion, we knew I.
&= #8211;In Recognition, we know P.
&#= 8226;This is just set of linear equations
Ok, maybe with some non-linear constraints.
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Linear Pose: 2D Translation
We know x,y,u,v, need to find translation. = ;
For one point, u1 - x1 = =3D tx ;  v1 - x1 =3D ty&= #13;
For more points we can solve a least squares problem.
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Linear Pose: 2D rotation, transla= tion and scale
 Notice a and b can take on any values.
 Equations linear in a, b, translation.
 Solve exactly with 2 po= ints, or = overconstrained system with more.
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Linear Pose: 3D Affine
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Pose: Scaled Orthographic Project= ion of Planar points
s1,3, s2,3 disappear.  Non-linear constraints disappear = with them.
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Non-linear pose
A bit trickier.  Some results:
2D rotation and translation.  Need 2 <= span style=3D'position:absolute;top:43.5%;left:12.17%;width:79.4%;height:6.75%'= >points.
3D scaled orthographic.  Need 3 points,= give 2 solutions. 
3D perspective, camera known.  Need 3 points.  Solve 4th degree polynomial.  4 solutions.
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Transforming the Object
We don’t really want to know pose, we wa= nt to know what the obje= ct looks like in that pose.
We start with:
Solve for pose:
= Project rest of points:
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Transforming object with Linear Combina= tions
No 3D model, but we’ve seen object twice before.
See four points in th= ird image, need to fi= ll in location of other points.=  
Just use rank theorem.
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4czXRcsLxdyoIjrqyE6QlANMNEQUSZBSTKw0lr/xW6UUGVPAIe6jLPgiQW0BRo3WFI3FkeYRhcoR ompAjeli4z3sBNTyZK6T52GBHfWwsAWc4hp/empTJbe5Pw6FA7eoQDXYwzoJyZGsMoAmCdRKgbFO IKxo3U9ZY9U6JmAVdrPLq4Rs58oTwLI9hGhodsxKWBn8dQSHlUAoAvXSeIIjEBhIAGhm2UB8hoCe yKMLAchhgS8wcJhQ2CkofkmXBewzkEHMAGgzENITHpMuTjDCaS1Q0Q0ws5mt/cD42GJaqrkgt44t FA6CS9x4RgAAOw== ------=_NextPart_01C4383C.6E28D720 Content-Location: file:///C:/A2CBB24E/Recognition_files/slide0176.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" CMSC 426: Image Processing (Computer Vision)
Recap: Recognition w/ RANSAC
<= span style=3D'font-size:75%'>1.Find features in model and image.
<= span style=3D'font-size:71%'>Such as corners.
<= span style=3D'font-size:75%'>2.Match enough to determine pose.
= Such as 3 = points for planar object, scaled orthographic projection.
<= span style=3D'font-size:75%'>3.Determine pose.
<= span style=3D'font-size:75%'>4.Project rest of object features into image.
<= span style=3D'font-size:75%'>5.Look to see how many image features they match.
= Example: w= ith bounded error, count how many object features project near an image feature.
<= span style=3D'font-size:75%'>6.Repeat steps 2-5 a bunch of times.
<= span style=3D'font-size:75%'>7.Pick pose that matches most features.
------=_NextPart_01C4383C.6E28D720 Content-Location: file:///C:/A2CBB24E/Recognition_files/slide0188.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" CMSC 426: Image Processing (Computer Vision)
Figure from “Object recognition using alignment,” D.P. Huttenlocher and S.= = Ullman, Proc. Int. Conf. Computer Vision, 1986, copyright IEEE, 1986
Figure 18.1 - caption tells the story
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Recognizing 3D Objects
&#= 8226;Previous approach will work.
= 226;But slow.  RANSAC considers n3<= /span>m3<= /span> possible matches.  About m3 correct. 
&#= 8226;Solutions:
= 211;Grouping.  Find features coming from = single object.
= 211;Viewpoint invariance.  Match to small s= et of model features that could produce them.
------=_NextPart_01C4383C.6E28D720 Content-Location: file:///C:/A2CBB24E/Recognition_files/slide0182.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" CMSC 426: Image Processing (Computer Vision)
Grouping: Continuity
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