Computer Vision Seminar Shape Representation Yaron Berlinsky 10032021
Computer Vision Seminar Shape Representation Yaron Berlinsky 10/03/2021
Shape Representation - what for? 4 To reason about an entity we must first represent the entity. 10/03/2021
Shape Representation - what for? • Real world Image processing • Shape representation • Image understanding shape 10/03/2021 recognition 0110010001000000100111 0010100111101
Topics 4 Definitions 4 Attributes 4 Popular Stratagies 10/03/2021
Definitions 4 Object 4 Abstraction 4 Representation 10/03/2021
Object 4 An object is something that can be seen or touched, material thing (Oxford dictionary) 10/03/2021
Abstraction 4 Idea of quality separate from actual examples (Oxford dictionary) 10/03/2021 • ball • sphere
Representation 4 A way of symbolizing an object 10/03/2021
Attributes Of A Good Representation 4 sufficient 4 wide domain 4 unique 4 unambiguous 4 generative 4 stable 4 convenient 10/03/2021
Sufficient Is this representation sufficient enough? Depends on the application. . . 10/03/2021
Wide Domain 4 Able to represent many different classes of entities 4 E. g. numbers for elements in a queue 3 2 10/03/2021 1
Unique 4 every distinct member of its domain has a single distinct representation. Not unique : dog unique : collie pitbull 10/03/2021 dog cocker-spaniel
Unambiguous 4 An entity may have different representations but no two distinct entities may have a common representation. שלוש 3 III 10/03/2021 שנים 2 II
Generative 4 Capable of directly generating (recovering) the represented entity 1 8 2 Chain-code : 436476872832 10/03/2021 7 3 6 4 5
Stable 4 small perturbations ( )הפרעות do not induce large changes in the representation of the entity. 10/03/2021
Convenient 4 A representation may exhibit all the characteristics that we have discussed so far and yet not be convenient for a task. e. g. an assembly line robot who’s task is to filter out rectangels form other shapes might use chaine code representation. Yet for a police computerized camera that is supposed to compare faces in the crowd to a DB of suspects this is not enough. 10/03/2021
Popular Strategies 4 Volume based : – Describe the object volumetrically – Combination of primitive volumes commonly used, eg. cubes, tetrahedra, and discs – Provide more access to global relationships – Do not provide direct surface information about the object – Can represent only closed (boundaryless) surfaces e. g. Symmetric Axis Transform 10/03/2021
Popular Strategies 4 Surface based : – Surface of object represented by a single closed parametric grid. – Better suited for partial surfaces. E. g. Parametric Bicubic Patches Gaussian- Image Representations 10/03/2021
Popular Strategies 4 Others: – Chain code. – Distance vs. Angle. – Fourier Transform Moment – Generalized Cylinders – Visual Potential 10/03/2021
Chain Code 10/03/2021
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Attributes 4 wide domain 4 unique 4 unambiguous 2 generative - 2 D only stable - depends on tolerance 10/03/2021
Distance vs. Angle 10/03/2021
Distance vs. Angle 4 Find point of balance. 4 Measure distance to edges. 4 Plot the graph of distance vs. angle. Taking the dist. vs. angle one step further we get. . . 10/03/2021
Fourier Descriptor 10/03/2021
Attributes 4 wide domain 4 unique 4 unambiguous 4 generative stable - depends upon tolerance 10/03/2021
Moment 4 find center of mass 4 the moment: 10/03/2021
Moment 10/03/2021
Moments 4 since we get invariant values the moments are not affected by transition or rotation. 4 By normalizing the values, we can make the moment be indifferent to scaling 10/03/2021
Attributes 4 wide domain 8 unique - no 8 unambiguous - no 8 generative - no 4 stable - no 10/03/2021
Parametric Bicubic Patches 4 Split the object to simpler bicubic patches that can be represented by relatively simple mathematical equations. 10/03/2021
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Attributes 4 generative 4 stable 4 popular in computer graphics 4 Possibility of several equally acceptable bicubic approximations to any given surface makes it inappropriate for surface matching 10/03/2021
Symmetric Axis Transform • A. k. a Blum Transform, Medial Axis Transform. • Formally : the object is the logical union of all its maximal discs. 10/03/2021
Symmetric Axis Transform(cont. ) 4 Description : – Locus of centers a. k. a symmetric axis. – Radius at each point 4 May be thought of as grass fire spreading from the border inwards. 10/03/2021
Attributes 4 wide domain 4 unique 4 unambiguous 4 generative 8 not stable - small changes affect dramatically 4 Primarily used in biological applications 10/03/2021
Generalized Cylinders 4 Binford 1971 4 an extension of SAT. 4 Shape represented by an ordinary cylinder sweeping the cross-section along an arbitrary space curve (axis/spine) 10/03/2021
Generalized Cylinders 4 Decomposition of 3 D shape-description problems into lower-order problems 10/03/2021
Generalized Cylinders 4 A generalized cylinder is thus defined by 2 a cross section, 2 an axis 2 a sweeping rule. 10/03/2021
Generalized Cylinders 10/03/2021
Generalized Cylinders 10/03/2021
Attributes 4 wide domain - depends on implementation (redundancy vs. wide domain ) 4 unique 4 generative 4 stability is doubtful 4 Decomposition of complex structures is difficult. 4 Used mainly for object recognition 4 been used in working systems. 10/03/2021
Gaussian Image 4 Surface normal vector information for any object can be mapped onto a unit sphere, called the Gaussian sphere. 4 Mapping is called the Gaussian image of the object. 10/03/2021
Extended Gaussian Image 4 The mapping is: Surface normals for each point of the object are placed so that their 4 tails lie at the center of the Gaussian sphere 4 heads lie on a point on the sphere appropriate to the particular surface orientation 10/03/2021
Extended Gaussian Image We can extend this process so that 4 a weight is assigned to each point on the Gaussian sphere equal to the area of the surface having the given normal 4 This mapping is called the extended Gaussian image (EGI). 4 Weights are represented by vectors parallel to the surface normals, with length equal to the weight 10/03/2021
EGI 10/03/2021
Attributes 4 wide domain 8 not unique 8 not unambiguous 8 not generative 4 stable - with limitations 4 invariant to translation and scaling 4 position independence 10/03/2021
Visual Potential 4 Aspect - topological structure of the singularities in a single view. 4 A graph in which each node represents an aspect of the object, and each edge the possibility of transiting from one aspect to another under motion of the observer [Turner 74]. 4 Represents in a concise way any visual experience an observer can obtain by looking at the object when traversing any orbit through space. 10/03/2021
Visual Potential 10/03/2021
Attributes 4 wide domain 4 unique 4 unambiguous 4 generative 7 not stable 10/03/2021
Summary 4 The above methods are deterministic; in practice, uncertainties in shape that result from the noise in measurement have to be considered [Ayache 88, Ikeuchi 88] 4 The above methods are based on geometric models, they are more appropriate for describing specific objects, particularly artificial ones with regular structures 10/03/2021
Summary 4 Symbolic models are more appropriate for natural objects that are better defined in terms of generic characteristics (e. g. . small, red, rough) than precise shape; useful for matching 10/03/2021
Questions? 10/03/2021
References 4 Books : – Nalwa “a guided tour of computer vision” – Gonzaless, “Image analysis and computer vision” – Jain 4 Web: – http: //web. mit. edu/manoli/ecimorph/www/code/MMorph. html – http: //www. cs. ubc. ca/~clee/cg/proj/index. html – http: //www. dai. ed. ac. uk/CVonline/LOCAL_COPIES/MARSHAL L/node 53. html#figuresame_EGI – http: //www. cs. uwa. edu. au/~cheng/index. html 10/03/2021
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