Recognizing Deformable Shapes Salvador Ruiz Correa (CSE/EE576 Computer Vision I)

Goal We are interested in developing algorithms for recognizing and classifying deformable object shapes from range data. We are interested in developing algorithms for recognizing and classifying deformable object shapes from range data. 3-D Output Surface Mesh 3-D Laser Scanner Input3-DObject This is a difficult problem that is relevant in several application fields. This is a difficult problem that is relevant in several application fields. Rangedata (Cloud of 3-D points) Post-processing

Applications Computer Vision: Computer Vision: - Scene analysis - Industrial Inspection - Robotics Medical Diagnosis: Medical Diagnosis: - Classification and - Detection of craniofacial deformations.

Basic Idea Generalize existing numeric surface representations for matching 3-D objects to the problem of identifying shape classes. Generalize existing numeric surface representations for matching 3-D objects to the problem of identifying shape classes.

Main Contribution An algorithmic framework based on symbolic shape descriptors that are robust to deformations as opposed to numeric descriptors that are often tied to specific shapes. An algorithmic framework based on symbolic shape descriptors that are robust to deformations as opposed to numeric descriptors that are often tied to specific shapes.

What Kind Of Deformations? Toy animals 3-D Faces Normal Mandibles Neurocranium Normal Abnormal Shape classes: significant amount of intra-class variability

Deformed Infants’ Skulls Sagittal Coronal Normal Sagittal Synostosis Bicoronal Synostosis Fused Sutures Metopic Occurs when sutures of the cranium fuse prematurely (synostosis).

More Craniofacial Deformations Facial Asymmetry Sagittal Synostosis Bicoronal Synostosis Unicoronal Synostosis Metopic Synostosis

Alignment-verification Alignment-verification 3-D Range Scene Recognized Models Objects Database Find correspondences using numeric signature information. Estimate candidate transformations. Verification process selects the transformation that produces the best alignment. Models

Related Literature (1) This approach has been used very successfully in This approach has been used very successfully in industrial machine vision. Relevant investigations that use numeric signature representations for matching include: Splash representation – Stein and Medioni (IEEE PAMI, 1992) Splash representation – Stein and Medioni (IEEE PAMI, 1992) Spin image representation – Johnson and Hebert (IEEE PAMI, 1999). Spin image representation – Johnson and Hebert (IEEE PAMI, 1999).

Related Literature (2) Spherical signatures – Ruiz-Correa et al. ( IEEE CVPR 2001). Spherical signatures – Ruiz-Correa et al. ( IEEE CVPR 2001). Shape distributions – Osada et al. (SMI, 2001,2002). Shape distributions – Osada et al. (SMI, 2001,2002). Reflective symmetry descriptors – Kazhdan et al. (Algorithmica 2003). Reflective symmetry descriptors – Kazhdan et al. (Algorithmica 2003).

Alignment-Verification Limitations The approach does not extend well to the problem of identifying classes of similar shapes. In general: of identifying classes of similar shapes. In general: Numeric shape representations are not robust to deformations. Numeric shape representations are not robust to deformations. There are not exact correspondences between model and scene. There are not exact correspondences between model and scene. Objects in a shape class do not align. Objects in a shape class do not align.

Component-Based Methodology NumericSignatures Components SymbolicSignatures ArchitectureofClassifiers + Recognition And Classification Of Deformable Shapes Overcomes the limitations of the alignment-verification approach define Describespatialconfiguration

Efficient Object Recognition (1) Developed spherical spin image representation (SSI) : computational complexity O(ms). Developed spherical spin image representation (SSI) : computational complexity O(ms). Standard spin image (SI): computational complexity O(nms) (n~10 3, m~10 4, s~10 3 ). Standard spin image (SI): computational complexity O(nms) (n~10 3, m~10 4, s~10 3 ). Developed compressed SSI representation that requires O(mk) floats, k~40. Developed compressed SSI representation that requires O(mk) floats, k~40. Standard SIC (PCA) algorithm also requires O(md) floats but the proportionality constant is ~10 bigger. Standard SIC (PCA) algorithm also requires O(md) floats but the proportionality constant is ~10 bigger.

Efficient Object Recognition (3) 3-D Models - Clutter - Occlusion

Efficient Object Recognition (2)

Outline Mathematical Background. Mathematical Background. Formalize recognition and classification problems. Formalize recognition and classification problems. Approach and implementation. Approach and implementation. Experimental validation: recognition and classification experiments. Experimental validation: recognition and classification experiments. Discuss future work. Discuss future work. Conclude. Conclude.

SVMs - Geometry (1) X X X X X X X X X X X X X X X X X X X X X X X X X Separate classes using a hyperplane X Input Space

SVMs (2) X X X X X X X X X X XX X X X X X X X X X X X X X X Separating Hyperplane Feature Space Plane is a function of the inner product of the points in feature space

SVMs (3) Input Space F( ) = F( X ) = X Feature Space

SVMs – Kernel Trick (4) Input Space F( Y ) = Z F( Y’ ) = Z’ Feature Space = = K(Y,Y’) = = K(Y,Y’) K, kernel function

SVMs – Kernel Trick (5) = = K(Y,Y’) = = K(Y,Y’) K, kernel function example: K(Y,Y’) = exp(- g 2 ||Y-Y’|| 2 )

SVMs (2) SVMs successful even in non-separable cases X X X X X X X X X X XX X X X X X X X X X X X X X X Feature Space m m

Recognition Problem (1) We are given a set of surface meshes {C 1,C 2,…,C n } which are random samples of two shape classes C We are given a set of surface meshes {C 1,C 2,…,C n } which are random samples of two shape classes C C1C1 C2C2 CkCk … CnCn …

Recognition Problem (2) The problem is to use the given meshes and labels to construct an algorithm that determines whether shape class members are present in a single view range scene. The problem is to use the given meshes and labels to construct an algorithm that determines whether shape class members are present in a single view range scene.

Classification Problem (1) We are given a set of surface meshes {C 1,C 2,…,C n } which are random samples of two shape classes C +1 and C -1, We are given a set of surface meshes {C 1,C 2,…,C n } which are random samples of two shape classes C +1 and C -1, where each surface mesh is labeled either by +1 or -1. where each surface mesh is labeled either by +1 or Normal Skulls C +1 Abnormal Skulls C -1 C1C1 C2C2 CkCk C k+1 C k+2 … CnCn …

Classification Problem (2) The problem is to use the given meshes and labels to construct an algorithm that predicts the label of a new surface mesh C new. The problem is to use the given meshes and labels to construct an algorithm that predicts the label of a new surface mesh C new. Is this skull normal (+1) or abnormal (-1)? C new

Classification Problem (3) We also consider the case of “missing” information: We also consider the case of “missing” information: 3-D Range Scene Single View Shape class of normal heads (+1) Shape class of abnormal heads (-1) Are these heads normal or abnormal? Clutter and Occlusion

Assumptions All shapes are represented as oriented surface meshes of fixed resolution. All shapes are represented as oriented surface meshes of fixed resolution. The vertices of the meshes in the training set are in full correspondence. The vertices of the meshes in the training set are in full correspondence. Finding full correspondences : hard problem yes … but it is approachable ( use morphable models technique: Blantz and Vetter, SIGGRAPH 99; C. R. Shelton, IJCV, 2000; Allen et al., SIGGRAPH 2003). Finding full correspondences : hard problem yes … but it is approachable ( use morphable models technique: Blantz and Vetter, SIGGRAPH 99; C. R. Shelton, IJCV, 2000; Allen et al., SIGGRAPH 2003).

Four Key Elements To Our Approach Architecture of Classifiers Numeric Signatures Components Symbolic Signatures Recognition And Classification Of Deformable Shapes

Numeric Signatures ArchitectureofClassifiers NumericSignatures Components SymbolicSignatures Encode Local Surface Geometry of an Object

Numeric Signatures: Spin Images Rich set of surface shape descriptors. Rich set of surface shape descriptors. Their spatial scale can be modified to include local and non-local surface features. Their spatial scale can be modified to include local and non-local surface features. Representation is robust to scene clutter and occlusions. Representation is robust to scene clutter and occlusions. P Spin images for point P 3-D faces

Components NumericSignatures Components SymbolicSignatures ArchitectureofClassifiers Equivalent Numeric Signatures: Encode Local Geometry of a Shape Class define

How To Extract Shape Class Components? …… ComponentDetector ComputeNumericSignatures Training Set SelectSeedPoints RegionGrowingAlgorithm Grown components around seeds

Labeled Surface Mesh Selected 8 seed points by hand Component Extraction Example RegionGrowing Grow one region at the time (get one detector per component) Detected components on a training sample

How To Combine Component Information? … Extracted components on test samples Note: Numeric signatures are invariant to mirror symmetry; our approach preserves such an invariance.

Symbolic Signatures NumericSignatures Components SymbolicSignatures Architecture of Classifiers Encode Geometrical Relationships Among Components

Symbolic Signature Symbolic Signature at P Labeled Surface Mesh Matrix storing component labels EncodeGeometricConfiguration Critical Point P

Symbolic Signature Construction Critical Point P a P b P a b Project labels to tangent plane at P tangent plane Coordinate system defined up to a rotation Normal

Symbolic Signatures Are Robust To Deformations P Relative position of components is stable across deformations: experimental evidence

Architecture of Classifiers Numeric Signatures Components Symbolic Signatures Architecture of Classifiers Learns Components And Their Geometric Relationships

Proposed Architecture (Classification Example) Input LabeledMesh ClassLabel(Abnormal) Verify spatial configuration of the components IdentifySymbolicSignatures IdentifyComponents Two classification stages SurfaceMesh

At Classification Time (1) Bank of ComponentDetectors Surface Mesh AssignsComponentLabels Labeled Surface Mesh Multi-wayclassifier Identify Components

Labeled Surface Mesh Bank of SymbolicSignaturesDetectors Symbolic pattern for components 1,2,4 At Classification Time (2) Symbolic pattern for components 5,6,8 AssignsSymbolicLabels Two detectors

Confidence Level Finding Critical Points On Test Samples 0 Critical Point 1 +1 Margin associated with the component detector classifiers

Architecture Implementation ALL our classifiers are (off-the-shelf) ν - Support Vector Machines ( ν - SVMs) (Schölkopf et al., 2000 and 2001). ALL our classifiers are (off-the-shelf) ν - Support Vector Machines ( ν - SVMs) (Schölkopf et al., 2000 and 2001). Component (and symbolic signature) detectors are one-class classifiers. Component (and symbolic signature) detectors are one-class classifiers. Component label assignment: performed with a multi-way classifier that uses pairwise classification scheme. Component label assignment: performed with a multi-way classifier that uses pairwise classification scheme. Gaussian kernel. Gaussian kernel.

Experimental Validation Recognition Tasks: 4 (T1 - T4) Classification Tasks: 3 (T5 – T7) No. Experiments: 5470 Setup RecognitionClassification Laser Rotary Table

Shape Classes

Enlarging Training Sets Using Virtual Samples Displacement Vectors Originals Morphs Twist (5deg) + Taper - Push + Spherify (10%) Push +Twist (10 deg) +Scale (1.2) Original Global Morphing Operators Morphs Physical Modeling (14) University of WashingtonElectrical Engineering

Other Approaches Tried standard alignment-verification. Tried standard alignment-verification. Alignment-verification with PCA. Alignment-verification with PCA. However, no systematic comparison was performed due to poor performance. However, no systematic comparison was performed due to poor performance. Existing methods for classifying shapes do not use range data. Existing methods for classifying shapes do not use range data. P. Golland, NIPS 2001, J. Matrin et al. IEEE PAMI P. Golland, NIPS 2001, J. Matrin et al. IEEE PAMI 1998.

Task 1: Recognizing Single Objects (1) No. Shape classes: 9. No. Shape classes: 9. Training set size: 400 meshes. Training set size: 400 meshes. Testing set size: 200 meshes. Testing set size: 200 meshes. No. Experiments: No. Experiments: No. Component detectors:3. No. Component detectors:3. No. Symbolic signature detectors: 1. No. Symbolic signature detectors: 1. Numeric signature size: 40x40. Numeric signature size: 40x40. Symbolic signature size: 20x20. Symbolic signature size: 20x20. No clutter and occlusion. No clutter and occlusion.

Task 1: Recognizing Single Objects (2) Snowman: 93%. Snowman: 93%. Rabbit: 92%. Rabbit: 92%. Dog: 89%. Dog: 89%. Cat: 85.5%. Cat: 85.5%. Cow: 92%. Cow: 92%. Bear: 94%. Bear: 94%. Horse: 92.7%. Horse: 92.7%. Human head: 97.7%. Human face: 76%. Recognition rates (true positives) (No clutter, no occlusion, complete models)

Tasks 2-3: Recognition In Complex Scenes (1) No. Shape classes: 3. No. Shape classes: 3. Training set size: 400 meshes. Training set size: 400 meshes. Testing set size: 200 meshes. Testing set size: 200 meshes. No. Experiments: No. Experiments: No. Component detectors:3. No. Component detectors:3. No. Symbolic signature detectors: 1. No. Symbolic signature detectors: 1. Numeric signature size: 40x40. Numeric signature size: 40x40. Symbolic signature size: 20x20. Symbolic signature size: 20x20. T2 – low clutter and occlusion. T2 – low clutter and occlusion.

Task 2-3: Recognition in Complex Scenes (2) ShapeClassTruePositivesFalsePositivesTruePositivesFalsePositives Snowmen91%31%87.5%28% Rabbit90.2%27.6%84.3%24% Dog89.6%34.6%88.12%22.1% Task 2 Task 3

Task 2-3: Recognition in Complex Scenes (3)

Task 4: Recognizing Human Heads (1) No. Shape classes: 1. No. Shape classes: 1. Training set size: 400 meshes. Training set size: 400 meshes. Testing set size: 250 meshes. Testing set size: 250 meshes. No. Experiments: 710. No. Experiments: 710. No. Component detectors:8. No. Component detectors:8. No. Symbolic signature detectors: 2. No. Symbolic signature detectors: 2. Numeric signature size: 70x70. Numeric signature size: 70x70. Symbolic signature size: 12x12. Symbolic signature size: 12x12.

Task 4: Recognizing Human Heads (2) Recognition Rate % Clutter % Clutter < 40 % Occlusion < 40 % Occlusion FP rate: ~1%, (44,0.9) (40,0.88)

Task 4: Recognizing Human Heads (3)

Task 5: Classifying Normal vs. Abnormal Human Heads (1) No. Shape classes: 6. No. Shape classes: 6. Training set size: 400 meshes. Training set size: 400 meshes. Testing set size: 200 meshes. Testing set size: 200 meshes. No. Experiments: No. Experiments: No. Component detectors:3. No. Component detectors:3. No. Symbolic signature detectors: 1. No. Symbolic signature detectors: 1. Numeric signature size: 50x50. Numeric signature size: 50x50. Symbolic signature size: 12x12. Symbolic signature size: 12x12.

Task 5: Classifying Normal vs. Abnormal Human Heads (1) ShapeClasses Classification Accuracy % Normal vs. Abnormal 1 98 Normal vs. Abnormal Abnormal 1 vs Abnormal 1 vs Abnormal 1 vs Full models Normal (convex combinations of Normal and Abnormal 1) 65%-35%50%-50%25%-75% Abnormal Five Cases

Task 6: Classifying Normal vs. Abnormal Human Heads In Complex Scenes(1) No. Shape classes: 2. No. Shape classes: 2. Training set size: 400 meshes. Training set size: 400 meshes. Testing set size: 200 meshes. Testing set size: 200 meshes. No. Experiments: No. Experiments: No. Component detectors:3. No. Component detectors:3. No. Symbolic signature detectors: 1. No. Symbolic signature detectors: 1. Numeric signature size: 100x100. Numeric signature size: 100x100. Symbolic signature size: 12x12. Symbolic signature size: 12x12.

Task 6: Classifying Normal vs. Abnormal Human Heads In Complex Scenes(1) ShapeClasses Classification Accuracy % Normal vs. Abnormal 1 88 RR full models (no clutter and occlusion) ~ 96% (250 experiments per class) Clutter < 15% and occlusion < 50% Range scenes – single view

Task 7: Classifying Normal vs. Abnormal Neurocranium (1) No. Shape classes: 2. No. Shape classes: 2. Training set size: 400 meshes. Training set size: 400 meshes. Testing set size: 200 meshes. Testing set size: 200 meshes. No. Experiments: No. Experiments: No. Component detectors:3. No. Component detectors:3. No. Symbolic signature detectors: 1. No. Symbolic signature detectors: 1. Numeric signature size: 50x50. Numeric signature size: 50x50. Symbolic signature size: 15x15. Symbolic signature size: 15x15.

Task 7: Classifying Normal vs. Abnormal Neurocranium (2) ShapeClasses Classificatio n Accuracy % Normal vs. Abnormal 89 No clutter and occlusion 100 Experiments Abnormal (sagittal synostosis ) Superimposed models Normal

Main Contributions (1) A novel symbolic signature representation of deformable shapes that is robust to intra-class variability and missing information, as opposed to a numeric representation which is often tied to a specific shape. A novel symbolic signature representation of deformable shapes that is robust to intra-class variability and missing information, as opposed to a numeric representation which is often tied to a specific shape. A novel kernel function for quantifying symbolic signature similarities. A novel kernel function for quantifying symbolic signature similarities.

Main Contributions (2) A region growing algorithm for learning shape class components. A region growing algorithm for learning shape class components. A novel architecture of classifiers for abstracting the geometry of a shape class. A novel architecture of classifiers for abstracting the geometry of a shape class. A validation of our methodology in a set of large scale recognition and classification experiments aimed at applications in scene analysis and medical diagnosis. A validation of our methodology in a set of large scale recognition and classification experiments aimed at applications in scene analysis and medical diagnosis.

Main Contributions (3) Our approach: Our approach: - Is general can be applied to a variety of shape classes. - Is robust to clutter and occlusion - It Works in practice - Is a step forward in 3-D object recognition research.

Future Work (1) Encouraging results but need to make a more extensive quantification in order to characterize the algorithm wrt: Encouraging results but need to make a more extensive quantification in order to characterize the algorithm wrt: - sensor noise and mesh resolution, - numeric and symbolic signature parameters, - intra-class variability.

Future Work (2) Need to find the break points. Need to find the break points. Investigate semi-automatic selection of seed points and critical points. At least, provide guidelines. Investigate semi-automatic selection of seed points and critical points. At least, provide guidelines. Combine our approach with the alignment- verification technique. Combine our approach with the alignment- verification technique. Simultaneous training of all classification stages. Simultaneous training of all classification stages.

Thanks! Now your questions …

Spare slides

So What Is A Component? Classification function, an outlier detector (one-class SVM) that defines two half-spaces in feature space: Classification function, an outlier detector (one-class SVM) that defines two half-spaces in feature space: Separating hyper-plane (feature space) Normal All mesh points of the shape class whose numeric signatures lie on this “side” belong to the component. Outliers on this side x x x x x x x x x

Enlarging Training Sets Using Virtual Samples Displacement Vectors Originals Morphs Twist (5deg) + Taper - Push + Spherify (10%) Push +Twist (10 deg) +Scale (1.2) Original Global Morphing Operators Morphs Physical Modeling (14) University of WashingtonElectrical Engineering

Complexity (Worst Case) Numeric (symbolic) signature construction: O(ns) Numeric (symbolic) signature construction: O(ns) Bank of detectors: O(nsc) Bank of detectors: O(nsc) Label Assigner: O(nsc 2 ) Label Assigner: O(nsc 2 )Where: n – number of scene points: ~10 4 n – number of scene points: ~10 4 s – signature size: ~ s – signature size: ~ c – number of detectors: ~10 c – number of detectors: ~10 University of WashingtonElectrical Engineering