1. 1 A Methodology for automatic retrieval of similarly shaped machinable components Mark Ascher - Dept of ECE

2. 2 Motivation Retrieval of similarly shaped components can: –Add functionality to existing CAD databases –allow for the reuse of process plans which can both speed up and reduce the cost of development. Challenges Retrieval of similarly shaped components has many challenges: –Multiple interpretations –Interacting features –Topological differences do not guarantee component dissimilarity –Graph matching solution is computationally intensive

3. 3 Examples of Challenges Example of components with similar features and different shapes Both Components Contain: 1 Slot 2 Blind Slots 1 Pocket Part1 Part2 Part1 Part2 idSlotBlindSlotStepPocketHole 1 1 2 2 0 0 1 10 0

4. 4 Examples of Challenges Example of multiple interpretations and representation complexity Part1 Part2 idSlotBlindSlotStepPocketHole 1 3 2 0 0 0 0 00 0 Part3 Part4 4 1 0 2 0 0 1 10 0

5. 5 Contributions Retrieval of sub pieces to cover a component –Use of Maximal Feature Sub-graphs to divide a component Use of type abstraction hierarchies to guide similarity search –Feature and interaction Histogram based –Ability to abstract Features and Interactions of machinable components –Ability to determine distances of features and interactions based on objective criterion

6. 6 Related Work Shape Based Similarity Retrieval (Eakins) –Two dimensional parts –retrieved complete components Volumetric Reasoning (Lee et al) and Planar Reasoning (Cohn et al) –Groundwork for symbolic volumetric reasoning –Does not address part matching Content Retrieval From Images Based on Knowledge of Shape (Hsu et al) –Worked with medical images –Presented the Type Abstraction Hierarchy Concept

7. 7 Related Work 3D Model Shape Based Similarity Retrieval (Osada et al, Regli et al) –Uses D2 Distance measures –Works well for simple models Feature Based Model Retrieval (Regli et al) –Retrieves complete models –Feature interaction representation too simplistic –No method for indexing

8. 8 Problem Formulation The problem simply stated is: Given a component find components in a database that have the same or the most similar shape to the given component. Given a component represented as a set of features F and a set of interactions between them I find the component in the database that contain the closest representation to the given component. The closest is defined as Where E is the existing part database, q indicates the query part, S is the set of Sub-parts in the query component. And df and di are the feature and interaction distance functions respectively.

9. 9 Problem Formulation Components represented as a qualitative model –Features are nodes –Interactions are directed labeled edges R 1,2, where the labels are nxm qualitative matrices –Requires a unique way to interpret a component as features

10. 10 Features A Features is represented as a 4-tuple (T, f, D, I) where: –T is the type (slot, hole, etc.) Slot –f is the sweep face (set of points) {(1,1,0),(1,2,0),(2,2,0),(2,1,0)} –D is the sweep direction (vector) (0,0,-1) –I is the sweep interval (distance) (2) Additional information that can be maintained for a feature –Finish –Accessibility –Tolerances –etc Slot I f D T=

11. 11 Set of Canonical Features Slot Pocket Blind Slot Blind Step Step Hole Note: Holes are modeled similar to pockets for Interaction Characterization, But sweep face is modeled as a center and radius

12. 12 Interactions Interactions Represented as an nxm matrix where: –n is the number of faces in feature 1(f1) –m is the number of faces in feature 2 (f2) –Entries are in the set { +, -, s, i} + indicates that f1 lies in the positive half space of f2 - indicates that f1 lies in the negative half space of f2 s indicates they lie on the same plane I indicates that the features interact R 5,2

13. 13 Interactions Continued If only orthonormal features are considered –Results in 6x6 interaction Matrices –The near diagonal data points contain the pertinent data –The number of unique columns is reduced to 4 types +s indicates a shared face with no internally points shared -s indicates a shared face with internally shared points -- indicates a face that is interior to both faces of the other feature -+ indicates a face that is not interior to one face of the other feature –The following Combinations are invalid: ++ can not be outside both faces parallel to the face of interest ss can not be the same as two faces which bound a feature +s-s+---

14. 14 Interactions Continued For feature interactions Pairs of parallel Faces need to be compared Resulting in 7 Feasible Combinations: -s Face 1Face 2Relation of faces to other Feature -s +s -+ -- -+ +s Both Faces Shared One Face Shared Other Inside One face shared, Other Outside Opp Not Possible Both Faces Inside One Face Inside, Other Outside Both Outside One Face Shared, Other Outside 1 2 4 5 6 7 3 Type

15. 15 Interactions Continued Each Interaction Type has an inverse. -s Face 1Face 2Inverse Interaction -s -+ -- -+ +s 1 3 2 6 5 4 7 1 2 4 5 6 7 3 Type

16. 16 Interactions Continued Several types indicate a family of interactions. -s Face 1Face 2Interaction Family -+ +s Intrusion Face Pass Through 3 7 6 Type ---+Improper Interaction5

17. 17 Show All Interactions Here

18. 18 Example of Interaction Directedness Delta Volume Slot to PocketPocket to Blindslot

19. 19 Definition of Closeness (Distance Measures) Distance measures characterize the distance between two features or two interactions. Objectives for the distance measures were: Determinable based on the data available Objectively based Additional desirable properties include: Ease of calculation Scalable to other features/interactions

20. 20 Feature Distance Measure Measures Considered For Comparison –Number of Faces created on the component Parallel to D Perpendicular to D –Number of internal Edges created on the component –Number of total Edges created on the component –Number of non-convex Corners created by feature –Number of Accessibility faces

21. 21 Interaction Distance Measure Measures Considered For Comparison –Number of Faces created on the component –Number of Edges created on the component –Number of convex Corners created on the component –Number of Corners created on the component –Histogram of Interaction Symbols {-, +, S, I} –Histogram of Parallel face types { (--,--), (-s,--),…} –Histogram of Single – Parallel Face interactions { --. +-, +s, -s} –Number of relative face changes to equate near diagonal values of one interaction to the other

22. 22 Maximal Feature Sub-Graph Maximal Features –Features that can not be subsumed by other features The Maximal Feature Sub-Graph is the graph containing only Maximal Features –Unique interpretation of a component –Contains fewer features

23. 23 Blocks of MFSG The Maximal Feature Sub-Graphs can be further sub- divided into blocks –Blocks are defined as Maximal sets of features that all interact –Blocks represent sub-pieces of a component that can be utilized for searching. –Isomorphism can be used to determine redundant blocks from a component Further reduces the search space

24. 24 Example Component

25. 25 Interaction Types Consideration of Maximal Orthonormal Features reduces the number of interaction types. –Maximal Features necessitate that the example component shown be reduced to two features A  C, and B  C  D. Volume D and C can not be combined as a Maximal Feature Volumes A, B, C, D alone are not Maximal Features Volume C can not be subdivided D C BA Example:

26. 26 Solution Approach The solution approach –Methods to reduce the search space –TAHs encode knowledge of existing components –TAHs encode knowledge for query relaxation –Separate hierarchies for features and interactions –Final comparison performed using graph isomorphism

27. 27 Solution Approach Continued Feature Type Hierarchy –Each level contains histograms of feature types –Feature types are combined into fewer buckets based on feature similarity –Similarity can be based on: Family (slot, pocket, hole)

28. 28 Example Component and Feature TAH 4 Features present in the part 2 slots, 1 step, and 1 pocket. The level of abstraction (level of query relaxation) indicates which of the histograms are compared to the query. This example groups features based on type. 4 2,2,1,0 2,0,0,1,1,0,0,0 SlotBlindSlotStepBlindStep Pocket Through PocketHole Through Hole SlotsSteps Pockets Holes All Features

29. 29 Solution Approach Continued Feature Interaction Hierarchy –Each level contains histograms of feature interactions –Feature interactions are combined into fewer buckets based on feature interaction sorts

30. 30 Example Component and Interaction TAH The features present have 9 Interactions: PI-2a(BST-3, BST-2), FI-2(BST-3, SL-2), FI-2(BST-3, SL-1), PI-3(BST-1, SL-1), PI-3(BST-1, SL-2), PP-2b(SL-1, SL-2), IB-1(BST-1,BST-2), PI-2a(BST-1, SL1), PI-2a(BST-1, SL2) 9 1,7,1,2,0 2,0,0,1,1,0,0,0 PI-0PI-1PI-3PI-2a PI-2bI-1 IP IB-1 BoundaryIntrusionPass Through Face All Interactions Improper Only 1,7,0,1,0,0,2,0,0,0 PIIP FP IF I BIIPP FBFI I … …

31. 31 TAH Comments The TAHs can be relaxed individually to allow for only feature relaxation or interaction relaxation The Hierarchies can be constructed such that only certain interaction or feature types are considered for relaxation

32. 32 Searching Searching is performed by comparing the feature and interaction histograms for the target component with those saved in the database –A TAH can direct the search to a similar feature set when exact matches can not be found. –A TAH can direct the search to a similar feature interaction set when exact matches can not be found –Histograms encode the knowledge about features and interactions in the database components

33. 33 Overview of Solution Approach - Query Processing Qualitative Model MFSG Search for Matching Histograms Extract Blocks and make a list Relax Query Pick a block Return Match Mark Block as Matched Blocks Remaining Is the block isomorphic to a previous block Match Found Return Match List Yes No Yes No Post Selection Processing

34. 34 Example Select: Match List From: TAHs Where: Same as Reference to b-rep Component Submitted Features Extracted (only maximal features shown) Feature Interactions This component contains: 27 Extractable features over 200 interactions Many potential interpretations!

35. 35 Example Continued MFSG Blocks Extracted Blocks determined to be isomorphic Further reduces the search space Example Component Database For purposes of illustration a sub-set of a database is presented TAHs constructed containing all of the blocks of existing components Maximal Feature Sub Graph

36. 36 Example Continued The block contains 3 steps The block contains 2 PI-3 interactions and 1 PI-2A interaction Component d’s block is determined to contain the same feature and interaction histograms and is returned as a match Example components Component Submitted

37. 37 Summary Methodology for intelligently searching for similarly shaped components presented –Spatial interactions modeled by a qualitative model –Generates a unique component model with the MFSG –Reduces search space through the use of MFSG blocks –Reduces computational intensiveness through encoding knowledge of features and interactions into TAHs Future Work Increase the size and complexity of the example database