A Methodology for automatic retrieval of similarly shaped machinable components

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

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. Examples of Challenges Both Components Contain: 1 Slot 2 Blind Slots 1 Pocket Example of components with similar features and different shapes Example of multiple interpretations and representation complexity

4. Contributions • Retrieval of sub pieces to cover a component • Method of dividing up component • Criticality of interactions forcing block combination • Use of type abstraction hierarchies to guide similarity search • Feature and interaction Histogram based

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

6. 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 • Simple feature interaction representation • No method for indexing

7. 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 and sorts of similarities for feature types and interactions find the component in the database that contain the closest representation to the given component • Components represented as a qualitative model • Features are nodes • Interactions are directed labeled edges R1,2, where the labels are nxm qualitative matricies • Requires a unique way to interpret a component as features

8. Features And Interactions • A Features is represented as a 4-tuple (T, f, D, I) where: • T is the type (slot, hole, etc.) • f is the sweep face • D is the sweep direction • I is the sweep interval • Additional information that can be maintained for a feature • Finish • Accessibility • etc

9. Features And 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 • Critical Interactions • Precedence setting • Forces a planning decision R5,2

10. 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

11. Solution Approach Continued • Feature Type Hierarchy • Each level contains histograms of feature types • Feature types are combined into fewer buckets based on feature similarity 5 Features present in the part 1 slot, 1 blind slot, 1 step, 1 blind step, and 1 through hole. The level of abstraction (level of query relaxation) indicates which of the histograms are compared to the query. Example: 5 2,2,0,1 1,1,1,1,0,0,1,0

12. 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

13. 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

14. 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

15. Blocks of MFSG • The Maximal Feature Sub-Graphs can be further sub-divided into blocks • Blocks are defined as 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

16. Example Component

17. Note on Blocks • Blocks that contain critical interactions must have all features containing critical interactions present.

18. 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

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

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

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

22. Example Continued Component Submitted Example components 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

23. 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 • Incorporate plan retrieval and merging