{"id":{"repo_id":"gmu","oai_identifier":"oai:MARS:1920/13737"},"canonical_url":"https://search.dev.ndltd.org/etd/gmu/oai:MARS:1920/13737","repository":{"repo_id":"gmu","name":"George Mason University","base_url":"https://mars.gmu.edu/server/oai/request"},"display":{"title":"Interactive Numerical Optimization and Predictive Geometry Registration","abstract":"Shape similarity is a fundamental problem in geometry processing, enabling applications such as surface correspondence, segmentation, and edit propagation. For example, a user may paint a stroke on one finger of a model and desire the edit to propagate to all fingers. Automatic approaches have difficulty matching user expectations, either due to an algorithm's inability to guess the scale at which the user is intending to edit or due to underlying deficiencies in the similarity metric (e.g., semantic information not present in the geometry). We propose an approach to interactively design self-similarity maps. We investigate two primitive operations, useful in a variety of scenarios: region and curve similarity. Users select example similar and dissimilar regions. Starting with an automatically generated multi-scale shape signature, our approach solves for a scale parameter and thresholds that group the example regions as specified. We propose a new Smooth Shape Diameter Signature (SSDS) as a more efficient alternative to the Heat or Wave Kernel Signature. If no such parameters can be found, our approach modifies the shape signature itself. Given a curve drawn on the surface, we perform hybrid discrete/continuous optimization to find similar curves elsewhere. We apply our approach for interactive editing scenarios: propagating mesh geometry, patterns duplication, and segmentation. These demonstrations lead to observations regarding the nature of optimization procedures within user-driven applications. In many interactive systems, user input initializes and launches an iterative optimization procedure. The goal is to provide assistive feedback to some creation/editing process. Examples include constraint-based GUI layout and complex snapping scenarios. Many geometric problems, such as fitting a shape to data, involve optimizations which may take seconds to complete (or even longer), yet require human guidance. In order to make these optimization routines practical in interactive sessions, simplifications or sacrifices must be made. Canonically, non-convex optimization problems are solved iteratively by taking a series of steps towards a solution. By their nature, there are many locally optimal solutions; which solution is found is highly dependent on an initial guess. There is a fundamental conflict between optimization and interactivity. Interrupting and restarting the optimization every time the user, e.g., moves the mouse prevents any solution from being computed until the user ceases interaction. Continuing to run the optimization procedure computes a perpetually outdated solution. This presents a particular unsolved challenge with respect to direct manipulation. Every time the user, e.g., moves the mouse, the entire optimization must be restarted with the new user input, since returning a stale result associated with the previous user state is undesirable. We propose predictive short-circuiting to reduce this fundamental tension. Our approach memoizes paths in the optimization's configuration space and predicts the trajectory of future optimization in real-time, leveraging common $C^1$ continuity assumptions. This enables direct manipulation of formerly sluggish interactions. We demonstrate our approach on geometric fitting tasks. Additionally, we evaluate complementary mouse motion prediction algorithms as a means to discard or skip optimization problems that are irrelevant to the user's intended initial configuration for a targeted optimization procedure. Predicting where the mouse cursor will be located at the end of an operation, such as dragging a model into a scene for alignment, allows us to preemptively begin solving the targeted problem before the user finishes their movement. We take advantage of the fact that the prediction indicates the approximate energy basin the optimization procedure will need to explore.","abstract_html":"Shape similarity is a fundamental problem in geometry processing, enabling applications such as surface correspondence, segmentation, and edit propagation. For example, a user may paint a stroke on one finger of a model and desire the edit to propagate to all fingers. Automatic approaches have difficulty matching user expectations, either due to an algorithm&#x27;s inability to guess the scale at which the user is intending to edit or due to underlying deficiencies in the similarity metric (e.g., semantic information not present in the geometry). We propose an approach to interactively design self-similarity maps. We investigate two primitive operations, useful in a variety of scenarios: region and curve similarity. Users select example similar and dissimilar regions. Starting with an automatically generated multi-scale shape signature, our approach solves for a scale parameter and thresholds that group the example regions as specified. We propose a new Smooth Shape Diameter Signature (SSDS) as a more efficient alternative to the Heat or Wave Kernel Signature. If no such parameters can be found, our approach modifies the shape signature itself. Given a curve drawn on the surface, we perform hybrid discrete/continuous optimization to find similar curves elsewhere. We apply our approach for interactive editing scenarios: propagating mesh geometry, patterns duplication, and segmentation. These demonstrations lead to observations regarding the nature of optimization procedures within user-driven applications. In many interactive systems, user input initializes and launches an iterative optimization procedure. The goal is to provide assistive feedback to some creation/editing process. Examples include constraint-based GUI layout and complex snapping scenarios. Many geometric problems, such as fitting a shape to data, involve optimizations which may take seconds to complete (or even longer), yet require human guidance. In order to make these optimization routines practical in interactive sessions, simplifications or sacrifices must be made. Canonically, non-convex optimization problems are solved iteratively by taking a series of steps towards a solution. By their nature, there are many locally optimal solutions; which solution is found is highly dependent on an initial guess. There is a fundamental conflict between optimization and interactivity. Interrupting and restarting the optimization every time the user, e.g., moves the mouse prevents any solution from being computed until the user ceases interaction. Continuing to run the optimization procedure computes a perpetually outdated solution. This presents a particular unsolved challenge with respect to direct manipulation. Every time the user, e.g., moves the mouse, the entire optimization must be restarted with the new user input, since returning a stale result associated with the previous user state is undesirable. We propose predictive short-circuiting to reduce this fundamental tension. Our approach memoizes paths in the optimization&#x27;s configuration space and predicts the trajectory of future optimization in real-time, leveraging common <span class=\"etd-inline-math\">C<sup>1</sup></span> continuity assumptions. This enables direct manipulation of formerly sluggish interactions. We demonstrate our approach on geometric fitting tasks. Additionally, we evaluate complementary mouse motion prediction algorithms as a means to discard or skip optimization problems that are irrelevant to the user&#x27;s intended initial configuration for a targeted optimization procedure. Predicting where the mouse cursor will be located at the end of an operation, such as dragging a model into a scene for alignment, allows us to preemptively begin solving the targeted problem before the user finishes their movement. We take advantage of the fact that the prediction indicates the approximate energy basin the optimization procedure will need to explore.","abstract_has_math":true,"creators":["Graus, Josef Andrew"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023","date_published":"2023","updated_at":"2026-07-27T19:51:44Z","subjects":["Interaction design process and methods","Mathematical optimization","Modeling and simulation","Shape analysis"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:1920/13737"],"render_values":[{"text":"hdl:1920/13737","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2023"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Interaction design process and methods","Mathematical optimization","Modeling and simulation","Shape analysis"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:1920/13737"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","values":["Shape similarity is a fundamental problem in geometry processing, enabling applications such as surface correspondence, segmentation, and edit propagation. For example, a user may paint a stroke on one finger of a model and desire the edit to propagate to all fingers. Automatic approaches have difficulty matching user expectations, either due to an algorithm's inability to guess the scale at which the user is intending to edit or due to underlying deficiencies in the similarity metric (e.g., semantic information not present in the geometry). We propose an approach to interactively design self-similarity maps. We investigate two primitive operations, useful in a variety of scenarios: region and curve similarity. Users select example similar and dissimilar regions. Starting with an automatically generated multi-scale shape signature, our approach solves for a scale parameter and thresholds that group the example regions as specified. We propose a new Smooth Shape Diameter Signature (SSDS) as a more efficient alternative to the Heat or Wave Kernel Signature. If no such parameters can be found, our approach modifies the shape signature itself. Given a curve drawn on the surface, we perform hybrid discrete/continuous optimization to find similar curves elsewhere. We apply our approach for interactive editing scenarios: propagating mesh geometry, patterns duplication, and segmentation. These demonstrations lead to observations regarding the nature of optimization procedures within user-driven applications. In many interactive systems, user input initializes and launches an iterative optimization procedure. The goal is to provide assistive feedback to some creation/editing process. Examples include constraint-based GUI layout and complex snapping scenarios. Many geometric problems, such as fitting a shape to data, involve optimizations which may take seconds to complete (or even longer), yet require human guidance. In order to make these optimization routines practical in interactive sessions, simplifications or sacrifices must be made. Canonically, non-convex optimization problems are solved iteratively by taking a series of steps towards a solution. By their nature, there are many locally optimal solutions; which solution is found is highly dependent on an initial guess. There is a fundamental conflict between optimization and interactivity. Interrupting and restarting the optimization every time the user, e.g., moves the mouse prevents any solution from being computed until the user ceases interaction. Continuing to run the optimization procedure computes a perpetually outdated solution. This presents a particular unsolved challenge with respect to direct manipulation. Every time the user, e.g., moves the mouse, the entire optimization must be restarted with the new user input, since returning a stale result associated with the previous user state is undesirable. We propose predictive short-circuiting to reduce this fundamental tension. Our approach memoizes paths in the optimization's configuration space and predicts the trajectory of future optimization in real-time, leveraging common $C^1$ continuity assumptions. This enables direct manipulation of formerly sluggish interactions. We demonstrate our approach on geometric fitting tasks. Additionally, we evaluate complementary mouse motion prediction algorithms as a means to discard or skip optimization problems that are irrelevant to the user's intended initial configuration for a targeted optimization procedure. Predicting where the mouse cursor will be located at the end of an operation, such as dragging a model into a scene for alignment, allows us to preemptively begin solving the targeted problem before the user finishes their movement. We take advantage of the fact that the prediction indicates the approximate energy basin the optimization procedure will need to explore."]},{"key":"dc:title","label":"Title","values":["Interactive Numerical Optimization and Predictive Geometry Registration"]}]}],"canonical_facts":{"dc:date.issued":["2023"],"dc:description.other":["Shape similarity is a fundamental problem in geometry processing, enabling applications such as surface correspondence, segmentation, and edit propagation. For example, a user may paint a stroke on one finger of a model and desire the edit to propagate to all fingers. Automatic approaches have difficulty matching user expectations, either due to an algorithm's inability to guess the scale at which the user is intending to edit or due to underlying deficiencies in the similarity metric (e.g., semantic information not present in the geometry). We propose an approach to interactively design self-similarity maps. We investigate two primitive operations, useful in a variety of scenarios: region and curve similarity. Users select example similar and dissimilar regions. Starting with an automatically generated multi-scale shape signature, our approach solves for a scale parameter and thresholds that group the example regions as specified. We propose a new Smooth Shape Diameter Signature (SSDS) as a more efficient alternative to the Heat or Wave Kernel Signature. If no such parameters can be found, our approach modifies the shape signature itself. Given a curve drawn on the surface, we perform hybrid discrete/continuous optimization to find similar curves elsewhere. We apply our approach for interactive editing scenarios: propagating mesh geometry, patterns duplication, and segmentation. These demonstrations lead to observations regarding the nature of optimization procedures within user-driven applications. In many interactive systems, user input initializes and launches an iterative optimization procedure. The goal is to provide assistive feedback to some creation/editing process. Examples include constraint-based GUI layout and complex snapping scenarios. Many geometric problems, such as fitting a shape to data, involve optimizations which may take seconds to complete (or even longer), yet require human guidance. In order to make these optimization routines practical in interactive sessions, simplifications or sacrifices must be made. Canonically, non-convex optimization problems are solved iteratively by taking a series of steps towards a solution. By their nature, there are many locally optimal solutions; which solution is found is highly dependent on an initial guess. There is a fundamental conflict between optimization and interactivity. Interrupting and restarting the optimization every time the user, e.g., moves the mouse prevents any solution from being computed until the user ceases interaction. Continuing to run the optimization procedure computes a perpetually outdated solution. This presents a particular unsolved challenge with respect to direct manipulation. Every time the user, e.g., moves the mouse, the entire optimization must be restarted with the new user input, since returning a stale result associated with the previous user state is undesirable. We propose predictive short-circuiting to reduce this fundamental tension. Our approach memoizes paths in the optimization's configuration space and predicts the trajectory of future optimization in real-time, leveraging common $C^1$ continuity assumptions. This enables direct manipulation of formerly sluggish interactions. We demonstrate our approach on geometric fitting tasks. Additionally, we evaluate complementary mouse motion prediction algorithms as a means to discard or skip optimization problems that are irrelevant to the user's intended initial configuration for a targeted optimization procedure. Predicting where the mouse cursor will be located at the end of an operation, such as dragging a model into a scene for alignment, allows us to preemptively begin solving the targeted problem before the user finishes their movement. We take advantage of the fact that the prediction indicates the approximate energy basin the optimization procedure will need to explore."],"dc:identifier":["hdl:1920/13737"],"dc:subject":["Interaction design process and methods","Mathematical optimization","Modeling and simulation","Shape analysis"],"dc:title":["Interactive Numerical Optimization and Predictive Geometry Registration"],"dc:type":["Dissertation"]},"updated_at":"2026-07-27T19:51:44Z"}