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US5995115A Expired / Lapsed US ⏱️ 0.0 years remaining

Computer system process and user interface for providing intelligent scissors for image composition

Assignee: Avid Technology Inc
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Filing: 1997-04-04
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Granted: 1999-11-30
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Expires: 2017-04-04
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Abstract

Abstract A video editing system capable of tracing and extracting objects in an image selects edges of the object to be traced based on an edge cost computation and on a rotational amount of the edge. The edge cost calculation method modulates the gradient magnitude of the pixel against the gradient direction of an edge to reduce the ambiguity often encountered during tracing as a result of background noise in the image. A method of editing the trace involves introducing control points between previously generated points in the trace. Because of a consistent edge selection criteria, based on a rotational amount of an edge, the characteristics of the previous edge are preserved, and an iterative editing process is eliminated. By basing the selection criteria on a rotation of the path, a total path rotation may be maintained with minimal extra compute operations.

Inventors

  • 👤 Garth A. Dickie

Bibliographic Details

Application Number —
Jurisdiction US
Data Source google_patents
Last Synchronized 2026-10-24 21:43
CPC Classifications
G; G06; G06T; G06T7/00; G06T7/10; G06T7/12; G06T2207/00; G06T2207/10; G06T2207/10016; G06T2207/20; G06T2207/20092; G06T2207/20101

Claims Analysis

Total Claims: 45
Claim 1
Independent Claim 123 words
A method for tracing an object in an image, comprising the steps of: selecting a first point on an edge of said object; determining a first path from the first point to a second point in the image; determining a cost of the first path; determining a second path from the first point to the second point; determining a cost of the second path; selecting one of the first and second paths, including, when the costs of the first and second paths are equal, by determining a first total rotation amount of the first path, determining a second total rotation amount of the second path, and selecting one of the first and second paths according to the first and second total rotation amounts.
Claim 2
Independent Claim 123 words
A method for tracing an object in an image, comprising the steps of: selecting a first point on an edge of said object; determining a first path from the first point to a second point in the image; determining a cost of the first path; determining a second path from the first point to the second point; determining a cost of the second path; selecting one of the first and second paths, including, when the costs of the first and second paths are equal, by determining a first total rotation amount of the first path, determining a second total rotation amount of the second path, and selecting one of the first and second paths according to the first and second total rotation amounts.
Claim 3
Dependent Claim 124 words
The method according to claim 1, wherein: the image comprises a plurality of pixels; the first and second points are each one of the pixels; the first path comprises three or more first-path pixels including the first and second points; the second path comprises three or more second-path pixels including the first and second points; the step of determining a first total rotation amount of the first path comprises the steps of determining a rotation amount between each adjacent pair of the first-path pixels and summing these rotation amounts; and the step of determining a second total rotation amount of the second path comprises the steps of determining a rotation amount between each adjacent pair of the second-path pixels and summing these rotation amounts.
Claim 4
Dependent Claim 193 words
The method according to claim 2, wherein the steps of determining a cost of the first path and determining a cost of the second path further each comprise the steps of: determining a gradient magnitude G(p) of each pixel p in the path; determining an edge direction E(p) for each pixel p in the path; determining a direction D(p,q) between said pixel p and a neighboring pixel q in the path; determining an edge orientation θ(p,q) between said pixel p and the neighboring pixel q; determining a cost of an edge from said pixel p to said neighboring pixel q according to the below formula: Halfcost (p,q)=D(p,q)(λ.sub.2 +λ.sub.3 +λ.sub.4 -(1-λ.sub.0)·G(p).sup.λ1 ·Multiplier(p,q) Halfcost (q,p)=D(q,p)(λ.sub.2 +λ.sub.3 +λ.sub.4 -(1-λ.sub.0)·G(q).sup.λ1 ·Multiplier(p,q) Cost(p,q)=Halfcost(p,q)+Halfcost(q,p) where Multiplier(p,q)=λ 3 +λ 4 Z(p)+λ 2 (π-2χ(p,q)/π, χ(p,q) is the lesser of |θ(p,q)-E(p,q)| or π-|θ(p,q)-E(p,q)|, Z(p) is a Laplacian zero-crossing of pixel p{Multiplier (p,q)=λ 3 +λ 4 Z(p)+λ 2 (π-2χ(p,q))/π}, and λ 0 -λ 4 are scaling factors of a tension variable, a gradient response gamma, a gradient direction influence, a gradient magnitude influence and a zero crossing influence, respectively, which are used to modulate the gradient magnitude G(p) against the gradient direction D(p).
Claim 5
Dependent Claim 17 words
The method according to claim 2, wherein: the rotation amount is measured in gradients of 45 degrees.
Claim 6
Dependent Claim 36 words
The method according to claim 1, wherein: the step of selecting one of the first and second paths according to the first and second total rotation amounts includes selecting according to a maximum total rotation amount.
Claim 7
Dependent Claim 36 words
The method according to claim 1, wherein: the step of selecting one of the first and second paths according to the first and second total rotation amounts includes selecting according to a minimum total rotation amount.
Claim 8
Independent Claim 175 words
A method for editing a trace of an object in an image, the trace comprising one or more paths, each including a pair of boundary points on a boundary of the object, the method comprising the steps of: selecting a path; selecting a control point between the pair of boundary points on the selected path; determining a first edited path from a first of the pair of boundary points of the selected path to the control point; determining a cost of the first edited path; determining a second edited path from the first of the pair of boundary points to the control point; determining a cost of the second edited path; selecting one of the first and second edited paths, including, when the costs of the first and second edited paths are equal, by determining a first total rotation amount of the first edited path, determining a second total rotation amount of the second edited path, and selecting one of the first and second edited paths according to the first and second total rotation amounts.
Claim 9
Independent Claim 175 words
A method for editing a trace of an object in an image, the trace comprising one or more paths, each including a pair of boundary points on a boundary of the object, the method comprising the steps of: selecting a path; selecting a control point between the pair of boundary points on the selected path; determining a first edited path from a first of the pair of boundary points of the selected path to the control point; determining a cost of the first edited path; determining a second edited path from the first of the pair of boundary points to the control point; determining a cost of the second edited path; selecting one of the first and second edited paths, including, when the costs of the first and second edited paths are equal, by determining a first total rotation amount of the first edited path, determining a second total rotation amount of the second edited path, and selecting one of the first and second edited paths according to the first and second total rotation amounts.
Claim 10
Dependent Claim 22 words
The method according to claim 7, wherein: of the one or more paths of the trace, only the selected path is modified.
Claim 11
Dependent Claim 138 words
A storage device in which is stored image data including object-trace data associated with an image, the object-trace data being generated by a method comprising the steps of: selecting a first point on an edge of the object, determining a first path from the first point to a second point in the image, determining a cost of the first path, determining a second path from the first point to the second point, determining a cost of the second path, selecting one of the first and second paths, including, when the costs of the first and second paths are equal, by determining a first total rotation amount of the first path, determining a second total rotation amount of the second path, and selecting one of the first and second paths according to the first and second total rotation amounts.
Claim 12
Dependent Claim 138 words
A storage device in which is stored image data including object-trace data associated with an image, the object-trace data being generated by a method comprising the steps of: selecting a first point on an edge of the object, determining a first path from the first point to a second point in the image, determining a cost of the first path, determining a second path from the first point to the second point, determining a cost of the second path, selecting one of the first and second paths, including, when the costs of the first and second paths are equal, by determining a first total rotation amount of the first path, determining a second total rotation amount of the second path, and selecting one of the first and second paths according to the first and second total rotation amounts.
Claim 13
Dependent Claim 148 words
The method of claim 7, wherein: the image comprises a plurality of pixels; the first edited path comprises three or more first-edited-path pixels of the plurality of pixels, including the control point and the first of the pair of boundary points of the selected path; the second edited path comprises three or more second-edited-path pixels of the plurality of pixels, including the control point and the first of the pair of boundary points of the selected path; the step of determining a first total rotation amount of the first edited path comprises the steps of determining a rotation amount between each adjacent pair of the first-edited-path pixels and summing these rotation amounts; and the step of determining a second total rotation amount of the second edited path comprises the steps of determining a rotation amount between each adjacent pair of the second-edited-path pixels and summing these rotation amounts.
Claim 14
Dependent Claim 186 words
The method of claim 10, wherein the steps of determining a cost of the first edited path and determining a cost of the second edited path further each comprise the steps of: determining a gradient magnitude G(p) of each pixel p in the path; determining an edge direction E(p) for each pixel p in the path; determining a direction D(p,q) between said pixel p and a neighboring pixel q in the path; determining an edge orientation θ(p,q) between said pixel p and the neighboring pixel q; determining a cost of an edge from said pixel p to said neighboring pixel q according to the below formula: Halfcost(p,q)=D(p,q)(λ.sub.2 +λ.sub.3 +λ.sub.4 -(1-λ.sub.0)·G(p).sup.λ1 ·Multiplier(p,q)) Halfcost(q,p)=D(q,p)(λ.sub.2 +λ.sub.3 +λ.sub.4 -(1-λ.sub.0)·G(q).sup.λ1 ·Multiplier(q,p)) Cost(p,q)=Halfcost(p,q)+Halfcost(q,p) where Multiplier (p,q)=λ 3 +λ 4 Z(P)+λ 2 (π-2χ(p,q))/π, X(p,q) is the lesser of |θ(p,q)-E(p,q)| or π-|θ(p,q)-E(p,q)|, Z(p) is a Laplacian zero-crossing of pixel p, and λ 0 -λ 4 are scaling factors of a tension variable, a gradient response gamma, a gradient direction influence, a gradient magnitude influence and a zero crossing influence, respectively, which are used to modulate the gradient magnitude G(p) against the gradient direction D(p).
Claim 15
Dependent Claim 16 words
The method of claim 10, wherein: the rotation amount is measured in gradients of 45 degrees.
Claim 16
Independent Claim 191 words
A method for editing a trace of an object in an image, the trace comprising one or more paths, each including a pair of boundary points on a boundary of the object, the method comprising the steps of: selecting a path; moving a first of the pair of boundary points of the selected path to a new location point along the boundary of the object; determining a first edited path from a second of the pair of boundary points of the selected path to the new location point; determining a cost of the first edited path; determining a second edited path from a second of the pair of boundary points of the selected path to the new location point; determining a cost of the second edited path; selecting one of the first and second edited paths, including, when the costs of the first and second edited paths are equal, by determining a first total rotation amount of the first edited path, determining a second total rotation amount of the second edited path, and selecting one of the first and second edited paths according to the first and second total rotation amounts.
Claim 17
Independent Claim 191 words
A method for editing a trace of an object in an image, the trace comprising one or more paths, each including a pair of boundary points on a boundary of the object, the method comprising the steps of: selecting a path; moving a first of the pair of boundary points of the selected path to a new location point along the boundary of the object; determining a first edited path from a second of the pair of boundary points of the selected path to the new location point; determining a cost of the first edited path; determining a second edited path from a second of the pair of boundary points of the selected path to the new location point; determining a cost of the second edited path; selecting one of the first and second edited paths, including, when the costs of the first and second edited paths are equal, by determining a first total rotation amount of the first edited path, determining a second total rotation amount of the second edited path, and selecting one of the first and second edited paths according to the first and second total rotation amounts.
Claim 18
Dependent Claim 21 words
The method of claim 13, wherein: of the one or more paths of the trace, only the selected path is modified.
Claim 19
Dependent Claim 150 words
The method of claim 13, wherein: the image comprises a plurality of pixels; the first edited path comprises three or more first-edited-path pixels of the plurality of pixels, including the new location point and the second of the pair of boundary points of the selected path; the second edited path comprises three or more second-edited-path pixels of the plurality of pixels, including the new location point and the second of the pair of boundary points of the selected path; the step of determining a first total rotation amount of the first edited path comprises the steps of determining a rotation amount between each adjacent pair of the first-edited-path pixels and summing these rotation amounts; and the step of determining a second total rotation amount of the second edited path comprises the steps of determining a rotation amount between each adjacent pair of the second-edited-path pixels and summing these rotation amounts.
Claim 20
Dependent Claim 185 words
The method of claim 15, wherein the steps of determining a cost of the first edited path and determining a cost of the second edited path further each comprise the steps of: determining a gradient magnitude G(p) of each pixel p in the path; determining an edge direction E(p) for each pixel p in the path; determining a direction D(p,q) between said pixel p and a neighboring pixel q in the path; determining an edge orientation θ(p,q) between said pixel p and the neighboring pixel q; determining a cost of an edge from said pixel p to said neighboring pixel q according to the below formula: Halfcost(p,q)=D(p,q)(λ.sub.2 +λ.sub.3 +λ.sub.4 -(1-λ.sub.0)·G(p).sup.λ1 ·Multiplier(p,q)) Halfcost(q,p)=D(q,p)(λ.sub.2 +λ.sub.3 +λ.sub.4 -(1-λ.sub.0)·G(q).sup.λ1 ·Multiplier(q,p)) Cost(p,q)=Halfcost(p,q)+Halfcost(q,p) where Multiplier(p,q)=λ 3 +λ 4 Z(P)+λ 2 (π-2χ(p,q))/π, χ(p,q) is the lesser of |θ(p,q)-E(p,q)| or π-|θ(p,q)-E(p,q)|, Z(p) is a Laplacian zero-crossing of pixel p, and λ 0 -λ 4 are scaling factors of a tension variable, a gradient response gamma, a gradient direction influence, a gradient magnitude influence and a zero crossing influence, respectively, which are used to modulate the gradient magnitude G(p) against the gradient direction D(p).
Claim 21
Dependent Claim 107 words
The method of claim 2, wherein the steps of determining a cost of the first path and determining a cost of the second path further each comprise the steps of: determining a gradient magnitude G(p) of at least one pixel p in the path; determining an edge orientation e(p,q) between the pixel p and a neighboring pixel q; determining an edge direction E(p) for the pixel p; determining an edge-orientation cost χ(p,q) that is the lesser of |θ(p,q)-E(p,q)| or π-|θ(p,q)-E(p,q)|; and determining a cost of an edge from the pixel p to the neighboring pixel q including modulating the edge-orientation cost χ(p,q) by the gradient magnitude G(p).
Claim 22
Dependent Claim 82 words
The method of claim 2, wherein the steps of determining a cost of the first path and determining a cost of the second path further each comprise the steps of: determining a gradient magnitude G(p) of at least one pixel p in the path; determining a Laplacian zero-crossing of the pixel p; and determining a cost of an edge from the pixel p to a neighboring pixel q including modulating the Laplacian zero-crossing of the pixel p by the gradient magnitude G(p).
Claim 23
Dependent Claim 69 words
The method of claim 2, wherein the steps of determining a cost of the first path and determining a cost of the second path farther each comprise the step of: determining a cost of an edge from at least one pixel p in the path to a neighboring pixel q including determining a value equal to a gradient magnitude G(p) of the pixel p raised to an exponential power.
Claim 24
Dependent Claim 42 words
The method of claim 19, wherein: the step of determining a value comprises determining a value equal to the gradient magnitude G(p) of the pixel p raised to an exponential power represented by a scaling factor of a gradient response gamma λ1.
Claim 25
Dependent Claim 148 words
A video system comprising: a storage device for storing image data including object-trace data associated with an object in an image; and an object tracer for extracting the object trace data from the image, constructed and adapted to select a first point on an edge of the object, determine a first path from the first point to a second point in the image, determine a cost of the first path, determine a second path from the first point to the second point, determine a cost of the second path, select one of the first and second paths, including to, when the costs of the first and second paths are equal, determine a first total rotation amount of the first path, determine a second total rotation amount of the second path, and select one of the first and second paths according to the first and second total rotation amounts.
Claim 26
Dependent Claim 148 words
A video system comprising: a storage device for storing image data including object-trace data associated with an object in an image; and an object tracer for extracting the object trace data from the image, constructed and adapted to select a first point on an edge of the object, determine a first path from the first point to a second point in the image, determine a cost of the first path, determine a second path from the first point to the second point, determine a cost of the second path, select one of the first and second paths, including to, when the costs of the first and second paths are equal, determine a first total rotation amount of the first path, determine a second total rotation amount of the second path, and select one of the first and second paths according to the first and second total rotation amounts.
Claim 27
Dependent Claim 16 words
The video system of claim 21, further comprising: a capture device for receiving the image data.
Claim 28
Dependent Claim 183 words
The video system of claim 21, further comprising: a trace editor for editing the object trace data, wherein the trace data comprises one or more paths, each including a pair of boundary points on a boundary of the object, the trace editor constructed and arranged to select a path, select a control point between the pair of boundary points on the selected path, determine a first edited path from a first of the pair of boundary points of the selected path to the control point, determine a cost of the first edited path, determine a second edited path from the first of the pair of boundary points to the control point, determine a cost of the second edited path, select one of the first and second edited paths, including to, when the costs of the first and second edited paths are equal, determine a first total rotation amount of the first edited path, determine a second total rotation amount of the second edited path, and select one of the first and second edited paths according to the first and second total rotation amounts.
Claim 29
Dependent Claim 199 words
The video system of claim 21, further comprising: a trace editor for editing the object trace data, wherein the trace data comprises one or more paths, each including a pair of boundary points on a boundary of the object, the trace editor constructed and arranged to select a path, move a first of the pair of boundary points of the selected path to a new location point along the boundary of the object; determine a first edited path from a second of the pair of boundary points of the selected path to the new location point; determine a cost of the first edited path; determine a second edited path from a second of the pair of boundary points of the selected path to the new location point; determine a cost of the second edited path; select one of the first and second edited paths, including to, when the costs of the first and second edited paths are equal, determine a first total rotation amount of the first edited path, determine a second total rotation amount of the second edited path, and select one of the first and second edited paths according to the first and second total rotation amounts.
Claim 30
Independent Claim 183 words
A method for tracing an object in an image comprising a plurality of pixels, comprising the steps of: selecting a first point on an edge of said object; determining a first path from the first point to a second point in the image; determining a cost of the first path; determining a second path from the first point to the second point; determining a cost of the second path; and selecting one of the first and second paths according to their costs, wherein the steps of determining the cost of the first path and determining the cost of the second path each comprise the steps of determining a gradient magnitude G(p) of at least one pixel p in the path, determining an edge orientation θ(p,q) between the pixel p and a neighboring pixel q, determining an edge direction E(p) for the pixel p, determining an edge-orientation cost χ(p,q) that is the lesser of |θ(p,q)-E(p,q)| or π-|θ(p,q)-E(p,q)|, and determining a cost of an edge from the pixel p to the neighboring pixel q including modulating the edge-orientation cost χ(p,q) by the gradient magnitude G(p).
Claim 31
Independent Claim 183 words
A method for tracing an object in an image comprising a plurality of pixels, comprising the steps of: selecting a first point on an edge of said object; determining a first path from the first point to a second point in the image; determining a cost of the first path; determining a second path from the first point to the second point; determining a cost of the second path; and selecting one of the first and second paths according to their costs, wherein the steps of determining the cost of the first path and determining the cost of the second path each comprise the steps of determining a gradient magnitude G(p) of at least one pixel p in the path, determining an edge orientation θ(p,q) between the pixel p and a neighboring pixel q, determining an edge direction E(p) for the pixel p, determining an edge-orientation cost χ(p,q) that is the lesser of |θ(p,q)-E(p,q)| or π-|θ(p,q)-E(p,q)|, and determining a cost of an edge from the pixel p to the neighboring pixel q including modulating the edge-orientation cost χ(p,q) by the gradient magnitude G(p).
Claim 32
Independent Claim 158 words
A method for tracing an object in an image comprising a plurality of pixels, comprising the steps of: selecting a first point on an edge of said object; determining a first path from the first point to a second point in the image; determining a cost of the first path; determining a second path from the first point to the second point; determining a cost of the second path; and selecting one of the first and second paths according to their costs, wherein the steps of determining the cost of the first path and determining the cost of the second path each comprise the steps of determining a gradient magnitude G(p) of at least one pixel p in the path, determining a Laplacian zero-crossing of the pixel p, and determining a cost of an edge from the pixel p to a neighboring pixel q including modulating the Laplacian zero-crossing of the pixel p by the gradient magnitude G(p).
Claim 33
Independent Claim 158 words
A method for tracing an object in an image comprising a plurality of pixels, comprising the steps of: selecting a first point on an edge of said object; determining a first path from the first point to a second point in the image; determining a cost of the first path; determining a second path from the first point to the second point; determining a cost of the second path; and selecting one of the first and second paths according to their costs, wherein the steps of determining the cost of the first path and determining the cost of the second path each comprise the steps of determining a gradient magnitude G(p) of at least one pixel p in the path, determining a Laplacian zero-crossing of the pixel p, and determining a cost of an edge from the pixel p to a neighboring pixel q including modulating the Laplacian zero-crossing of the pixel p by the gradient magnitude G(p).
Claim 34
Independent Claim 145 words
A method for tracing an object in an image comprising a plurality of pixels, comprising the steps of: selecting a first point on an edge of said object; determining a first path from the first point to a second point in the image; determining a cost of the first path; determining a second path from the first point to the second point; determining a cost of the second path; and selecting one of the first and second paths according to their costs, wherein the steps of determining the cost of the first path and determining the cost of the second path each comprise the step of determining a cost of an edge from at least one pixel p in the path to a neighboring pixel q including determining a value equal to a gradient magnitude G(p) of the pixel p raised to an exponential power.
Claim 35
Independent Claim 145 words
A method for tracing an object in an image comprising a plurality of pixels, comprising the steps of: selecting a first point on an edge of said object; determining a first path from the first point to a second point in the image; determining a cost of the first path; determining a second path from the first point to the second point; determining a cost of the second path; and selecting one of the first and second paths according to their costs, wherein the steps of determining the cost of the first path and determining the cost of the second path each comprise the step of determining a cost of an edge from at least one pixel p in the path to a neighboring pixel q including determining a value equal to a gradient magnitude G(p) of the pixel p raised to an exponential power.
Claim 36
Dependent Claim 42 words
The method of claim 27, wherein: the step of determining a value comprises determining a value equal to the gradient magnitude G(p) of the pixel p raised to an exponential power represented by a scaling factor of a gradient response gamma λ1.
Claim 37
Dependent Claim 36 words
The method of claim 7, wherein: the step of selecting one of the first and second edited paths according to the first and second total rotation amounts includes selecting according to a maximum total rotation amount.
Claim 38
Dependent Claim 36 words
The method of claim 7, wherein: the step of selecting one of the first and second edited paths according to the first and second total rotation amounts includes selecting according to a minimum total rotation amount.
Claim 39
Dependent Claim 16 words
The method of claim 15, wherein: the rotation amount is measured in gradients of 45 degrees.
Claim 40
Dependent Claim 36 words
The method of claim 13, wherein: the step of selecting one of the first and second edited paths according to the first and second total rotation amounts includes selecting according to a maximum total rotation amount.
Claim 41
Dependent Claim 36 words
The method of claim 13, wherein: the step of selecting one of the first and second edited paths according to the first and second total rotation amounts includes selecting according to a minimum total rotation amount.
Claim 42
Dependent Claim 171 words
A computer program product for use with a computing system having a processor and a storage device for storing image data including object-trace data associated with an object in an image, the computer program product comprising a computer usable medium having embodied therein computer readable program code method steps for extracting the object trace data from the image, the method steps comprising: selecting a first point on an edge of the object, determining a first path from the first point to a second point in the image, determining a cost of the first path, determining a second path from the first point to the second point, determining a cost of the second path, selecting one of the first and second paths, including, when the costs of the first and second paths are equal, determining a first total rotation amount of the first path, determining a second total rotation amount of the second path, and selecting one of the first and second paths according to the first and second total rotation amounts.
Claim 43
Dependent Claim 171 words
A computer program product for use with a computing system having a processor and a storage device for storing image data including object-trace data associated with an object in an image, the computer program product comprising a computer usable medium having embodied therein computer readable program code method steps for extracting the object trace data from the image, the method steps comprising: selecting a first point on an edge of the object, determining a first path from the first point to a second point in the image, determining a cost of the first path, determining a second path from the first point to the second point, determining a cost of the second path, selecting one of the first and second paths, including, when the costs of the first and second paths are equal, determining a first total rotation amount of the first path, determining a second total rotation amount of the second path, and selecting one of the first and second paths according to the first and second total rotation amounts.
Claim 44
Dependent Claim 181 words
The computer program product of claim 34, wherein the method steps further comprise: editing the object trace data, wherein the trace data comprises one or more paths, each including a pair of boundary points on a boundary of the object, including the steps of selecting a path, selecting a control point between the pair of boundary points on the selected path, determining a first edited path from a first of the pair of boundary points of the selected path to the control point, determining a cost of the first edited path, determining a second edited path from the first of the pair of boundary points to the control point, determining a cost of the second edited path, selecting one of the first and second edited paths, including to, when the costs of the first and second edited paths are equal, determining a first total rotation amount of the first edited path, determining a second total rotation amount of the second edited path, and selecting one of the first and second edited paths according to the first and second total rotation amounts.
Claim 45
Dependent Claim 197 words
The computer program product of claim 34, wherein the method steps further comprise: editing the object trace data, wherein the trace data comprises one or more paths, each including a pair of boundary points on a boundary of the object, including the steps of selecting a path, moving a first of the pair of boundary points of the selected path to a new location point along the boundary of the object; determining a first edited path from a second of the pair of boundary points of the selected path to the new location point; determining a cost of the first edited path; determining a second edited path from a second of the pair of boundary points of the selected path to the new location point; determining a cost of the second edited path; select one of the first and second edited paths, including to, when the costs of the first and second edited paths are equal, determining a first total rotation amount of the first edited path, determining a second total rotation amount of the second edited path, and selecting one of the first and second edited paths according to the first and second total rotation amounts.

References Cited (Backward Citations)

US5666440A Cited
US5537490A Cited
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EP0633548A2 Cited
US5703963A Cited

USPTO Annuity & Maintenance Windows

Annuity Stage Window Opens Payment Deadline Surcharge Period Until Estimated Fee Status
3.5 Years (Year 4) 2002-11-29 2003-05-31 2003-11-30 $2000.00 Window Closed / Lapsed
7.5 Years (Year 8) 2006-11-29 2007-05-31 2007-11-30 $3760.00 Window Closed / Lapsed
11.5 Years (Year 12) 2010-11-29 2011-05-31 2011-11-30 $7700.00 Window Closed / Lapsed

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