Curve smoothing without shrinking
AssigneeAbode Systems Incorporated
InventorNaresh Chand Gupta
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Abstract
A system generates a smoothed curve from a noisily drawn, multi-segmented curve by minimizing an energy function for a smoothed curve which fits between end-points of the drawn curve. The energy function has three components: a distortion component, a smoothing component and a shrink component. Numerical analysis methods are applied to evaluate the energy function and to identify the smoothed curve with the lowest energy. The transposed curve with the lowest energy value is selected as the smoothed curve.
Claims51
A computer-implemented method for generating a smoothed curve from a drawn curve, comprising:
- defining an energy constraint associated with the drawn curve, the energy constraint having a shrink component, a distortion component, and a smoothness component;
- and
- generating the smoothed curve by minimizing the energy constraint.
A computer-implemented apparatus for generating a smoothed curve from a drawn curve, the apparatus comprising instructions operable to cause a programmable processor to:
- define an energy constraint associated with the drawn curve, the energy constraint having a shrink component, a distortion component, and a smoothness component;
- and
- generate the smoothed curve by minimizing the energy constraint.
A computer system for characterizing a drawn curve defined by a sequence of points on a two-dimensional space, comprising:
- a display;
- a user input device;
- and
- a processor coupled to the display and the user input device, the processor having instructions embedded therein to:
- determine a distortion component D associated with the smoothed curve in accordance with D = ∑ i = 0 N - 1 ( ( u i - x i ) 2 + ( v i - y i ) 2 )
- where (xi,yi) represent a point on the drawn curve (ui,vi) represent a point on the smoothed curve;
- determine a smoothing component S associated with the smoothed curve in accordance with:
- S = ∑ i = 0 N - 1 ( u i - u i + 1 ) 2 + ( v i - v i + 1 ) 2
- determine a shrink component B for a systematic shift in accordance with:
- B = [ ∑ i = 1 N - 1 ( v i · l i + u i · m i ) + M ] 2
- and
- generate one or more smoothed curves, each curve having an energy value E expressed in terms of the distortion component, the smoothing component and the shrink component in accordance with:
- E=D+λ2*S+γ2*B
- where λ is the smoothness parameter, γ is the distortion parameter;
- and
- select the smoothed curve with the minimum energy as the smoothed curve.
An apparatus for generating a smoothed curve from a drawn curve, comprising:
- means for defining an energy constraint associated with the drawn curve, the energy constraint having a shrink component, a distortion component, and a smoothness component;
- and
- means for generating the smoothed curve by minimizing the energy constraint.
A computer-implemented method for generating a smoothed curve from a drawn curve, comprising:
- defining an energy constraint associated with the drawn curve, the energy constraint having a shrink component;
- and
- generating the smoothed curve by minimizing the energy constraint.
A computer readable medium with instructions for generating a smoothed curve from a drawn curve, the medium comprising instructions operable to cause a programmable processor to:
- define an energy constraint associated with the drawn curve, the energy constraint having a shrink component, a distortion component, and a smoothness component;
- and
- generate the smoothed curve by minimizing the energy constraint.
A computer-implemented method for characterizing a drawn curve defined by a sequence of points on a two-dimensional space, comprising:
- determining a distortion component D associated with the smoothed curve in accordance with:
- D = ∑ i = 0 N - 1 ( ( u i - x i ) 2 + ( v i - y i ) 2 )
- where (xi,yi) represent a point on the drawn curve and (ui,vi) represent a point on the smoothed curve;
- determining a smoothing component S associated with the smoothed curve in accordance with:
- S = ∑ i = 0 N - 1 ( u i - u i + 1 ) 2 + ( v i - v i + 1 ) 2
- determining a shrink component B for a systematic shift in accordance with:
- B = [ ∑ i = 1 N - 1 ( v i · l i + u i · m i ) + M ] 2
- and
- generating one or more smoothed curves, each curve having an energy value E expressed in terms of the distortion component, the smoothing component and the shrink component in accordance with:
- E=D+λ2*S+γ2*B
- where λ is the smoothness parameter, γ is the distortion parameter;
- and selecting the smoothed curve with the minimum energy as the smoothed curve.
A computer-implemented method for generating a smoothed curve from a drawn curve, comprising:
- defining an energy constraint associated with the drawn curve, the energy constraint having a shrink component and at least one of a distortion component and a smoothness component;
- and
- generating the smoothed curve by minimizing the energy constraint.
Dependencies are inferred from the claim text.