Measuring linear separations in digital radiographs

• US 20050135668A1
• Filed: 05/07/2004
• Published: 06/23/2005
• Est. Priority Date: 12/23/2003
• Status: Active Grant

• Current Assignee: Leidos, Inc. (Leidos Holdings, Inc.)
• Original Assignee: Science Applications International Corporation
• Inventors: Smith, Scott T., Rush, Gary M., Polichar, Raulf M.
• Granted Patent: US 7,260,255 B2
• Time in Patent Office: Days
• US Class Current: 382/141
• CPC Class Codes: G01V 5/0008 Detecting hidden objects, e.g. weapons, explosives sorting of materials or articles according to radioactive properties B07C5/342; investigating or analysing materials by the use of wave or particle radiation G01N23/00
• CPC Class Codes: G01V 5/20 Detecting prohibited goods, e.g. weapons, explosives, hazardous substances, contraband or smuggled objects

Abstract

Digital pixel data is obtained from radiographic imaging of one or more objects, and corresponds to an imaged area containing a feature to be measured. A data profile for a region around the measured feature is created from the digital pixel data. A reference profile is then created from the data profile. The reference profile represents an expected data profile for a reference condition of the objects, and accounts for the point spread function of the imager. The difference between the data profile and the reference profile is calculated. Based on that difference, the degree by which the actual condition of the objects varies from the reference condition is determined. The calculated difference can be compared to a lookup table mapping previously calculated differences to degrees of variation from the reference condition. The calculated difference can also be used as an input to an experimentally derived formula.

Claims

1. A method for increasing measurement precision in digital radiography, comprising:

(a) receiving digital radiographic data for one or more objects in an actual condition;

(b) creating a first data profile based on the received data, the first data profile corresponding to a selected region of the one or more objects and being associated with the actual condition;

(c) deriving a second data profile from the received data, the second data profile representing an expected data profile for the one or more objects when in a reference condition;

(d) calculating a difference between the first data profile created in step (b) and the second data profile derived in step (c); and

(e) determining, based upon the calculated difference, a degree by which the actual condition varies from the reference condition in the selected region.

2. The method of claim 1, wherein step (c) comprises deriving the second data profile from the first data profile.

3. The method of claim 1, wherein the one or more objects comprise two objects having substantially dissimilar densities, and wherein the degree by which the actual condition varies from the reference condition corresponds to a linear separation between the two objects.

4. The method of claim 3, wherein the linear separation between the two objects is of the same order of magnitude as a major portion of a point spread function for an imager used to generate the data received in step (a).

5. The method of claim 1, wherein step (b) further comprises:

(i) creating an initial data profile from pixel data values corresponding to a first portion of an area imaged by an imager, the first portion being generally coincident with the selected region,

(ii) creating a normalizing data profile from pixel data values corresponding to a second portion of the area imaged by the imager, and

(iii) normalizing the initial data profile by the normalizing data profile to yield a normalized data profile.

6. The method of claim 5, wherein step (c) comprises deriving the second data profile from the normalized data profile.

7. The method of claim 1, wherein the second data profile comprises a first section approximated by

$H$

[ 1 - ∑

x = x 0 x final ⁢

 

⁢

P ⁡

( x , M , σ

) ] ,

and wherein;

P(x,M,σ

) is a Gaussian point spread function for an imager used to generate the digital radiographic data received in step (a),

x is a location along a measurement axis in the plane of an image of the one or more objects,

M is the location of a boundary of one of the one or more objects,

σ

is a standard deviation of the point spread function,

x₀ and x_final are locations along the measurement axis and located on opposite sides of the boundary of the one object, and

H is a constant.

8. The method of claim 7, further comprising:

(f) estimating M based on the maximum of the first derivative of the first data profile created in step (b).

9. The method of claim 8, further comprising:

(g) calculating differences between the second data profile from step (c) using varying values for M and the first data profile from step (b); and

(h) choosing, based on the differences calculated in step (g), an optimized value for M.

10. The method of claim 7, wherein the one or more objects comprise two objects having substantially dissimilar densities, wherein the degree by which the actual condition varies from the reference condition corresponds to a linear separation between the two objects, and further comprising:

(f) deriving functions for lines corresponding to second and third sections of the second data profile on opposite sides of the first section along the measurement axis; and

(g) fitting the first section to the second and third sections.

11. The method of claim 7, wherein step (e) comprises determining the degree by which the actual condition varies from the reference condition using a formula m=[Δ

(m)−

a₀*R′

(m)_MAX−

b₀]/[a₁*R′

(m)_MAX+b₁], wherein;

m is a distance along the measurement axis,

Δ

(m) is a difference between the first data profile and the second data profile,

R′

(m)_MAX is the maximum of the first derivative of the first data profile, and

a₀, a₁, b₀ and b₁ are constants.

12. The method of claim 11, wherein a₀, a₁, b₀ and b₁ are constants derived from measurements of test samples having known values for m.

13. The method of claim 1, wherein step (e) comprises comparing the calculated difference from step (d) with a lookup table, the lookup table comprising values for differences associated with known degrees of variation from the reference condition.

14. The method of claim 1, wherein step (a) comprises receiving data generated by creating successive sets of overlapping images.

15. A computer-readable medium having stored thereon data representing sequences of instructions which, when executed by a processor, cause the processor to perform steps comprising:

(a) receiving digital radiographic data for one or more objects in an actual condition;

(b) creating a first data profile based on the received data, the first data profile corresponding to a selected region of the one or more objects and being associated with the actual condition;

(c) deriving a second data profile from the received data, the second data profile representing an expected data profile for the one or more objects when in a reference condition;

(d) calculating a difference between the first data profile created in step (b) and the second data profile derived in step (c); and

(e) determining, based upon the calculated difference, a degree by which the actual condition varies from the reference condition in the selected region.

16. The computer-readable medium of claim 15, wherein step (c) comprises deriving the second data profile from the first data profile.

17. The computer-readable medium of claim 15, wherein the one or more objects comprise two objects having substantially dissimilar densities, and wherein the degree by which the actual condition varies from the reference condition corresponds to a linear separation between the two objects.

18. The computer-readable medium of claim 17, wherein the linear separation between the two objects is of the same order of magnitude as a major portion of a point spread function for an imager used to generate the data received in step (a).

19. The computer-readable medium of claim 15, wherein step (b) further comprises:

(i) creating an initial data profile from pixel data values corresponding to a first portion of an area imaged by an imager, the first portion being generally coincident with the selected region,

(ii) creating a normalizing data profile from pixel data values corresponding to a second portion of the area imaged by the imager, and

(iii) normalizing the initial data profile by the normalizing data profile to yield a normalized data profile.

20. The computer-readable medium of claim 19, wherein step (c) comprises deriving the second data profile from the normalized data profile.

21. The computer-readable medium of claim 15, wherein the second data profile comprises a first section approximated by

$H$

[ 1 - ∑

x = x 0 x final ⁢

 

⁢

P ⁡

( x , M , σ

) ] ,

and wherein;

P(x,M,σ

) is a Gaussian point spread function for an imager used to generate the digital radiographic data received in step (a),

x is a location along a measurement axis in the plane of an image of the one or more objects,

M is the location of a boundary of one of the one or more objects,

σ

is a standard deviation of the point spread function,

x₀ and x_final are locations along the measurement axis and located on opposite sides of the boundary of the one object, and

H is a constant.

22. The computer-readable medium of claim 21, comprising additional data representing sequences of instructions which, when executed by a processor, cause the processor to perform additional steps comprising:

(f) estimating M based on the maximum of the first derivative of the first data profile created in step (b).

23. The computer-readable of claim 22, comprising additional data representing sequences of instructions which, when executed by a processor, cause the processor to perform additional steps comprising:

(g) calculating differences between the second data profile from step (c) using varying values for M and the first data profile from step (b); and

(h) choosing, based on the differences calculated in step (g), an optimized value for M.

24. The computer-readable medium of claim 21, wherein the one or more objects comprise two objects having substantially dissimilar densities, wherein the degree by which the actual condition varies from the reference condition corresponds to a linear separation between the two objects, and comprising additional data representing sequences of instructions which, when executed by a processor, cause the processor to perform additional steps comprising:

(f) deriving functions for lines corresponding to second and third sections of the second data profile on opposite sides of the first section along the measurement axis; and

(g) fitting the first section to the second and third sections.

25. The computer-readable medium of claim 21, wherein step (e) comprises determining the degree by which the actual condition varies from the reference condition using a formula m=[Δ

(m)−

a₀*R′

(m)_MAX−

b₀]/[a₁*R′

(m)_MAX+b₁], wherein;

m is a distance along the measurement axis,

Δ

(m) is a difference between the first data profile and the second data profile,

R′

(m)_MAX is the maximum of the first derivative of the first data profile, and

a₀, a₁, b₀ and b₁ are constants.

26. The computer-readable medium of claim 25, wherein a₀, a₁, b₀ and b₁ are constants derived from measurements of test samples having known values for m.

27. The computer-readable medium of claim 15, wherein step (e) comprises comparing the calculated difference from step (d) with a lookup table, the lookup table comprising values for differences associated with known degrees of variation from the reference condition.

28. The computer-readable medium of claim 15, wherein step (a) comprises receiving data generated by creating successive sets of overlapping images.

29. A method for determining a linear separation distance between two objects having substantially dissimilar densities, comprising:

(a) receiving digital image data for the objects, the data created using an imager having a Gaussian point spread function with a standard deviation of the same order of magnitude as the separation distance;

(b) creating an initial data profile from a first set of pixel data values from the image data received in step (a), the first set of pixel data values corresponding to a first region of an area imaged by the imager;

(c) creating a normalizing data profile from a second set of pixel data values from the image data received in step (a), the second set of pixel data values corresponding to a second region of the image area;

(d) normalizing the initial data profile by the normalizing data profile to yield a normalized data profile;

(e) deriving a reference data profile from the normalized data profile, the reference data profile representing an expected data profile for the first region when the objects have a reference separation, the reference data profile having a first section approximated by

$H<br><br>\left[1-\underset{x=x_0}{\overset{x_{\mathrm{final}}}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>P<br><br>\left(x,M,\mathrm{\sigma <br><br>}\right)\right],$

 

wherein;

P(x,M,σ

) is the Gaussian point spread function for the imager,

x is a location along an axis of the separation between the objects,

M is the location of a boundary of one of the objects,

σ

is the standard deviation of the imager point spread function,

x₀ and x_final are linear locations along the separation axis and located on opposite sides of the boundary, and

H is a constant;

(f) estimating M based on the maximum of the first derivative of the normalized data profile;

(g) calculating differences between the reference data profile with varying values for M and the normalized data profile;

(h) choosing, based on the differences calculated in step (g), an optimized value for M;

(i) deriving functions for lines corresponding to second and third sections of the reference data profile on opposite sides of the first section along the separation axis;

(j) fitting the first section to the second and third sections; and

(k) determining the degree of variance from the reference separation using the formula s=[Δ

(s)−

a₀*R′

(s)_MAX−

b₀]/[a₁*R′

(s)_MAX+b₁], wherein;

s is the object separation,

Δ

(s) is a difference between the normalized data profile and the reference data profile,

R′

(s)_MAX is the maximum of the first derivative of the normalized data profile, and

a₀, a₁, b₀ and b₁ are constants derived from measurements of test samples having known separations.