Multiscale edge detection and fiber enhancement using differences of oriented means

• US 8,385,657 B2
• Filed: 07/31/2008
• Issued: 02/26/2013
• Est. Priority Date: 08/01/2007
• Status: Expired due to Fees

• Current Assignee: Yeda Research and Development Co. Ltd. (Weizmann Institute of Science)
• Original Assignee: Yeda Research and Development Co. Ltd. (Weizmann Institute of Science)
• Inventors: Basri, Ronen Ezra, Galun, Meirav, Brandt, Achiezer
• Primary Examiner(s): PATEL, KANJIBHAI B
• Application Number:
  US12/671,293
• Publication Number:
  US 20100202701A1
• Time in Patent Office: 1,671 Days
• Field of Search: 382/195, 382/254, 382260-270, 382274-275, 382/305, 382/312, 382/199, 358/1.2, 358/3.27, 345/647, 345/660, 375/254
• US Class Current: 382/199
• CPC Class Codes: G06T 2207/10056 Microscopic image
• CPC Class Codes: G06T 2207/30024 Cell structures in vitro; Tissue sections in vitro
• CPC Class Codes: G06T 7/13 Edge detection
• CPC Class Codes: G06V 10/443 by matching or filtering
• CPC Class Codes: G06V 20/695 Preprocessing, e.g. image segmentation

Abstract

Method, apparatus and computer program product that uses a novel algorithm for edge detection suitable for both natural as well as noisy images. A scale adaptive threshold is used along with a recursive decision process to reveal the significant edges of all lengths and orientations and to localize them accurately even in low-contrast and very noisy images. Further the algorithm is use for fiber detection and enhancement by utilizing stochastic completion-like process from both sides of a fiber. The algorithm relies on an efficient multiscale algorithm for computing all “significantly different” oriented means in an image in 0(N log p), where N is the number of pixels in the image, and p is the length of the longest structure of interest. Experimental results on both natural and noisy images present confirmation of the method, apparatus and computer program product.

Claims

1. A method for electronically processing an electronically stored image by a computer having a processor, circuitry for controlling the processor and memory for simultaneously extracting edges of all lengths, whether the image is a natural or a noisy image, and for enabling visualization of the edges, by one of displaying the resulting image on a monitor, storing such images in a memory for future visualization, developing copies of images, and printing a copy of the resulting image comprising the steps of:

a. storing an image in O (N log ρ

), where N is the number of pixels in the image, and ρ

is the length of the longest edge structure of interest pixel by pixel in the memory of the computer;

b. storing non-transitory computer coded instructions for configuring computer circuitry for programming the processor of the computer for;

i. filtering the stored image to obtain a set of responses that measures difference of oriented means of various lengths and orientations, and to construct all significantly different oriented means at all locations, lengths, and orientations in the image;

ii. said filtering being carried out by a multiscale edge detection algorithm based on I(x, y) denoting a continuous function representing image intensities given in a two-dimensional domain and the oriented means comprising the family of averages of I(x, y) being denoted along rectangular patches of a given center location x=(x, y), length L, width w, and orientation θ

with w set to a small constant yielding elongated oriented means;

iii. processing the oriented means via integrals of the form

2. The method of claim 1 wherein step b. vii. Is carried out by denoting by σ

_local, a local estimate of the noise, the maximum of the two empirical standard deviations on either side, and removing edges for which

3. The method of claim 1 wherein step b. ii. Is carried out by constructing differences of oriented means by adding and subtracting width-1 oriented means of the appropriate length to obtain a family of width-1 oriented means, F(x, L, w, θ

) defined over an infinite set of locations, lengths, and orientations, but under minimal smoothness assumptions of I(x, y), and obtain any oriented mean in this family from only a finite collection of oriented means with oriented means at interim locations, lengths, and orientations determined by interpolation with an accuracy dependent on spatial and angular resolutions.

4. The method of claim 1 further including the steps of:

xii. marking detected edges either “

red”

or “

blue”

, by classifying their gradient orientation relative to a pre-specified canonical orientation and creating two maps, one for the edges marked red and one for the edges marked blue;

xii. constructing two diffusion maps, one for the red and the other for the blue edge maps, by convolving each with a Gaussian filter, and then multiplying the two diffusion maps to obtain the enhanced fibers.

5. The method of claim 1 wherein the image is nerve cells and the method identifies the branching axonal structures in the image and measures their total length.

6. Apparatus for processing an image whether the image is a natural or a noisy image to extract simultaneously edges of all lengths and for enabling visualization of the edges by a computer having a processor, circuitry for controlling the processor and memory for simultaneously extracting edges of all lengths, whether the image is a natural or a noisy image, and for enabling visualization of the edges, by one of displaying the resulting image on a monitor, storing such images in a memory for future visualization, developing copies of images, and printing a copy of the resulting image comprising:

a. a computer having a processor, circuitry for controlling the processor and memory for electronically processing an electronically stored image;

b. circuitry for storing an image in O (N log ρ

), where N is the number of pixels in the image, and ρ

is the length of the longest edge structure of interest pixel by pixel in the memory of the computer;

c. said memory storing non-transitory computer coded instructions for configuring computer circuitry for programming the processor of the computer for;

i. filtering the stored image to obtain a set of responses that measures difference of oriented means of various lengths and orientations, and to construct all significantly different oriented means at all locations, lengths, and orientations in the image;

ii. said filtering being carried out by a multiscale edge detection algorithm based on I(x, y) denoting a continuous function representing image intensities given in a two-dimensional domain and the oriented means comprising the family of averages of I(x, y) being denoted along rectangular patches of a given center location x=(x, y), length L, width w, and orientation θ

with w set to a small constant yielding elongated oriented means;

iii. processing the oriented means via integrals of the form

7. The apparatus of claim 6 wherein the computer circuitry is further configured for programming the processor of the computer for carrying out testing of identified potential edges for statistical significance by denoting by σ

_local, a local estimate of the noise, the maximum of the two empirical standard deviations on either side, and removing edges for which

8. The apparatus of claim 6 wherein the computer circuitry is further configured for programming the processor of the computer for carrying out filtering by constructing differences of oriented means by adding and subtracting width-1 oriented means of the appropriate length to obtain a family of width-1 oriented means, F(x, L, w, θ

) defined over an infinite set of locations, lengths, and orientations, but under minimal smoothness assumptions of I(x, y), and obtain any oriented mean in this family from only a finite collection of oriented means with oriented means at interim locations, lengths, and orientations determined by interpolation with an accuracy dependent on spatial and angular resolutions.

9. The apparatus of claim 6 wherein the computer circuitry is further configured for programming the processor of the computer for marking detected edges either “

red”

or “

blue”

, by classifying their gradient orientation relative to a pre-specified canonical orientation and creating two maps, one for the edges marked red and one for the edges marked blue, and for constructing two diffusion maps, one for the red and the other for the blue edge maps, by convolving each with a Gaussian filter, and then multiplying the two diffusion maps to obtain the enhanced fibers.

10. The apparatus of claim 6 wherein the image is nerve cells and the apparatus identifies the branching axonal structures in the image and measures their total length.

11. A non-transitory computer readable storage medium storing non-transitory computer readable instructions wherein execution of the instructions program a processor of a computer to electronically process an image stored in the computer memory to simultaneously extract edges of all lengths, whether the image is a natural or a noisy image, and for enabling visualization of the edges, by one of displaying the resulting image on a monitor, storing such images in a memory for future visualization, developing copies of images, and printing a copy of the resulting image;

wherein the image is stored in O (N log ρ

), where N is the number of pixels in the image, and ρ

is the length of the longest edge structure of interest, pixel by pixel in the memory of the computer;

said non-transitory computer readable instructions programming the processor of the computer for;

i. filtering the stored image to obtain a set of responses that measures difference of oriented means of various lengths and orientations, and to construct all significantly different oriented means at all locations, lengths, and orientations in the image;

ii. said filtering being carried out by a multiscale edge detection algorithm based on I(x, y) denoting a continuous function representing image intensities given in a two-dimensional domain and the oriented means comprising the family of averages of I(x, y) being denoted along rectangular patches of a given center location x=(x, y), length L, width w, and orientation θ

with w set to a small constant yielding elongated oriented means;

iii. processing the oriented means via integrals of the form

12. The non-transitory computer readable storage medium of claim 11 wherein the testing of identified edges Is carried out by denoting by σ

_local, a local estimate of the noise, the maximum of the two empirical standard deviations on either side, and removing edges for which

13. The non-transitory computer readable storage medium of claim 11 wherein the filtering is carried out by constructing differences of oriented means by adding and subtracting width-1 oriented means of the appropriate length to obtain a family of width-1 oriented means, F(x, L, w, θ

) defined over an infinite set of locations, lengths, and orientations, but under minimal smoothness assumptions of I(x, y), and obtain any oriented mean in this family from only a finite collection of oriented means with oriented means at interim locations, lengths, and orientations determined by interpolation with an accuracy dependent on spatial and angular resolutions.

14. The non-transitory computer readable storage medium of claim 11 further programs the computer for marking detected edges either “

red”

or “

blue”

, by classifying their gradient orientation relative to a pre-specified canonical orientation and creating two maps, one for the edges marked red and one for the edges marked blue; and

for constructing two diffusion maps, one for the red and the other for the blue edge maps, by convolving each with a Gaussian filter, and then multiplying the two diffusion maps to obtain the enhanced fibers.

15. The non-transitory computer readable storage medium of claim 11 wherein the image is nerve cells and the non-transitory instructions program the computer for identifying the branching axonal structures in the image and measuring their total length.