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WO2007078258A1 - Obtention d'une valeur seuil de division d'un jeu de donnees sur la base d'une variance de classe et du contraste entre classes - Google Patents

Obtention d'une valeur seuil de division d'un jeu de donnees sur la base d'une variance de classe et du contraste entre classes Download PDF

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Publication number
WO2007078258A1
WO2007078258A1 PCT/SG2006/000257 SG2006000257W WO2007078258A1 WO 2007078258 A1 WO2007078258 A1 WO 2007078258A1 SG 2006000257 W SG2006000257 W SG 2006000257W WO 2007078258 A1 WO2007078258 A1 WO 2007078258A1
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WIPO (PCT)
Prior art keywords
classes
threshold value
term
contrast
dataset
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Application number
PCT/SG2006/000257
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English (en)
Inventor
Yu Qiao
Qingmao Hu
Guoyu Qian
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Agency For Science, Technology And Research
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Publication of WO2007078258A1 publication Critical patent/WO2007078258A1/fr

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Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/90—Dynamic range modification of images or parts thereof
    • G06T5/92—Dynamic range modification of images or parts thereof based on global image properties
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/40—Image enhancement or restoration using histogram techniques
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/10—Segmentation; Edge detection
    • G06T7/11—Region-based segmentation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/10—Segmentation; Edge detection
    • G06T7/136—Segmentation; Edge detection involving thresholding
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/10—Segmentation; Edge detection
    • G06T7/194—Segmentation; Edge detection involving foreground-background segmentation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10072—Tomographic images
    • G06T2207/10088—Magnetic resonance imaging [MRI]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/30—Subject of image; Context of image processing
    • G06T2207/30004—Biomedical image processing
    • G06T2207/30016—Brain

Definitions

  • the present invention relates to a method for processing a data set containing one or more images (typically, but not limited to, medical images, such as scans of a brain) to obtain a threshold which can be used to partition the image(s) into "object" and background regions.
  • the invention further relates to systems employing the method.
  • Histogram-based thresholding methods in which a threshold value is determined by analyzing an intensity histogram, are well-known as global thresholding techniques.
  • Various criteria for obtaining the threshold have been studied. Among them, the most frequently used is an algorithm which selects the threshold such that the between-class variance of the data points above the threshold and not greater than the threshold is minimized (Otsu N., "A thresholding selection method from gray-level histograms", IEEE Transactions on System, Man and Cybernetics 1979; 9(1): 62-66.).
  • object pixels which are respectively the pixels having an intensity not greater than and above the threshold T.
  • probabilities that a pixel is a member of classes CO and C1 are respectively:
  • between-class variance depend on the threshold T, but their sum does not. Therefore maximizing the between-class variance is equivalent to minimizing within-class variance.
  • the within-class variance measures the homogeneity within object and background. This criterion, however, works poorly for segmentation of small objects from complex background. Specifically, when the size of background is much larger than that of object and the intensity distribution of background is complex (non-unimodal), the optimum threshold by Otsu tends to dichotomize the image into object and background of size as equal as possible. This is because the contrast between object and background has no explicit influence on threshold selection.
  • Fig. 1(a) is an MRA (magnetic resonance angiography) image of a portion of a brain.
  • a region of interest (ROI) is indicated by the light rectangle.
  • Three generally-circular blood vessels are visible within this region.
  • Fig. 1(b) shows the intensity histogram for this image.
  • the distribution of the background intensities is bimodal with strong peaks at about 10 and about 30, and the points in the histogram relating to the three blood vessels are scattered centred at the small peak around intensity 100.
  • Fig. 1(c) shows the result of applying Otsu's thresholding algorithm to the dataset of Fig. 1(a).
  • the pixels above the derived threshold (object pixels) are shown as white and those not greater than the threshold (background pixels) as black.
  • Fig. 1(d) shows the result of selecting the threshold by the "minimum error method". Again, the three blood vessels cannot be segmented.
  • the present invention aims to provide new and useful methods and systems for obtaining a threshold for partitioning a data set comprising an image.
  • the present invention proposes obtaining the threshold as a value which partitions a dataset of intensity values into two classes, by minimizing a weighted sum of (i) a term which varies with the within-class variance of the classes and (ii> a term which varies inversely with the contrast between the classes.
  • the weighted sum may be denoted as:
  • G( ⁇ y (T)) is the term including the within-class
  • the process for selecting 7 amounts to finding the T* such that
  • the weighted sum may be defined as:
  • the term may be defined respectively as:
  • J( ⁇ , T) (I - ⁇ ) In ⁇ w (T) - ⁇ ln
  • m ⁇ (T) - m Q (T) , (5) J(X 1 T) (l-X) (6)
  • the weighting factor ⁇ may be predetermined based on values which have been effective for previous datasets. For example, a supervised learning process may be carried out involving a user and a plurality of additional datasets which together constitute a "learning set". For each dataset in the learning set, the user is presented with the results of the thresholding process for each of a number of values of the weighting factor, and for each dataset the user selects the value of the weighting factor for which, in his view, the thresholding process is optimal.
  • the selection process may, for example, be a feedback process in which the user is presented with the results of the process for a certain value of the weighting factor, and then instructs the algorithm to be repeated with a higher or lower weighting factor.
  • the weighting factors thus derived for each member of the learning set may then be used for future datasets which obey at least one similarity criterion with the learning set.
  • the weighting factor may be determined automatically, based on measured properties of the image and prior knowledge of the image. For example, the weighting factor may be selected such that it leads to a selection of a threshold such that the resultant segmented image is consistent with prior knowledge. For example, the weighting factor may be selected to be within a range of values which are determined using prior knowledge of the maximum and minimum proportions which the object should occupy within a region of interest of the image. The weighting factor may, for example, be defined as a median value within this range. Alternatively or additionally, the weighting factor may be selected to be within, and optionally a median value within, a range consistent with prior knowledge of the intensity contrast between the two classes.
  • FIG. 1 which is composed of Figs. 1(a) to 1(d), illustrates processing a first experimental dataset using a known thresholding algorithm
  • Fig. 2 shows steps in an embodiment of the present invention
  • Fig. 3 shows possible sub-steps to carry out one of the steps of Fig. 2;
  • Fig. 4 shows the results of the applying the embodiment of Fig. 2 to the dataset of Fig. 1 ;
  • Fig. 5 which is composed of Figs. 5(a) and 5(b), shows results of a numerical analysis of parameters used by the embodiment in relation to the dataset of Fig. 1. Detailed description of the embodiments
  • FIG. 2 the steps of a method which is an embodiment of the invention are illustrated.
  • a region of interest within an experimental dataset is defined.
  • J ⁇ J ( ⁇ - ⁇ ) ⁇ w (T) - ⁇ m,(T) - m Q (T)
  • the optimum threshold value T is selected by minimizing J(A , T) with respect to T for a fixed ⁇ , i.e.
  • the parameter ⁇ is a weight that balances the within-class variance and the
  • ⁇ should be in the range of [0, 1).
  • the weight ⁇ is application dependent, and in a second step of the method (step 20) the value of ⁇ is selected. This value is denoted as ⁇ *.
  • one suitable way to estimate an appropriate value of ⁇ is by supervised learning. This method is suitable if a number of images with similar properties (for example, having similar intensity distributions and/or similar object proportions) are available for segmentation.
  • the desired ⁇ can be manually determined for each of these images in turn by trying out a number of values for ⁇ , and by a human operator making a visual judgment for each image of the best value for ⁇ . Then the selected ⁇ can be used to segment similar images. For example, the proportion of cerebral vessels in most two-dimensional slices of a 3D MRA dataset varies within a small range.
  • a neuroradiologist can manually adjust the value of /I to extract the desired vessels from background on a selected slice, and this value of A can then be applied to the segmentation of other slices.
  • An alternative way of selecting ⁇ is based on any prior knowledge about the image.
  • the knowledge about the proportion of the object in medical images may be derived from anatomical knowledge or other a priori knowledge, while the knowledge about the intensity contrast may be evaluated directly from a statistical analysis of the image to the analysed, or obtained from a statistical analysis of similar images.
  • P 0 be the proportion of the region of interest which is occupied by the object.
  • the prior knowledge about the object proportion is that
  • the prior knowledge about intensity contrast can be expressed as m, ⁇ m o -m ⁇ ⁇ m h (8)
  • the threshold T* satisfying (8) can be found. Once this is done, the corresponding object proportion and intensity contrast can be calculated and denoted as P 0 ( ⁇ ) and
  • the following procedure, illustrated in Fig. 3, can estimate an appropriate ⁇ satisfying constraints (7) and (8), and thus perform step 20 of
  • step 21 ⁇ is set to 0.
  • step 22 the corresponding value of T * is obtained.
  • step 23 we calculate the object proportion P 0 ( ⁇ ) and contrast
  • step 24 it is determined whether the object proportion and contrast satisfy the predetermined constraints.
  • step 25 it is determined whether ⁇ is not less than
  • step 26 the value of ⁇ is increased by a predetermined step value. Otherwise, in a step 27, the values of ⁇ which in step 24 were found to satisfy the constraints are reviewed. The method finds the minimum and maximum ⁇
  • the method finds the minimum and maximum ⁇ such that
  • the method determines ⁇ min ⁇ 3x ) .
  • the assumed values for mi and nri h are 50 and 75 respectively.
  • the value of ⁇ * found in step 27 is 0.054, and the value of the T* is 69.
  • the derived proportion of the object P 0 is 1.6%.
  • Fig. 5(a) shows the how the value of J(A , T) varies with T for each of six values of ⁇
  • Fig. 5(b) shows the derived value of T* for a range of values of ⁇
  • the criterion of minimising J(/t , T) gives T* a low value, where the within-class variance dominates, so the derived threshold is close to that of the Otsu method.
  • the within-class variance and the intensity contrast are balanced to yield a desirable threshold. This happens for ⁇ in about the range of 0:013 to 0:094.

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Image Analysis (AREA)

Abstract

L'invention concerne un procédé permettant d'obtenir une valeur seuil T qui divise un jeu de données, tel qu'une image médicale, en deux classes qui sont composées de pixels ayant respectivement une valeur d'intensité non supérieure à la valeur seuil et inférieure à la valeur seuil. La valeur seuil T est sélectionnée pour réduire au minimum une somme pondérée (i) d'un terme qui varie avec la variance intra-classe des classes et (ii) d'un terme qui varie inversement avec le contraste entre les classes. La somme pondérée dépend d'un facteur de pondération ? qui peut être sélectionné sur la base d'un procédé d'apprentissage supervisé utilisant des jeux de données similaires ou bien obtenu par une connaissance à priori du jeu de données.
PCT/SG2006/000257 2006-01-06 2006-09-04 Obtention d'une valeur seuil de division d'un jeu de donnees sur la base d'une variance de classe et du contraste entre classes WO2007078258A1 (fr)

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US60/756,554 2006-01-06

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112396061A (zh) * 2020-11-25 2021-02-23 福州大学 基于目标灰度倾向加权的Otsu目标检测方法
CN118967642A (zh) * 2024-08-13 2024-11-15 保利长大工程有限公司 一种基于图像识别的混凝土板面板检测系统及其方法

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Publication number Priority date Publication date Assignee Title
WO2000016696A1 (fr) * 1998-09-18 2000-03-30 Arch Development Corporation Methode d'evaluation de l'etendue d'une tumeur dans des images obtenues par resonance magnetique
WO2001073682A1 (fr) * 2000-03-28 2001-10-04 The University Of Chicago Procede, systeme et support lisible par ordinateur servant a identifier des radiographies de la poitrine au moyen de techniques de cartographie d'image et de correspondance de modeles
WO2002103065A2 (fr) * 2001-06-20 2002-12-27 Koninklijke Philips Electronics N.V. Procede de segmentation d'images numeriques
US20030214290A1 (en) * 2002-05-15 2003-11-20 Van Muiswinkel Arianne M.C. Retrospective selection and various types of image alignment to improve DTI SNR
US6882748B2 (en) * 1999-03-02 2005-04-19 University Of Adelaide Method for image texture analysis
WO2005057493A1 (fr) * 2003-12-10 2005-06-23 Agency For Science, Technology And Research Procedes et appareil pour la binarisation d'images
EP1557792A2 (fr) * 2004-01-19 2005-07-27 Konica Minolta Medical & Graphic, Inc. Système pour le traitement d'images médicaux

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2000016696A1 (fr) * 1998-09-18 2000-03-30 Arch Development Corporation Methode d'evaluation de l'etendue d'une tumeur dans des images obtenues par resonance magnetique
US6882748B2 (en) * 1999-03-02 2005-04-19 University Of Adelaide Method for image texture analysis
WO2001073682A1 (fr) * 2000-03-28 2001-10-04 The University Of Chicago Procede, systeme et support lisible par ordinateur servant a identifier des radiographies de la poitrine au moyen de techniques de cartographie d'image et de correspondance de modeles
WO2002103065A2 (fr) * 2001-06-20 2002-12-27 Koninklijke Philips Electronics N.V. Procede de segmentation d'images numeriques
US20030214290A1 (en) * 2002-05-15 2003-11-20 Van Muiswinkel Arianne M.C. Retrospective selection and various types of image alignment to improve DTI SNR
WO2005057493A1 (fr) * 2003-12-10 2005-06-23 Agency For Science, Technology And Research Procedes et appareil pour la binarisation d'images
EP1557792A2 (fr) * 2004-01-19 2005-07-27 Konica Minolta Medical & Graphic, Inc. Système pour le traitement d'images médicaux

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KITTLER ET AL.: "Minimum Error Thresholding", PATTERN RECOGNITION, vol. 19, no. 1, 1986, pages 41 - 47, XP002090977 *
OTSU N.A.: "A Threshold Selection Method from Gray-Level Histograms", IEEE TRANSACTIONS ON SYSTEM, MAN AND CYBERNETICS, vol. SMC-9, no. 1, January 1979 (1979-01-01), pages 62 - 66, XP002386459 *

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112396061A (zh) * 2020-11-25 2021-02-23 福州大学 基于目标灰度倾向加权的Otsu目标检测方法
CN118967642A (zh) * 2024-08-13 2024-11-15 保利长大工程有限公司 一种基于图像识别的混凝土板面板检测系统及其方法
CN118967642B (zh) * 2024-08-13 2025-03-14 保利长大工程有限公司 一种基于图像识别的混凝土板面板检测系统及其方法

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