Mammographic texture synthesis: second-generation
clustered lumpy backgrounds using a
genetic algorithm

doi:10.1364/OE.16.007595

Mammographic texture synthesis: second-generation clustered lumpy backgrounds using a genetic algorithm

Cyril Castella, Karen Kinkel, François Descombes, Miguel P. Eckstein, Pierre-Edouard Sottas, Francis R. Verdun, and François O. Bochud »View Author Affiliations

Optics Express, Vol. 16, Issue 11, pp. 7595-7607 (2008)
http://dx.doi.org/10.1364/OE.16.007595

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Abstract

Synthetic yet realistic images are valuable for many applications in visual sciences and medical imaging. Typically, investigators develop algorithms and adjust their parameters to generate images that are visually similar to real images. In this study, we used a genetic algorithm and an objective, statistical similarity measure to optimize a particular texture generation algorithm, the clustered lumpy backgrounds (CLB) technique, and synthesize images mimicking real mammograms textures. We combined this approach with psychophysical experiments involving the judgment of radiologists, who were asked to qualify the visual realism of the images. Both objective and psychophysical approaches show that the optimized versions are significantly more realistic than the previous CLB model. Anatomical structures are well reproduced, and arbitrary large databases of mammographic texture with visual and statistical realism can be generated. Potential applications include detection experiments, where large amounts of statistically traceable yet realistic images are needed.

1. Introduction

The problem of human perception and performance in radiology detection tasks has been studied in numerous frameworks in the past: detection of a tumor on computer tomographic images of the liver [1

P. F. Judy, R. G. Swensson, R. D. Nawfel, and K. H. Chan, “Contrast detail curves for liver CT,” Med.Phys. 19, 1167–1174 (1992). [CrossRef]

S. E. Seltzer, P. F. Judy, R. G. Swensson, K. H. Chan, and R. D. Nawfel, “Flattening of the contrast-detail curve for large lesions on liver CT images,” Med. Phys. 21, 1547–1555 (1994). [CrossRef] [PubMed]

], stenosis in a blood vessel on fluoroscopic images [3

M.P. Eckstein and J.S. Whiting, “Visual signal detection in structured backgrounds. I. Effect of number of possible spatial locations and signal contrast,” J. Opt. Soc. Am. A 13, 1777–1787 (1996). [CrossRef]

], filling defects in X-ray coronary angiograms [4

Y. Zhang, B. T. Pham, and M. P. Eckstein, “Evaluation of JPEG 2000 Encoder Options: Human and Model Observer Detection of Variable Signals in X-Ray Coronary Angiograms,” IEEE Trans. Med. Imaging 23, 613–632 (2004). [CrossRef] [PubMed]

], nodules on pulmonary radiographs [5

E. A. Krupinsky and H. Roehring, “Pulmonary nodule detection and visual search: P45 and P104 monochrome versus color monitor displays,” Acad. Radiol. 9, 638–645 (2002).

], or microcalcifications on mammograms [6

F.O. Bochud, J.-F. Valley, F.R. Verdun, C. Hessler, and P. Schnyder, “Estimation of the noisy component of anatomical backgrounds,” Med. Phys. 26, 1365–1370 (1999). [CrossRef] [PubMed]

]. The aim of such studies is to determine the role on diagnostic detection of the inherent parameters of the images like resolution or contrast, the imaging unit acquisition parameters or the anatomy in the detection process. Many of such studies are psychophysical experiments involving radiologists or trained naïve [7

D. S. Brettle, E. Berry, and M. A. Smith, “The effect of experience on detectability in local area anatomical noise,” BJR 80, 186–193 (2007). [CrossRef]

] observers.

In particular, there has been a large interest in developing models that can predict human observer performance for detection tasks as a function of the image characteristics and the observer properties [8-10

R.F. Wagner and D.G. Brown., “Unified SNR analysis of medical imaging systems,” Phys. Med. Biol. 30, 489–518 (1985). [CrossRef]

]. These models aim at avoiding subjective methods to evaluate image quality and/or objective yet time-consuming methods such as psychophysical studies [11

L. Chen and H. H. Barrett, “Task-based lens design with application to digital mammography,” J. Opt. Soc. Am. A 22, 148–167 (2005). [CrossRef]

,12

M. A. Kupinski, E. Clarkson, J. H. Hoppin, L. Chen, and H. H. Barrett, “Experimental determination of object statistics from noisy images,” J. Opt. Soc. Am. A 20, 421–429 (2003). [CrossRef]

]. Models for objects superimposed on various types of real backgrounds or computer generated noises patterns have been developed and applied to the detection of lesions in radiological images [13-16

K. J. Myers, H. H. Barrett, M. C. Borgstrom, D. D. Patton, and G. W. Seeley, “Effect of noise correlation on detectability of disk signals in medical imaging,” J. Opt. Soc. Am. A 2, 1752–1759 (1985). [CrossRef] [PubMed]

Both psychophysical and model observer approaches require a large number of images to obtain accurate results. Real images or regions of interest (ROIs) would be ideal, but in most cases the number of available clinical images is limited. In addition, the question arises about reproducibility of the results with sets of images obtained with other imaging systems, digitization methods, or image post-processing. An alternative to using real images is to use computer generated images. This would allow for generation of unlimited number of samples with known and well-controlled statistical properties. Such images might have adjustable properties that would not depend on imaging device characteristics or digitization processes.

Two major methods have been explored for producing synthetic images mimicking mammograms. First, complete three-dimensional simulation of the breast components and properties, in conjunction with imaging device simulation, which is expected to produce very realistic images [17-19

B. Bliznakova, Z. Bliznakov, V. Bravou, Z. Kolitsi, and N. Pallikarakis, “A three-dimensional breast software phantom for mammography simulation,” Phys. Med. Biol. 48, 3699–3719 (2003). [CrossRef] [PubMed]

]. However, the complexity and computational cost associated with such modeling and the difficulty of taking into account breast compression can often be a limitation in the quality of the resulting images. For that reason, 2D approaches have been investigated, using backgrounds constituted by the summation of elementary bright structures called blobs [11

L. Chen and H. H. Barrett, “Task-based lens design with application to digital mammography,” J. Opt. Soc. Am. A 22, 148–167 (2005). [CrossRef]

,20

J. P. Rolland and H. H. Barrett, “Effect of random background inhomogeneity on observer detection performance,” J. Opt. Soc. Am. A 9, 649–658 (1992). [CrossRef] [PubMed]

,21

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, “Statistical texture synthesis of mammographic images with clustered lumpy backgrounds,” Opt. Express 4, 33–43 (1999). [CrossRef] [PubMed]

]. These lumpy backgrounds, as named originally by Rolland and Barrett [20

J. P. Rolland and H. H. Barrett, “Effect of random background inhomogeneity on observer detection performance,” J. Opt. Soc. Am. A 9, 649–658 (1992). [CrossRef] [PubMed]

], were designed to reproduce general lumpy textures. Bochud et al. [21

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, “Statistical texture synthesis of mammographic images with clustered lumpy backgrounds,” Opt. Express 4, 33–43 (1999). [CrossRef] [PubMed]

] generalized the model to clustered lumpy backgrounds (CLB), matching the Wiener spectra of real mammograms and synthetic backgrounds and empirically optimizing the parameters to obtain images which were as visually realistic as possible. Lumpy backgrounds and CLB images have the advantage of having analytically computable statistical properties, and are stationary within their boundaries. Statistical descriptions of general lumpy and CLB objects have been further investigated by Kupinsky et al. [12

M. A. Kupinski, E. Clarkson, J. H. Hoppin, L. Chen, and H. H. Barrett, “Experimental determination of object statistics from noisy images,” J. Opt. Soc. Am. A 20, 421–429 (2003). [CrossRef]

]. However, for this model as for most of 3D or 2D methods, thorough and objective assessment of visual realism and similarity of statistical properties to real images has not been carried out. The main obstacle has been the difficulty of defining criteria for the assessment.

For synthetic images to be used by humans and model observers then necessary criteria are that the images look visually similar to the real images (visual realism) and that the statistical properties of the synthetic images match to larger degree those of the real images (statistical realism). Although these criteria are typically aimed at when creating synthetic backgrounds, the process is commonly approached through trial and error and comparison of a few synthetic and real images. The purpose of the current work was to systematically optimize the visual and statistical realism using a genetic algorithm as search optimization routine.

Specifically, our aim in this study was to extend and optimize the CLB model and to objectively assess the realism of the obtained images. For this purpose, we used a database of 1000 square ROIs selected from real mammograms, and defined a metric based on the Mahalanobis distance to compute the statistical distance between real images and synthetic CLB images. The CLB parameters were optimized using a genetic algorithm in order to minimize the Mahalanobis distance. Psychophysical experiments involving radiologists and radiographers were then designed in order to evaluate the visual realism of the synthetic images.

2. Material and methods

2.1 Clustered lumpy background (CLB) model

Lumpy backgrounds are synthetic, digital images generated by superposition of elementary bright blobs. The number of blobs is randomly sampled according to a Poisson process and the blob centers are placed at random locations uniformly distributed in the image. Lumpy backgrounds were originally designed by Rolland and Barrett [20

J. P. Rolland and H. H. Barrett, “Effect of random background inhomogeneity on observer detection performance,” J. Opt. Soc. Am. A 9, 649–658 (1992). [CrossRef] [PubMed]

] with circularly symmetric blobs b(r), so that the image g could be written as:

g (r) = \sum_{k = 1}^{K} b (r - r_{k}),

(1)

where r _k is the center position of the k^th blob, and K the total number of blobs in the image.

Later, Bochud, et al., [21

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, “Statistical texture synthesis of mammographic images with clustered lumpy backgrounds,” Opt. Express 4, 33–43 (1999). [CrossRef] [PubMed]

] generalized this model to clusters of exponential, not necessarily circular symmetric blobs. Clustered lumpy backgrounds (CLB) are produced by randomly choosing a number of clusters, K, following a Poisson process, and distributing them randomly on the image plane. For each cluster, a random number of blobs, N_k, are positioned randomly around the cluster center according to a probability density function (pdf) ϕ(r). Finally, all blobs belonging to the same k^th cluster are rotated by an angle θ_k before being summed to obtain the final image g(r):

g (r) = \sum_{k = 1}^{K} \sum_{n = 1}^{N_{k}} b (r - r_{k} - r_{kn}, R_{θ k})

(2)

All parameters and their distributions are summarized in Table 1. The general functional expression of the blob has been chosen as:

b (r, R_{θ}) = \exp (- α \frac{{∥ R_{θ} r ∥}^{β}}{L (R_{θ} r)}),

(3)

where α and β are real parameters, and L is the characteristic length of an ellipse with half axes equal to L_x and L_y [21

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, “Statistical texture synthesis of mammographic images with clustered lumpy backgrounds,” Opt. Express 4, 33–43 (1999). [CrossRef] [PubMed]

]. One of the major advantages of CLB technique is that some statistical properties of g(r) like its power spectrum can be analytically computed from the model parameters.

Table 1. Definitions and distributions of the CLB model parameters.

Variable Definition		Distribution
K	number of clusters	poisson with mean value K₀
r _k	position of the k^th cluster	uniform across image
N_k	number of blobs within the k^th cluster	poisson with mean value N₀
θ_k	rotation angle of the blobs in the k^th cluster	uniform between 0 and 2π
R _θ	rotation matrix of angle θ	N/A
r _kn	position of the n^th blob within the k^th cluster	Gaussian pdf ϕ(r)
b(r,R _θ)	blob profile rotated at angle θ	N/A

Fig. 1. (1.55 MB) Movie showing the construction of a CLB image. This example has two CLB layers with isotropic orientation of the blobs. [Media 1]

The free parameters of the CLB model are thus {α,β,L_x,L_y,σ_x,σ_y,K₀,N₀}, where σ_x and σ_y are the standard deviations of the Gaussian pdf, ϕ(r), in x and y directions respectively. These 8 parameters had been empirically optimized in the original study [21

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, “Statistical texture synthesis of mammographic images with clustered lumpy backgrounds,” Opt. Express 4, 33–43 (1999). [CrossRef] [PubMed]

], on the basis of visual inspections of the images and comparison of Wiener spectrum with that of real mammograms. These values were used as a starting point for our study.

In order to improve the realism of CLB images, we introduced two variations into the model. First, we superimposed another CLB onto the image computed from Eq. (2), with fixed parameters α=2.0, β=0.9, L_x=50 pixels, L_y=5 pixels, σ_x=10 pixels, σ_y=10 pixels, and free parameters K₀’<<K₀ and N₀’. The inclusion of a small amount of long and narrow blobs aims to better reproduce the fibrous structures of real mammograms.

The second variation was included to favor oriented structures similar to those visible on real mammograms. At the whole breast scale, these structures arise from the projection of the ducts converging towards the nipple, or from suspensory ligaments. For this purpose, the pdf of the rotation angle was changed from uniform to Gaussian with a mean equal to θ₀ and a standard deviation of π/6. With this change, the large scale oriented structures were constructed by the summation of clusters with similar orientation. The mean parameter,θ₀, was changed randomly with uniform pdf between 0 and 2π for each realization. If two superimposed layers were used for the image, both used the same θ₀.

An example of a synthetic image generation is shown on Fig. 1.

2.2 Optimization of the CLB parameters with a genetic algorithm

Genetic algorithms are a family of computational models inspired by evolution [22

D. Whitley, “A Genetic Algorithm Tutorial,” Stat. Comput. 4, 65–85 (1994). [CrossRef]

]. The free parameters of a given optimization problem are encoded on a chromosome-like data structure, and selection and recombination operators are applied in order to allow a population of potential solutions to evolve towards the optimal solution of the problem. The initial population is usually chosen randomly in the search space, and the corresponding chromosomes are evaluated through a fitness function. The best chromosomes are given better reproduction and survival opportunities. Following, crossover and mutation operators are applied in order to generate a new population of equal cardinality. These processes of evaluation, crossover and mutation are repeated until a user-defined (sub-)optimal value of the fitness function is reached, or when the best chromosome of the population has not been improved for a given number of generations.

Genetic algorithms have a great potential for non-linear function optimization in multi-dimensional spaces, since the intrinsic parallel structure of the optimization process is highly efficient for exploring multiple locations in the search space simultaneously, and avoiding local extrema. They can be used for binary or real coded problems, and many specific reproduction/mutation operators and techniques have been designed [23

A. E. Eiden, R. Hinterding, and Z. Michalewicz, “Parameter Control in Evolutionary Algorithms,” IEEE Trans. Evol. Comput. 3, 124–141, 1999. [CrossRef]

] in order to create specific algorithms for handling a wide range of optimization problems.

According to Eqs. (2) and (3), a classical CLB implementation requires a set of eight real parameters {α,β,L_x,L_y,σ_x,σ_y,K₀,N₀}. For the 2-layer CLB, the addition of {K₀ ’,N₀’} increases the number of parameters to ten. The statistical properties of CLB images depend in a non-analytical way on the parameters. Their optimization is furthermore complicated by the stochastic nature of the realizations for a same set of parameters. The optimization of the eight parameters of the previously published CLB model [21

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, “Statistical texture synthesis of mammographic images with clustered lumpy backgrounds,” Opt. Express 4, 33–43 (1999). [CrossRef] [PubMed]

] were limited to maximize the similarity of basic gray level (GL) histogram properties and Wiener spectrum of the synthetic and real mammographic textures, and to produce images qualitatively similar to real mammograms ROIs. No other consideration was taken into account in order to evaluate the mathematical realism of the obtained synthetic images. One key aspect of the present study was to introduce a metric based on Mahalanobis distance for quantifying similarity between synthetic and real images.

For this purpose, 36 statistical features based on complementary textural patterns analysis methods were computed. We used the GL histogram properties, the gray-level co-occurrence matrices (GLCM) [24-26

M. Sonka, V. Hlavak, and R. Boyle. Image processing, Analysis and Machine Vision (Brooks/Cole, Pacific Grove, Ca, 1999).

], the primitives matrices [25

M. Tuceryan and A. K. Jain. “Texture Analysis,” in The Handbook of Pattern Recognition and Computer Vision, C. H. Chen, L. F. Pau, and P. Wang, eds., (World Scientific Publishing Co, River Edge, NJ, 1998).

], the neighborhood gray tone difference matrix (NGTDM) [27

M. Amadasun and R. King, “Textural features corresponding to textural properties,” IEEE Trans. Syst. Man, Cybern. 19, 1264–1274 (1989). [CrossRef]

], and the fractal dimension [28

C. B. Caldwell, S. J. Stappelton, D. W. Holdsworth, R. A. Jong, W. J. Weiser, G. Cooke, and M. J. Yaffe, “Characterisation of mammographic parenchymal pattern by fractal dimension,” Phys. Med. Biol. 35, 235–247 (1990). [CrossRef] [PubMed]

], and computed the features for 1000 square ROIs within digital mammograms [29

C. Castella, K. Kinkel, M. P. Eckstein, P.-E. Sottas, F. R. Verdun, and F. O. Bochud, “Semiautomatic Mammographic Parenchymal Patterns Classification Using Multiple Statistical Features,” Acad. Radiol. 14, 1486–1499 (2007). [CrossRef] [PubMed]

]. These 256 by 256 pixels square regions were selected from the central breast areas of digital mammograms. We used a database of 88 patients who underwent screening exams on a GE Senograph 2000D full-field digital detector [31

S. Vedantham, A Karellas, S. Suryanarayanan, D. Albagli, S. Han, E.J. Tkaczyk, C.E. Landberg, B. Opsahl-Ong, P.R. Granfors, I. Levis, C.J. D’Orsi, and R.E. Hendrick, “Full breast digital mammography with an amorphous silicon-based flat panel detector: Physical characteristics of a clinical prototype,” Med. Phys. 27, 558–567 (2000). [CrossRef] [PubMed]

,32

S. Muller, “Full-field digital mammography designed as a complete system,” Eur. J. Radiol. 31, 25–34 (1999). [CrossRef] [PubMed]

], with one craniocaudal (CC) and one mediolateral oblique (MLO) view per breast per patient.

Features derived from the GL histogram were standard deviation, skewness, kurtosis, and balance [30

Z. Huo, M. L. Giger, D. E. Wolverton, W. Zhong, S. Cumming, and O. I. Olopade, “Computerized analysis of mammographic parenchymal patterns for breast cancer assessment. Feature selection,” Med. Phys. 27, 4–12 (2000). [CrossRef] [PubMed]

]. They describe the general properties of the overall gray level distribution, including the histogram shape and symmetry. GLCM features were energy, entropy, maximum, contrast, and homogeneity. GLCM give information about the spatial relationships of GL in structural patterns. Primitives matrices (also known as run-length matrices) characterize the size and shape of textural patterns in an image. Short primitive emphasis, long primitive emphasis, gray level uniformity, and primitive length uniformity provided four more features. Additionally, four statistical parameters were computed from NGTDM: coarseness, contrast, complexity, and strength. These features were designed by Amadasun and King in order to give mathematical descriptions of the subjective aspect of images with such textural properties [27

M. Amadasun and R. King, “Textural features corresponding to textural properties,” IEEE Trans. Syst. Man, Cybern. 19, 1264–1274 (1989). [CrossRef]

]. Finally, the fractal dimension was computed. This feature is related to the complexity of textural patterns, a low fractal dimension denoting a rather homogeneous image structure. These 18 statistical quantities were computed for each of the 1000 mammograms ROIs, providing information about the structural patterns from the mm to the cm scale. As structures in mammograms typically range from about 1 mm to a few cm, this statistical analysis was also performed at another scale on the same ROIs in order to characterize the larger scale textural properties. For this purpose, each ROI was averaged on square 8×8 pixels blocks, and the same 18 parameters were computed again, making a total of 36 features. An exhaustive description of the mathematical definitions of the statistical features used in this work have been published in a previous study [29

Once all 36 features of a given synthetic or real image were measured and grouped into a single vector v, the Mahalanobis distance d was given by:

d = {[{(v - μ)}^{T} K^{- 1} (v - μ)]}^{\frac{1}{2}},

(4)

where µ represents the mean vector over the real images and K is the covariance matrix:

μ = \frac{1}{n} \sum_{i = 1}^{n} v_{i}

(5)

K = \frac{1}{n - 1} \sum_{i = 1}^{n} {(v_{i} - μ)}^{T} (v_{i} - μ),

(6)

with n=1000 being the size of the reference database.

The chromosomes in our genetic algorithm implementation were sets of 8- or 10-dimensional real vectors representing CLB parameters values. The genetic algorithm used the average Mahalanobis distance d computed over m=10 successive CLB realizations as the fitness function for evaluating the chromosomes, and was designed to minimize it. This averaging was done in order to avoid erroneous evaluation caused by the random nature of the CLB algorithm. Preliminary trials with smaller values of m had indeed been unsuccessful, because the fitness function was too unstable for accurately evaluating the chromosomes. Since the feature distributions are rather compact around their average values for a given set of CLB parameters, the choice of m=10 was a good trade-off between computational cost and fitness function stability. Rank-weighted selection of the parents, and elitist strategy were employed for the reproduction operators.

Crossover of two chromosomes c ¹ and c ² consisted in averaging half of the genes, keeping the others unchanged. The genes to be averaged were chosen randomly with equal probabilities. The crossover between c ¹ and c ² occurred with probability p_c, leaving both genes unchanged otherwise. The best chromosome remained unchanged from one generation to the next, which is the definition of elitist strategy. After the crossover processes, all but the elite chromosome underwent individual gene mutation with probability p_m, monotonically decreasing during the evolution [33

T. Bäck and M. Schütz. “Intelligent mutation rate control in canonical genetic algorithms,” in Proceedings of the 9^th International Symposium on Foundations of Intelligent Systems, number 1079 in Lectures notes in Artificial Intelligence, Z. Ras and M. Michalewicz, eds., (Springer, London, UK, 1996), pp. 158–167.

For each gene G, evolution was restricted to an interval [G_min, G_max], starting from random values between these bounds. The latter were deduced from the original CLB model as: {G _min, G _max}={.8G _Opex99, 1.2G_Opex99 }. These figures come from the assumption that the original model [21

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, “Statistical texture synthesis of mammographic images with clustered lumpy backgrounds,” Opt. Express 4, 33–43 (1999). [CrossRef] [PubMed]

], referred as Opex99 in this text, could be used as a starting point for the optimization process.

Preliminary optimizations had indeed shown that this restriction of the search space ensured that the Wiener spectrum of the synthetic images remained close to the one of the original CLB model, which had been designed in order to match the spectrum of real mammograms. All parameters of the genetic algorithm and their meaning are given in Table 2. Four variations of the CLB model were successively optimized: 1-layer classical CLB with isotropic orientation of the clusters (referred further in text as simpiso type), 2-layer CLB with isotropic orientation of the clusters (doubiso), 2-layer CLB with favored orientation of the clusters (doubori), and 1-layer CLB with favored orientation of the clusters (simpori).

Table 2. Genetic algorithm parameters used for optimizing CLB variables.

Parameter	Meaning	Value
L	Number of genes in a chromosome	8 or 10
S	Size of the chromosomes population	51
m	Number of realizations of a chromosome for evaluating its fitness function	10
p_c	Crossover probability	0.8

2.3 Evaluation of the visual realism of the synthetic images

The role of the genetic algorithm was to ensure that the synthetic CLB images would have statistical properties similar to real images. Although this point was necessary for future model observer experiments for example, it was certainly not a sufficient condition for using them in psychophysical detection experiments. Human perception is highly dependent on properties of the background as well as those of the neural processing and coding of visual information. Thus, similar statistical properties for a pair of images does not necessarily imply their visual resemblance to human observers. To evaluate the visual realism of the four optimized CLB types and compare it to the original CLB, a study was conducted with three radiologists and two radiographers.

The three main structures types that are likely to be found in real mammograms were evaluated: glandular areas, fatty areas, and fibers [34

American College of Radiology, Breast Imaging Reporting and Data System Atlas (American College of Radiology, Reston, Va, 2003).

]. The observers were first presented a series of 20 real images representative of each structure type. The selection of these reference images was based on the choices of one of the radiographers, and then confirmed by the opinion of a radiologist. The presentation of the reference images also allowed the radiologists to get acquainted to the display screen, light conditions, and definitions used for the three structure types. After this training phase, 50 realizations of each CLB model variation were presented in random order. The four variations developed with the GA, and the original CLB [21

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, “Statistical texture synthesis of mammographic images with clustered lumpy backgrounds,” Opt. Express 4, 33–43 (1999). [CrossRef] [PubMed]

] were displayed in 10 blocks of 25 images. The order of presentation for each CLB type was randomized within each block.

For each image, the observers were asked to tell whether or not they observed a given structure (glandular areas, fatty areas, fibers). For each affirmative answer, they were asked to grade the realism of the structure, based on a 10-grade scale evaluation. In order to ensure a consistent inter-observer use of the scale, the observers were clearly informed before the rating experiments that they should use grades 7 to 10 for images that could be expected to be observed on real mammograms, and grades 1 to 6 for insufficiently realistic images. In the latter case, the observers were given the possibility to further evaluate which features looked unrealistic by using one or more checkboxes representing possible defaults: too disorganized, too rectilinear, too much contrast, too fuzzy, or appearance of 3D-like artifacts. Additionally, the radiologists were asked to mention if some structure resembled a tumor (mass). This latter question was aimed at determining whether unwanted pathological (tumor-like) patterns arose from the CLB superimposition algorithm.

The 12-bits CLB images were converted to 256 gray levels before being displayed on a laptop screen. Their mean gray level value and standard deviation were adjusted to 110 and 35 respectively, in order to obtain images lying in the central dynamic range region of the display. The observers had the possibility to adjust the display brightness and contrast by observing a mammography test pattern at the beginning of the experiment. The laptop display was a practical choice, since the visualization experiments were to be conducted in several dark rooms. For the proposed task, all radiologists and radiographers unanimously reported adequate conditions to confidently assess the realism of the three structure types, since they were to be compared to real digital mammograms ROIs displayed on the same screen at the beginning of the test, and since no detection and/or classification tasks had to be conducted for this study. The 256 by 256 pixels synthetic images display size was 9 by 9 cm. According to preliminary discussions with the radiologists, the size of the image structures at this scale corresponded to the typical scale obtained when zooming on a digital mammography display unit.

3. Results

3.1 CLB parameters optimizations

Although genetic algorithms with elitist strategy usually have the property to be monotonically converging towards extrema of the fitness function, the example fitness function history on Fig. 2 shows that it decreased relatively regularly during 20-30 generations, and then had a more chaotic behavior. This was observed for all model variations, and can be explained by the random nature of the m realizations per chromosome that were computed for evaluating its fitness function. The same CLB parameters lead to images with similar overall statistical properties, but the 36 features we used in this study allowed for evaluating their variations much more precisely. The fitness function of a given chromosome could thus vary from a generation to another, and the best chromosome of generation T’ could be rejected to a higher rank at T’+1, even by chromosomes that had worse performance at generation T’. The upper series in Fig. 2 shows that the median fitness function of the population was less sensitive to this phenomenon. The evolution process was conducted during 100 generations for each of the variation of the CLB model, and the best chromosome of the evolution history was selected for computing the fitness function averages presented on Fig. 3, on the basis of 200 realizations per model.

Fig. 2. Example of fitness function history. The upper series represents the median value of the fitness function evaluated on the population at generation t, and the lower series indicates the value for the best chromosome.

Fig. 3. Fitness function computed from 200 realizations with the optimized set of CLB parameters for all model variations. The error bars represent the standard deviation of the realizations’ fitness function. The fitness function averaged over 200 real images is shown for comparison.

Figure 3 shows that the gain obtained by tuning the CLB parameters with the genetic algorithm is at least a factor of 2 for average Mahalanobis distance, compared to the original values (Opex99 [21

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, “Statistical texture synthesis of mammographic images with clustered lumpy backgrounds,” Opt. Express 4, 33–43 (1999). [CrossRef] [PubMed]

] series), depending on the model used. ANOVA analysis and Tukey HSD Test were performed in order to compare the fitness function values for all series. The results (F=615.7, p<0.001, HSD[.01]=2.32) indicate that the difference in Mahalanobis distance between Opex99 and all others series is statistically significant (p<.01). The difference between doubiso series and the three other optimized models is also significant (p<.01). Finally, even after the optimization, a significant difference between real images and each synthetic series remained (p<.01).

Figure 4 presents typical examples of images created with the different CLB parameters. The real mammogram ROI was selected from a medium-density breast. The optimized CLB parameters for generating these 256 by 256 pixels images are detailed in Appendix A. Typical computation time needed for computing the 200 realizations and their associated Mahalanobis distance was 40 minutes, which represents 12 seconds/realization.

Fig. 4. Examples of realizations for the different types of CLB variations. (a) ROI selected from a real mammograms; (b) 1-layer CLB, Opex99 [21

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, “Statistical texture synthesis of mammographic images with clustered lumpy backgrounds,” Opt. Express 4, 33–43 (1999). [CrossRef] [PubMed]

] parameters (referred in text as Opex99); (c) 2-layer CLB, isotropic orientation of the clusters (doubiso); (d) 2-layer CLB, favored orientation of the clusters (doubori); (e) 1-layer CLB, favored orientation of the clusters (simpori); (f) 1-layer CLB, optimized version of (b) (simpiso).

Fig. 5. Comparison of the real images and optimized CLB Wiener spectra. Pixel size is 0.1 mm. Only one series of synthetic images (doubiso) is shown. Other series have very similar spectra.

The Wiener spectra of real and synthetic mammograms is shown on Fig. 5. The spectra have a power-law form W(f)=K/f^b , where f is the radial frequency [6

F.O. Bochud, J.-F. Valley, F.R. Verdun, C. Hessler, and P. Schnyder, “Estimation of the noisy component of anatomical backgrounds,” Med. Phys. 26, 1365–1370 (1999). [CrossRef] [PubMed]

,35

A. Burgess and P. Judy, “Signal detection in power-law noise: effect of spectrum exponent,” J. Opt. Soc. Am. A 24, B52–B60 (2007). [CrossRef]

]. The exponent values are b=3.02±0.02 for the real images, and b=2.92±0.01 for the CLB (mean ± standard error).

3.2 Evaluating the realism of synthetic textures

Figure 6 summarizes the results for visual realism evaluation experiments performed by the radiologists (KK, ES, NH) and the radiographers (FD, PS). About 2% of the grades were classified as outliers according to Chauvenet criterion [36

J. R. Taylor, An Introduction to Error Analysis , (University Science Books, Mill Valley, Ca, 1982).

]. The corresponding data were removed before the statistical analysis presented in Table 3. The rejected outliers did not change any of the values of the 10, 25, 50, 75, and 90^th percentiles shown on Fig. 6, where the box plots summarize all marks given by the five observers to each series of images.

Fig. 6. Realism marks given by the observers (radiologists and radiographers) for the glandular areas, fatty areas, and fibers. The boxes represent the 25^th, 50^th, and 75^th percentiles, and the whiskers the limits for the 10^th and 90^th percentiles.

Table 3. Visual realism evaluation by the five observers for glandular (GL) and fatty (FA) areas, and fibers (FI). Bold values indicate statistically significantly realistic evaluations (one sided Student t-test, α=5%, β=0.8, H0: µ=6.5). Italic values correspond to the mean and standard error.

Obs.	Opex99			Doubiso			Doubori			Simpori			Simpiso
	GL	FA	FI	GL	FA	FI	GL	FA	FI	GL	FA	FI	GL	FA	FI
KK	6.80	7.18	7.85	7.18	7.96	7.94	7.40	7.96	8.78	7.22	7.76	7.92	5.00	6.47	4.93
ES	6.65	6.87	6.87	7.68	7.70	7.73	6.68	6.81	6.81	6.98	7.05	7.11
NH	7.68	7.68	7.68	9.00	9.00	9.00	7.68	7.68	7.68	6.96	6.96	6.96		(b)
FD	7.47	8.16	7.00	7.68	8.04	6.87	7.54	7.93	7.03	7.44	7.71	7.08
PS	7.65	7.77	(a)	8.40	8.14	7.58	7.23	7.15	6.18	7.55	7.46	7.67	4.67	4.95	4.09
Mean	7.3	7.5	7.4	8	8.2	7.8	7.3	7.5	7.3	7.2	7.4	7.3	4.8	5.7	4.5
	±0.2	±0.2	±0.3	±0.3	±0.2	±0.4	±0.2	±0.2	±0.4	±0.1	±0.2	±0.2	±0.2	±0.8	±0.4

For each synthetic image, the radiologists evaluated the realism of the three structures types (glandular areas, fatty areas, and fibers), whereas the two radiographers chose not to give their opinion in some cases, when they judged that a given structure covered a too small part of the ROI to be evaluated. This mainly happened for the evaluation of fibers, which are less visible in Opex99 and simpiso series. This latter series (simpiso) was only evaluated by the first two observers which took part in the study. T-tests of the first two observers’ data (α=5% and β=.8) showed that the simpiso series was significantly lower from the apriori selected threshold for realism (6.5) and thus statistically significantly visually unrealistic. It may be useful to repeat here that the observers were asked before the experiments to use a 10-grade scale with a threshold separating sufficiently realistic (grades 7 to 10) from insufficiently realistic (grades 1-6) images.

Bold values in Table 3 indicate that nearly all structures were considered significantly realistic at 5% confidence level (above the a priori selected threshold of grade 6.5) for the first four CLB models. After the evaluation of the first two observers, it was decided to further discard the simpiso series, since the grades given by these observers indicated that these images lack visual realism, compared to the other series.

When compared to each other, Opex99, doubori and simpori series obtain comparable overall performance for all structures types, while doubiso series outperforms them for all structures types when the results are averaged over the 5 observer. 1-way ANOVA analysis and Tukey HSD Test performed among these four series indicated that the average grade for doubiso images is significantly higher than for all other series for the glandulary areas (p<.01 in each case), fatty areas (p<.01), and fibers (p<.05).

Additionally, a two-way ANOVA was conducted in order to estimate separately the influence of the two model variations: the addition of the second layer with large blobs on one hand, and the preferred orientation of the blobs on the other. The grades given by the five observers were pooled together, and separate analyses were carried out for glandular areas, fatty areas, and fibers. The visual realism was significantly better for the images containing two layers (doubiso, doubori) than for images created with one layer only (simpiso, simpori), for all structure types (p<.01 in all cases). Images with an isotropic distribution of blob orientation (simpiso, doubiso) were judged significantly (p<.01) more realistic than images with preferred blob orientations (simpori, doubori) for the glandular areas. However, this effect was not statistically significant for fatty areas (p=.08) and fibers (p=.27).

4. Discussion

Although the implementation of the genetic algorithm became complex due to the inherent random nature of CLB model, the optimization produced images which statistical properties were significantly closer to real mammographic images than the original CLB. As the chromosomes’ evolution continued for more than 50 generations after the optimal parameters presented in Table 4 had been found, these values can thus be confidently considered as optimal for the developed model variations. It is difficult to intuitively interpret the absolute Mahalanobis distances in Fig. 3, since several statistical parameters, among the 36 used for defining that metric, are correlated in a complex way. However, a benchmark can be given by the distance computed for the 200 real mammograms ROIs, which is equal to 5.7±1.8 (mean ± SD, see Fig. 3). This indicates that from the statistical point of view, the synthetic images obtained by the models tuned by the genetic algorithm are much closer to real images than the original Opex99 series, but also that they cannot be considered indistinguishable from real images. Allowing enlarged bounds for G_min and G_max would lead to optimized chromosomes with better fitness function, but preliminary tests had shown that when given more freedom, the blobs dimensions evolved to points as small as G_min,Lx by G_min,Ly, lowering the average Mahalanobis distance down to about 10-15 depending on the model, but losing all visual realism. This emphasized the need for a realism evaluation conducted not only for the objective, statistical point of view through the Mahalanobis distance metric, but also for the subjective, visual aspect of the optimized model.

Concerning the model variations and their effect on the visual evaluation by the radiologists and radiographers, the favored orientation of the structures in simpori and doubori series was generally recognized as such by the observers, and their main drawback was that in some cases this orientation was too obvious and artificial, giving them the feeling of seeing three-dimensional structures instead of flat projections. This defect was particularly mentioned in simpori series, while the few large scale structures of doubori seemed to hide or mask the main layer composed of the smaller blobs. On the other hand, the observers found that some of the isotropic images were too disorganized to correctly represent real mammograms. This was the main reason for discarding the display of simpiso series for the last three observers in the psychophysical study. The presence of the second layer CLB in doubori did not improve or deteriorate significantly the visual aspect of simpori series, but the difference was clearly shown by the observers’ evaluations for the isotropic series: they reported unorganized images with too much contrast for the 1-layer series, and selected the 2-layer doubiso images as best overall series. The only limitation mentioned by the radiologists for that series was that for some images (about 10% of the set), bright points caused by blobs superimposition might be interpreted as clusters of microcalcifications. However, for visual experiments of mass detection, they confirmed that this downside would not be critical, since they are not affected by the presence of mm-scale microcalcifications when looking for cm-scale structures like masses.

A remaining question is the visual variability of the synthetic textures. As for most of other models, it is much smaller than that of real images. This has been partly solved by converting the CLB output float images to 12-bit images using randomly chosen values of mean gray level and standard deviation following real image corresponding distributions. One could have imagined using “floating” values for CLB parameters as well, but this possibility was not applied in our study. Another possibility is to separately use genetic optimization to fit the CLB parameters to ROIs from mammograms corresponding to individual patients or groups of patients. Since the real images have intrinsic variability sources like breast dimension and composition or quantum noise that are difficult to fully reproduce with CLB model, experienced radiologists would probably be able to distinguish between real and synthetic backgrounds. In order to focus the observers’ rating task on the different optimized CLB models, real mammograms ROIs were used as reference images only in the experiments, and the observers were not asked to rate other real images. However, we are confident that the optimized CLB provide excellent candidates for designing and conducting realistic mass detection tasks and that the results can be generalized to clinically relevant tasks, since recent findings [16

C. Castella, C. K. Abbey, M. P. Eckstein, F. R. Verdun, K. Kinkel, and F. O. Bochud, “Human linear template with mammographic backgrounds estimated with a genetic algorithm,” J. Opt. Soc. Am. A 24, B1–B12 (2007).

] with these backgrounds suggest that human observers use similar strategies with both background types.

5. Conclusion

Using a genetic algorithm and variations of the original CLB model, we were able to synthesize images which resulted in significantly closer visual and statistical properties to real images than those arising from the original CLB model. These models and parameters allow for generating an arbitrary number of such images while improving their realism. The synthetic images may find direct applications in detection experiments involving human or model observers since the visual and statistical characteristics have both been deemed by the current study to be similar to that of real images. In particular, the doubiso series were deemed to have visual characteristics very close to real images, even if their statistical properties are more distant from real images than for the other model variations simpori and doubori.

Compared to other image synthesis techniques, our technique is limited to the generation of square ROIs. However, it has the advantage of being able to quickly generate a large number of images, with traceable statistical properties, and visually representing all major structures types (glandular areas, fatty areas, fibers) that are visible on real mammograms. An interesting application of the technique described in this work would be to generate separate optimizations of the CLB model for different breast density classes. However, the methodology presented in this study is not limited to mammography and may be easily generalized to other medical or non-medical images. The only need is a sufficiently large database of reference textures for defining the Mahalanobis distance used as fitness function by the genetic algorithm for tuning the CLB parameters. Further work may also focus on other blob functional forms than the exponential blobs used in this study, and their influence on visual and statistical properties of the synthetic images.

Appendices

Appendix A: Optimal CLB parameters for each model variation

The CLB parameters mentioned used for generating the ROIs of Fig. 4 are given in Table 4.

Table 4. Optimized CLB parameters for the various CLB models.

Series	α	β	L_x	L_y	σ_x	σ_y	K₀	N₀	K₀’	N₀’
Opex99	2.1	0.5	5	2	12	12	600	20	N/A	N/A
Doubiso	2.31	0.57	4.09	1.76	13.27	13.92	643.81	20.21	61.47	5.60
Doubori	2.49	0.53	4.14	1.61	11.17	14.29	709.96	20.37	78.00	5.01
Simpori	2.51	0.54	4.53	1.66	10.67	13.33	714.44	23.14	N/A	N/A
Simpiso	2.47	0.59	4.19	1.63	11.02	12.27	674.97	16.53	N/A	N/A

Acknowledgments

The authors are grateful to Elsabe Scott, MD, Nigel Howart, MD, Christel Elandoy, and Philippe Spring for their participation in the psychophysical experiments. This work was supported by Swiss National Science Foundation under Grant No.320000-113863/1.

References and Links

1.	P. F. Judy, R. G. Swensson, R. D. Nawfel, and K. H. Chan, “Contrast detail curves for liver CT,” Med.Phys. 19, 1167–1174 (1992). [CrossRef]
2.	S. E. Seltzer, P. F. Judy, R. G. Swensson, K. H. Chan, and R. D. Nawfel, “Flattening of the contrast-detail curve for large lesions on liver CT images,” Med. Phys. 21, 1547–1555 (1994). [CrossRef] [PubMed]
3.	M.P. Eckstein and J.S. Whiting, “Visual signal detection in structured backgrounds. I. Effect of number of possible spatial locations and signal contrast,” J. Opt. Soc. Am. A 13, 1777–1787 (1996). [CrossRef]
4.	Y. Zhang, B. T. Pham, and M. P. Eckstein, “Evaluation of JPEG 2000 Encoder Options: Human and Model Observer Detection of Variable Signals in X-Ray Coronary Angiograms,” IEEE Trans. Med. Imaging 23, 613–632 (2004). [CrossRef] [PubMed]
5.	E. A. Krupinsky and H. Roehring, “Pulmonary nodule detection and visual search: P45 and P104 monochrome versus color monitor displays,” Acad. Radiol. 9, 638–645 (2002).
6.	F.O. Bochud, J.-F. Valley, F.R. Verdun, C. Hessler, and P. Schnyder, “Estimation of the noisy component of anatomical backgrounds,” Med. Phys. 26, 1365–1370 (1999). [CrossRef] [PubMed]
7.	D. S. Brettle, E. Berry, and M. A. Smith, “The effect of experience on detectability in local area anatomical noise,” BJR 80, 186–193 (2007). [CrossRef]
8.	R.F. Wagner and D.G. Brown., “Unified SNR analysis of medical imaging systems,” Phys. Med. Biol. 30, 489–518 (1985). [CrossRef]
9.	M. P. Eckstein, C. K. Abbey, and F. O. Bochud, “Practical guide to model observers in real and synthetic noisy backgrounds,” in Handbook of Medical Imaging, Physics & Psychophysics, K. Beutel, H. Kundel, and K. Vanmetter, eds (SPIE Press, Bellingham, Washington, 2000).
10.	H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley, Hoboken, NJ, 2004).
11.	L. Chen and H. H. Barrett, “Task-based lens design with application to digital mammography,” J. Opt. Soc. Am. A 22, 148–167 (2005). [CrossRef]
12.	M. A. Kupinski, E. Clarkson, J. H. Hoppin, L. Chen, and H. H. Barrett, “Experimental determination of object statistics from noisy images,” J. Opt. Soc. Am. A 20, 421–429 (2003). [CrossRef]
13.	K. J. Myers, H. H. Barrett, M. C. Borgstrom, D. D. Patton, and G. W. Seeley, “Effect of noise correlation on detectability of disk signals in medical imaging,” J. Opt. Soc. Am. A 2, 1752–1759 (1985). [CrossRef] [PubMed]
14.	F. O. Bochud, C. K. Abbey, and M. P. Eckstein, “Visual signal detection in structured backgrounds. III. Calculation of figures of merit for model observers in statistically nonstationary backgrounds,” J. Opt. Soc. Am. A 17, 193–205 (2000). [CrossRef]
15.	F. O. Bochud, C. K. Abbey, and M. P. Eckstein, “Search for lesions in mammograms: Non-Gaussian observer response,” Med. Phys. 31, 24–36 (2004). [CrossRef] [PubMed]
16.	C. Castella, C. K. Abbey, M. P. Eckstein, F. R. Verdun, K. Kinkel, and F. O. Bochud, “Human linear template with mammographic backgrounds estimated with a genetic algorithm,” J. Opt. Soc. Am. A 24, B1–B12 (2007).
17.	B. Bliznakova, Z. Bliznakov, V. Bravou, Z. Kolitsi, and N. Pallikarakis, “A three-dimensional breast software phantom for mammography simulation,” Phys. Med. Biol. 48, 3699–3719 (2003). [CrossRef] [PubMed]
18.	P. R. Bakic, M. Albert, D. Brzakovic, and A. D. Maidment, “Mammogram synthesis using a 3D simulation. I. Breast tissue model and image acquisition simulation,” Med. Phys. 29, 2131–9 (2002). [CrossRef] [PubMed]
19.	P. R. Bakic, M. Albert, D. Brzakovic, and A. D. Maidment, “Mammogram synthesis using a 3D simulation. II. Evaluation of synthetic mammogram texture,” Med. Phys. 29, 2140–2151 (2002). [CrossRef] [PubMed]
20.	J. P. Rolland and H. H. Barrett, “Effect of random background inhomogeneity on observer detection performance,” J. Opt. Soc. Am. A 9, 649–658 (1992). [CrossRef] [PubMed]
21.	F. O. Bochud, C. K. Abbey, and M. P. Eckstein, “Statistical texture synthesis of mammographic images with clustered lumpy backgrounds,” Opt. Express 4, 33–43 (1999). [CrossRef] [PubMed]
22.	D. Whitley, “A Genetic Algorithm Tutorial,” Stat. Comput. 4, 65–85 (1994). [CrossRef]
23.	A. E. Eiden, R. Hinterding, and Z. Michalewicz, “Parameter Control in Evolutionary Algorithms,” IEEE Trans. Evol. Comput. 3, 124–141, 1999. [CrossRef]
24.	M. Sonka, V. Hlavak, and R. Boyle. Image processing, Analysis and Machine Vision (Brooks/Cole, Pacific Grove, Ca, 1999).
25.	M. Tuceryan and A. K. Jain. “Texture Analysis,” in The Handbook of Pattern Recognition and Computer Vision, C. H. Chen, L. F. Pau, and P. Wang, eds., (World Scientific Publishing Co, River Edge, NJ, 1998).
26.	R. M. Haralick, K. Shanmugam, and I. Dinstein. “Textural Features for Image Classification,” IEEE Trans. Syst. Man. Cybern. 3, 610–662 (1973). [CrossRef]
27.	M. Amadasun and R. King, “Textural features corresponding to textural properties,” IEEE Trans. Syst. Man, Cybern. 19, 1264–1274 (1989). [CrossRef]
28.	C. B. Caldwell, S. J. Stappelton, D. W. Holdsworth, R. A. Jong, W. J. Weiser, G. Cooke, and M. J. Yaffe, “Characterisation of mammographic parenchymal pattern by fractal dimension,” Phys. Med. Biol. 35, 235–247 (1990). [CrossRef] [PubMed]
29.	C. Castella, K. Kinkel, M. P. Eckstein, P.-E. Sottas, F. R. Verdun, and F. O. Bochud, “Semiautomatic Mammographic Parenchymal Patterns Classification Using Multiple Statistical Features,” Acad. Radiol. 14, 1486–1499 (2007). [CrossRef] [PubMed]
30.	Z. Huo, M. L. Giger, D. E. Wolverton, W. Zhong, S. Cumming, and O. I. Olopade, “Computerized analysis of mammographic parenchymal patterns for breast cancer assessment. Feature selection,” Med. Phys. 27, 4–12 (2000). [CrossRef] [PubMed]
31.	S. Vedantham, A Karellas, S. Suryanarayanan, D. Albagli, S. Han, E.J. Tkaczyk, C.E. Landberg, B. Opsahl-Ong, P.R. Granfors, I. Levis, C.J. D’Orsi, and R.E. Hendrick, “Full breast digital mammography with an amorphous silicon-based flat panel detector: Physical characteristics of a clinical prototype,” Med. Phys. 27, 558–567 (2000). [CrossRef] [PubMed]
32.	S. Muller, “Full-field digital mammography designed as a complete system,” Eur. J. Radiol. 31, 25–34 (1999). [CrossRef] [PubMed]
33.	T. Bäck and M. Schütz. “Intelligent mutation rate control in canonical genetic algorithms,” in Proceedings of the 9^th International Symposium on Foundations of Intelligent Systems, number 1079 in Lectures notes in Artificial Intelligence, Z. Ras and M. Michalewicz, eds., (Springer, London, UK, 1996), pp. 158–167.
34.	American College of Radiology, Breast Imaging Reporting and Data System Atlas (American College of Radiology, Reston, Va, 2003).
35.	A. Burgess and P. Judy, “Signal detection in power-law noise: effect of spectrum exponent,” J. Opt. Soc. Am. A 24, B52–B60 (2007). [CrossRef]
36.	J. R. Taylor, An Introduction to Error Analysis , (University Science Books, Mill Valley, Ca, 1982).

OCIS Codes
(100.2960) Image processing : Image analysis
(170.3830) Medical optics and biotechnology : Mammography
(330.5000) Vision, color, and visual optics : Vision - patterns and recognition

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: January 23, 2008
Revised Manuscript: April 10, 2008
Manuscript Accepted: April 16, 2008
Published: May 12, 2008

Virtual Issues
Vol. 3, Iss. 6 Virtual Journal for Biomedical Optics

Citation
Cyril Castella, Karen Kinkel, François Descombes, Miguel P. Eckstein, Pierre-Edouard Sottas, Francis R. Verdun, and François O. Bochud, "Mammographic texture synthesis: second-generation clustered lumpy backgrounds using a genetic algorithm," Opt. Express 16, 7595-7607 (2008)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-16-11-7595

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References

P. F. Judy, R. G. Swensson, R. D. Nawfel, and K. H. Chan, "Contrast detail curves for liver CT," Med. Phys. 19, 1167-1174 (1992). [CrossRef]
S. E. Seltzer, P. F. Judy, R. G. Swensson, K. H. Chan, and R. D. Nawfel, "Flattening of the contrast-detail curve for large lesions on liver CT images," Med. Phys. 21, 1547-1555 (1994). [CrossRef] [PubMed]
M. P. Eckstein and J. S. Whiting, "Visual signal detection in structured backgrounds. I. Effect of number of possible spatial locations and signal contrast," J. Opt. Soc. Am. A 13, 1777-1787 (1996). [CrossRef]
Y. Zhang, B. T. Pham, and M. P. Eckstein, "Evaluation of JPEG 2000 Encoder Options: Human and Model Observer Detection of Variable Signals in X-Ray Coronary Angiograms," IEEE Trans. Med. Imaging 23, 613-632 (2004). [CrossRef] [PubMed]
E. A. Krupinsky and H. Roehring, "Pulmonary nodule detection and visual search: P45 and P104 monochrome versus color monitor displays," Acad. Radiol. 9, 638-645 (2002).
F. O. Bochud, J.-F. Valley, F. R. Verdun, C. Hessler, and P. Schnyder, "Estimation of the noisy component of anatomical backgrounds," Med. Phys. 26, 1365-1370 (1999). [CrossRef] [PubMed]
D. S. Brettle, E. Berry, and M. A. Smith, "The effect of experience on detectability in local area anatomical noise," BJR 80, 186-193 (2007). [CrossRef]
R. F. Wagner and D. G. Brown, "Unified SNR analysis of medical imaging systems," Phys. Med. Biol. 30, 489-518 (1985). [CrossRef]
M. P. Eckstein, C. K. Abbey, and F. O. Bochud, "Practical guide to model observers in real and synthetic noisy backgrounds," in Handbook of Medical Imaging, Physics & Psychophysics, K. Beutel, H. Kundel, and K. Vanmetter, eds (SPIE Press, Bellingham, Washington, 2000).
H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley, Hoboken, NJ, 2004).
L. Chen and H. H. Barrett, "Task-based lens design with application to digital mammography," J. Opt. Soc. Am. A 22, 148-167 (2005). [CrossRef]
M. A. Kupinski, E. Clarkson, J. H. Hoppin, L. Chen, and H. H. Barrett, "Experimental determination of object statistics from noisy images," J. Opt. Soc. Am. A 20, 421-429 (2003). [CrossRef]
K. J. Myers, H. H. Barrett, M. C. Borgstrom, D. D. Patton, and G. W. Seeley, "Effect of noise correlation on detectability of disk signals in medical imaging," J. Opt. Soc. Am. A 2, 1752-1759 (1985). [CrossRef] [PubMed]
F. O. Bochud, C. K. Abbey, and M. P. Eckstein, "Visual signal detection in structured backgrounds. III. Calculation of figures of merit for model observers in statistically nonstationary backgrounds," J. Opt. Soc. Am. A 17, 193-205 (2000). [CrossRef]
F. O. Bochud, C. K. Abbey, and M. P. Eckstein, "Search for lesions in mammograms: Non-Gaussian observer response," Med. Phys. 31, 24-36 (2004). [CrossRef] [PubMed]
C. Castella, C. K. Abbey, M. P. Eckstein, F. R. Verdun, K. Kinkel, and F. O. Bochud, "Human linear template with mammographic backgrounds estimated with a genetic algorithm," J. Opt. Soc. Am. A 24, B1-B12 (2007).
B. Bliznakova, Z. Bliznakov, V. Bravou, Z. Kolitsi, and N. Pallikarakis, "A three-dimensional breast software phantom for mammography simulation," Phys. Med. Biol. 48, 3699-3719 (2003). [CrossRef] [PubMed]
P. R. Bakic, M. Albert, D. Brzakovic, and A. D. Maidment, "Mammogram synthesis using a 3D simulation. I. Breast tissue model and image acquisition simulation," Med. Phys. 29, 2131-9 (2002). [CrossRef] [PubMed]
P. R. Bakic, M. Albert, D. Brzakovic, and A. D. Maidment, "Mammogram synthesis using a 3D simulation. II. Evaluation of synthetic mammogram texture," Med. Phys. 29, 2140-51 (2002). [CrossRef] [PubMed]
J. P. Rolland and H. H. Barrett, "Effect of random background inhomogeneity on observer detection performance," J. Opt. Soc. Am. A 9, 649-658 (1992). [CrossRef] [PubMed]
F. O. Bochud, C. K. Abbey, and M. P. Eckstein, "Statistical texture synthesis of mammographic images with clustered lumpy backgrounds," Opt. Express 4, 33-43 (1999). [CrossRef] [PubMed]
D. Whitley, "A Genetic Algorithm Tutorial," Stat. Comput. 4, 65-85 (1994). [CrossRef]
A. E. Eiden, R. Hinterding, and Z. Michalewicz, "Parameter Control in Evolutionary Algorithms," IEEE Trans. Evol. Comput. 3, 124-141 1999. [CrossRef]
M. Sonka, V. Hlavak, and R. Boyle, Image processing, Analysis and Machine Vision (Brooks/Cole, Pacific Grove, Ca, 1999).
M. Tuceryan and A. K. Jain, "Texture Analysis," in The Handbook of Pattern Recognition and Computer Vision, C. H. Chen, L. F. Pau, and P. Wang, eds., (World Scientific Publishing Co, River Edge, NJ, 1998).
R. M. Haralick, K. Shanmugam, and I. Dinstein, "Textural Features for Image Classification," IEEE Trans. Syst. Man. Cybern. 3, 610-62 (1973). [CrossRef]
M. Amadasun and R. King, "Textural features corresponding to textural properties," IEEE Trans. Syst. Man, Cybern. 19, 1264-1274 (1989). [CrossRef]
C. B. Caldwell, S. J. Stappelton, D. W. Holdsworth, R. A. Jong, W. J. Weiser, G. Cooke, and M. J. Yaffe, "Characterisation of mammographic parenchymal pattern by fractal dimension," Phys. Med. Biol. 35, 235-247 (1990). [CrossRef] [PubMed]
C. Castella, K. Kinkel, M. P. Eckstein, P.-E. Sottas, F. R. Verdun, and F. O. Bochud, "Semiautomatic Mammographic Parenchymal Patterns Classification Using Multiple Statistical Features," Acad. Radiol. 14, 1486-1499 (2007). [CrossRef] [PubMed]
Z. Huo, M. L. Giger, D. E. Wolverton, W. Zhong, S. Cumming, and O. I. Olopade, "Computerized analysis of mammographic parenchymal patterns for breast cancer assessment. Feature selection," Med. Phys. 27, 4-12 (2000). [CrossRef] [PubMed]
S. Vedantham, A. Karellas, S. Suryanarayanan, D. Albagli, S. Han, E. J. Tkaczyk, C. E. Landberg, B. Opsahl-Ong, P. R. Granfors, I. Levis, C. J. D??Orsi, and R. E. Hendrick, "Full breast digital mammography with an amorphous silicon-based flat panel detector: Physical characteristics of a clinical prototype," Med. Phys. 27, 558-567 (2000). [CrossRef] [PubMed]
S. Muller, "Full-field digital mammography designed as a complete system," Eur. J. Radiol. 31, 25-34 (1999). [CrossRef] [PubMed]
T. Bäck and M. Schütz. "Intelligent mutation rate control in canonical genetic algorithms," in Proceedings of the 9th International Symposium on Foundations of Intelligent Systems, number 1079 in Lectures notes in Artificial Intelligence, Z. Ras and M. Michalewicz, eds., (Springer, London, UK, 1996), pp. 158-167.
American College of Radiology, Breast Imaging Reporting and Data System Atlas (American College of Radiology, Reston, Va, 2003).
A. Burgess and P. Judy, "Signal detection in power-law noise: effect of spectrum exponent," J. Opt. Soc. Am. A 24, B52-B60 (2007). [CrossRef]
J. R. Taylor, An Introduction to Error Analysis (University Science Books, Mill Valley, Ca, 1982).

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