Segmentation of Stochastic Images using ... - Jacobs University

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Chapter 6 Segmentation of Stochastic Images Using Elliptic SPDEs 10 random variables mean only ε = 0.2h, µ = 1/300 ε = 0.4h, µ = 1/300 ε = 0.4h, µ = 1/400 ε = 0.4h, µ = 1/400 E Image Var n/a E Phase Field Var n/a Figure 6.15: Mean and variance of the image and phase field for varying ε and µ using the US data. For comparison, we added the result from the deterministic method applied on the mean. reveals that both approaches lead to similar results, but again, the GSD implementation is 100 times faster than performing Monte Carlo simulation with a suitable number of samples. Ultrasound Samples The conversion of the input samples into the polynomial chaos as described in Section 5.2 leads to the representation of the stochastic US image with 286 coefficients per pixel. Thus, a visualization of this stochastic image via stochastic moments like expected value and variance is necessary. Fig. 6.15 shows the expected value and the variance of the phase field φ and the smoothed image u for settings of the smoothing coefficient µ and the phase field width ε. The algorithm needs about 100 iterations, i.e. alternating solutions of (6.16) for u and φ, to compute a solution. However, in the first steps, the convergence is fast and after about 10 iterations, there is no visible difference in u and φ. From the variance image of the phase field, the identification of regions where the input distribution has a strong influence on the segmentation result (areas with high variance) is straightforward. A benefit of the new stochastic edge detection via the phase field φ is that it allows for an identifi- 74
6.2 Ambrosio-Tortorelli Segmentation on Stochastic Images without edge linking edge linking edge linking + adaptive E Image Var E Phase Field Var Figure 6.16: Comparison of the stochastic Ambrosio-Tortorelli model (left column) with the extended model using the edge linking procedure described in Section 2.3.3 (middle column) and a combination of the edge linking and adaptive grid approach (right column). Note that these results are computed with the same parameter set. The differences in the results are due to the additional edge linking parameter c only. 75
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Segmentation of Stochastic Images u
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Abstract The task of segmentation,
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7.5 Segmentation of Stochastic Imag
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Chapter 1 Introduction The developm
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Figure 1.3: This thesis combines fi
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the presentation of the stochastic
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Chapter 2 Image Segmentation and Li
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Page 131 and 132: Bibliography [14] L. Ambrosio and M
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Bibliography [81] B. N. Khoromskij
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Bibliography [113] A. Nouy. A gener
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Bibliography [147] J. Tryoen, O. Le
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Segmentation of Stochastic Images using ... - Jacobs University

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