Image segmentation with dynamic artifacts detection and bias correction

Figure 1.  Example cases 1 & 2. Top: Coronal MRI slice. Input image and initial segmentation contour are shown in the top-right corner. The image is heavily affected by intensity bias, such that the classical CV model fails. The superior parts of the white-matter are undersegmented, while the inferior regions are markedly oversegmented. CV+X is not very helpful, here. In contrast, CV+B fixes the problem: the extracted structure is nearly flat (the brain is essentially two-phase piecewise constant), while CV+XB marks some non-brain pixels as outliers. Bottom: This synthethic image is a combination of piecewise constant regions affected by strong noise and oscillating bias. Again, CV fails, and artifacts detection not appropriate. Bias correction greatly improves the segmentation, but errors persist since from the simple initialization the algorithm converges to a wrong local minimum (upper part of left hand structure)

Figure 2.  Example cases 3 & 4. Top: The seemingly simple scene is not segmentable by the CV model alone, due to strong bias. CV+X wrongly classifies bright regions as artifacts. Bias correction (CV+B) results in accurate segmentation of the T-object. Bottom: The vessel structure is not accurately segmented by classical CV: superior parts are oversegmented due to brightening, inferior parts are undersegmented due to darkening. CV+X is inappropriate, while CV+B fixes the problem and leads to much improved vessel segmentation

Figure 3.  Example cases 5 & 6. Top: Compare to ex. 4 in figure 2.Bottom: Three-phase piecewise constant synthetic image. The goal is to separate the two black ellipses from the gray background, considering the white ring to be an occlusion artifact. CV, however, groups the white ring with the light background. CV+X successfully identifies the ring as artifact, and closes the black ellipses thanks to the interface regularization. The bias correction is misleading, since much of the white ring will be considered overly illuminated background (CV+B, CV+XB), the corners being captured as transient artifacts (CV+XB)

Figure 4.  Results by region-scalable-fitting (RSF) [24]. Left: Starting from generic initialization (as used in our method), RSF fails to capture the correct bias/segmentation result.Right: Starting from a tuned initialization (as provided in [24]), RSF produces the desired bias resistant region-based image segmentation result. Note that for optimally chosen number of iterations, $i$ (as provided in [24]), the computation time is about an order of magnitude slower than our proposed method, as reported in table 1

Figure 5.  Microscopy example cases. Top: This AFM image is severely affected by inhomogeneity compared to pattern contrast. As a result, classical CV segmentation fails. The proposed CV+XB model is able to capture some of the bias as such, and correctly segments some of the actual pattern. The central-square contour initialization, however, provokes an incorrect bias field estimate at early stages of the optimization, and leads to an incorrect local minimum, misclassifying the central portions. Middle: Starting from a near-optimal contour initialization of a single pattern element, the CV model still fails entirely. The proposed CV+XB model is not misled into incorrect minima, anymore, and successfully separates bias from actual pattern contrast. Bottom: The CV+XB model captures most of the inhomogeneity present in this AFM sample image and leads to reasonable segmentation of the diamond pattern. (Note: The inversion of foreground/background between CV and CV+XB models is arbitrary and triggered by domain size

Figure 6.  Further microscopy examples. Top: Seemingly "easy" AFM sample, actually affected by strong inhomogeneity at different scales. CV+XB yields a flattened structural image and correct pattern segmentation. Second set: Fluorescence microscopy image suffering from strong bias and artifacts, failing classical CV. CV+XB corrects bias and captures most artifacts. Third set: AFM sample with crack (white) and bend (darkening). The darkening is beyond recovery, but the crack is correctly identified as artifact. Bottom: Artifact detection collects bright spots and the dark line, resulting in correct stripe-pattern segmentation