All chosen adaptive threshold methods are applied to three types of images calculated based on full colour synthetic image (see Figure top-left image):
Figure 4 Artificial image and three types of images calculated based on full colour image. The artificial image (bottom-left) constructed as described in article and its B-channel of RGB (bottom-right), its “brown” axis (top-right) and its brown (more ...)
•B channel of RGB colour image in Figure (bottom-left),
•monochromatic image calculated accordingly to the presented earlier equation as brown component extracted from all RGB channels in Figure (bottom-right),
•brown part of image obtained by colour deconvolution with three colours: blue, brown and the rest called the third component in Figure (top-right).
5 artificial images (from A to E) segmentation results for all objects in image (without rejection of the objects touching image border) are presented as number of found objects, the sensitivity, the specificity and four coefficients of similarity in Tables , and . In Table are presented results for monochromatic images constituted as B-channel, Table presents results for monochromatic images constituted by deconvolution and Table presents results for monochromatic images constituted as brown color extracted from RGB channels. These tables show that results for each artificial image are close for each method of segmentation applied to particular image. Generally the best results are those of segmentation applied to brown component after colour deconvolution, the mean and the standard deviation of the value of the number of found objects calculated as difference between the number of found objects and the number of ’true’ objects in template for all segmentation methods is -0.2 ±0.6 while 2.3 ±6.9 for monochromatic image with brown color extracted from RGB called ’brown channel’ and 6.0 ±13.9 for the blue channel from RGB. The mean of the sensitivity calculated for all segmentation methods is 0.9264 ±0.0611, 0.8366 ±0.1571, 0.9432 ±0.0764 respectively while mean of the specificity calculated in this data are 0.9981 ±0.0035, 0.9858 ±0.0264, 0.9886 ±0.0235. So 5 artificial images are similar one to each other and all objects in all images can be treated as homogeneous population of tested objects.
The results of adaptive threshold comparison computed on channel BLUE (channel BLUE from RGB)
The results of adaptive threshold comparison computed on brown colour images after colour deconvolution of RGB image
The results of adaptive threshold comparison computed on the “brown channel” calculated from RGB image
The next step of comparison and evaluation concerns rather methods of adaptive threshold so it have been done on the level of single object (not single image). Because objects that touch borders are segmented with holes or cavities what cause that in most cases these object disappear during the step of size filtering in further evaluation it was taking in to account only these objects which do not touching image border. As new designed method will be applied to the virtual slides which will be analysed by parallel algorithms dealing with images which are fragments of virtual slides selected with covering margins so the rejection of objects touching image border would be compensate on the level of results connection.
The evaluation of the segmentation results of single object is presented as B-A plots for such objects’ features as area of object, roundness, eccentricity and so. The comparison of objects’ area in pixels for all except one segmentation methods (for five methods) calculated for each of 3 types of monochromatic images collecting various information about brown colour from five true colour artificial images are presented in Figure A-I. The Yasuda method was excluded from presentation because of its performance; it does not select certain fraction of object and at the same time it selects essential fraction of false positive objects for all types of images (for blue channel 103, for brown colour 63, for results of colour deconvolution only 2) so its plots are not presented in the paper. Some of the plots in Figure (A, B, C, D, G and H) consist of about 70 non-touching image border objects from 5 synthetic images, while the others (E, F and I) present combined plots showing distinguishable by colours 3 or 4 methods’ results together. In Figure and Figure objects segmented by the Niblack method are presented in red, by the Sauvola method in blue, the Bernsen method in green, the White method in black and the Palumbo method in yellow.
Figure 5 The Bland-Altman plots of area feature. The Bland-Altman plots of area feature. (A) Bernsen method of segmentation applied to image after colour deconvolution; (B) Sauvola method of segmentation applied to image after colour deconvolution; (C) Sauvola (more ...)
Figure 6 The Bland-Altman plots of shape features. The Bland-Altman plots of shape features. (A)solidity, Bernsen method of segmentation on image after colour deconvolution; (B)roundness, Bernsen method of segmentation on image after colour deconvolution; (C) (more ...)
It is visible in Figure that results of almost all methods applied to images after colour deconvolution (A, B, C, F) are better than applied to blue channel of RGB (G, H, I) and to the brown component extracted from all channels of RGB (D, E); the latter seems to be the worst. Generally, it is visible that some B-A plots of area comparison between template objects and detected objects show systematic under-segmentation of area. Bernsen method (Figure A) and Niblack, Palumbo, and White methods (Figure F) applied to images after colour deconvolution and White method applied to brown component monochromatic image (Figure D) and to blue channel of RGB (Figure H) shows that there is a bias in the segmented object area. This bias is visible as objects’ area decrease in comparison to the corresponding template object area but all these method are accurate and precise in objects number. For the Bernsen method accurate and precise both are equal 1 while for the modified Sauvola method are equal 1 and 0.9722 respectively. At the same time the size of object detected by: Sauvola method applied to image after colour deconvolution (Figure B), Bernsen method applied to the blue channel from RGB, Palumbo method also applied to the blue channel and Yasuda method applied to all three types of monochromatic images (not presented in paper) seems not biased in objects’ area detection. But some of methods mentioned above in various degree detect extra objects in background (false positive object, FP). For the Sauvola method the number of FP objects is minimal (2 from 72) while for the Yasuda method these numbers are vast as it was mention above. These results are the reason that the Yasuda method is excluded from further consideration. To find method which is accurate enough in area detection the comparison as B-A plots, between area of the segmented and the ‘true’ object from template, is done. The difference between area of the segmented and the ‘true’ object from template for the Sauvola method applied to the result of image deconvolution for all selected object (Figure B) are ranged between -100 to 1400 pixels and for true positive objects only (Figure C) between ±80 pixels while the Bernsen method applied to blue channel of RGB (Figure G) and the Palumbo method (yellow circles in Figure F) applied to blue channel of RGB are ranged in ±130 pixels and ±170 pixels. So the error in area detection is the lowest if the objects are selected by the Sauvola method but only if false positive object are excluded based on the other information.
To reject extra objects selected by the Sauvola method two sources of information could be used: - from biased in object size segmentation method which produce accurate and precise result in number of detected objects so these results can be used to mark true positive object among the Sauvola method results or - from objects found by the Sauvola method can be filtered by any or by all of described below shape coefficients classifier.
To find segmentation method that gives precise number of detected objects and at the same time decrease objects’ size by homogeneous area rejection around objects’ periphery, only methods applied to image after colour deconvolution (Figure A,F) or blue channel (Figure G,H,I) should be taken into consideration. B-A plots for the area feature for monochromatic image from brown color extracted from RGB (Figure E) shows rather biased results (from -100 to -350 pixels) because of presence of cavities and holes in large fraction of segmented objects. So the following three methods: the Bernsen method applied to the results of colour deconvolution (Figure A) and to blue channel of RGB (Figure G) and the White method applied to blue channel (Figure H) are taken into consideration.
The choice among previously mentioned methods and/or among the shape determined object filtration are examined based on B-A plots comparing shape features: perimeter, solidity, roundness and axis ratio, and two features which describe relative position (co-localization) of segmented and template objects: eccentricity and quasi B-A plots described further in this section. These quasi B-A plots show distribution of erroneously detected area (FP) as the function of the distance between centroids of selected and template objects. They have been calculated for all methods (6), all types of monochromatic image with various colour information (3) and all features (6), but only some of them, these which have impact in conclusions, are shown in Figure and Figure .
Figure 7 The co-localization features. The co-localization features: eccentricity (A, C) and defined by authors quasi B-A plots (B, D). (A) Bland-Altman plot of eccentricity, Bernsen method of segmentation on image after colour deconvolution; (B) quasi B-A plot (more ...)
B-A plots in Figure present shape features (except axis ratio which results are similar to presented features): - solidity which shows if increase of objects’ size to achieve convex area is homogeneously distributed (Figure A,D,G), - roundness which shows if ratio of area to squared perimeter is independent from objects’ roundness (Figure B,E,F) and - perimeter length which shows if the changes in perimeter length compared to the template objects perimeter are independent from perimeter length (Figure C,F,I). All these features are presented for the Bernsen method applied to the image after colour deconvolution (Figure A,B,C) in the context of the plots of sum of the Bernsen and the White methods applied to blue channel of RGB image (Figure D,E,F). The first method plots present much more homogeneous distribution than the second group of plots which are presented below (respectively Figure D,E,F). These three shape features plots proof that error in object area detection (decrease of object size described above) for the Bernsen method applied to image after colour deconvolution is homogeneously distributed around object and do not affect its shape. Plots of B-A presented in Figure (G, H, I) present also all previously described shapes coefficient for the Sauvola method applied to the result of image deconvolution. The values of false positive objects appear to be drastically different than the values of these coefficients for true positive objects. Based on this knowledge it is possible to form criteria (classifier) of false positive objects rejection from the set of results. So the Bernsen and the Souvola methods applied to result of deconvolution and shape coefficients (mainly solidity or perimeter) are the best candidates to be used in new hybrid method construction but only if the Bernsen method results of true positive objects indicate part of the Souvola method results.
B-A plots in Figure presents co-localization features: eccentricity (Figure A,C) and defined by authors new coefficient (Figure B,D) which shows if the distance between two centroids is correlated with the ratio of the sum of false negative and false positive pixels divided by true positive pixels. Eccentricity defined as the ratio of the distance between the foci of the ellipse and its major axis length is calculated for ellipse that has the same second-moments as an object. Homogeneous distribution of error without any bias both for the Sauvola and the Bernsen method for eccentricity is achieved. It shows that erroneously detected area in both cases does not cause significant changes in ellipse which is an estimate of object. As this information do not tell us if errors in detected area moves centroid position more than within circle of reduce equal 1 pixel the new B-A like plots have been analysed. These plots are presented in Figure (B, D) and they show that fraction of object which in consequence of error in peripheral part detection moves centroid of segmented object in comparison to the corresponding template object of distance between 1 and 2.5 pixels is less than 20% of objects (for the Bernsen method 12 objects from 70 but for the Sauvola method 14 objects from 72). So in most results of the Bernsen and the Souvola methods the error in area detection is homogeneously located on peripheral part of object if we applied these method to the monochromatic image after colour deconvolution. It proofs that the Brensen method results can be used as true positive objects markers (particularly if they are eroded using mathematical morphology operation [49
]) and these markers should indicate inside of some of the Sauvola method results; all objects which are not marked are FP objects and can be rejected.
Figure presents segmentation results calculated for the chosen fragment of image shown in Figure (top-left) more detail for all types of the monochromatic images: in the first raw for B-channel, in the second raw for the result of deconvolution and the bottom raw for the results of brown component extraction. These results are presented as the various colour outlines of the detected objects. In left column of Figure there are results of four methods: (1) Niblack method, in red colour, (2) Yasuda method, in green colour, (3) Palumbo method, in gray colour, and (4) Sauvola method, in blue colour. While in the right column there are only two: (1) White method, in red colour, and (2) Bernsen method, in green colour. Other colours which appear in image arising by the low of primary colour adding only for the overlapping outlines: yellow colour as result of green colour added to red colour, magenta colour as result of blue colour added to red colour, cyan colour as result of green colour added to red colour and white colour as result of adding all tree colours. The left part of each image is imposed on the template, while the right part, without the template. Both parts show the mutual localization of the detected lines relative to each other and to the template objects. Visual evaluation of the Figure shows that template cover almost all detected objects outlines because detected object are smaller o just in size of template object so the difference of particular method results can be observed in right part of each image. All white pixels in left parts of all images and all yellow pixels in right parts shows agreement in selected outlines while the lines in other colours shows distance between results. These distances are relatively small for results of the segmentation performed with monochromatic image which is results of deconvolution and which is B-channel image (Figure A-D). There is presented only one FP object segmented by the Sauvola method in Figure C while in Figure A there are much more FP objects (in green colour) segmented by the Yasuda method. So all method of results comparison strengths our belief that the process of colour deconvolution produce monochromatic image with best performance of brown colour component.
Figure 8 Image segmentation results. The sub-images present overlapped results of adaptive threshold methods in the left column for: the Niblack method (in red), the Sauvola method (in blue), the Yasuda method (in green) and the Palumbo method (in gray) and in (more ...)