Gabriel Olive

Gilles Olive

Mentha spicata var. spicata (L.

Introduction

Medauroidea extradentata, a stick insect originally from the district of Annam, Vietnam. Although its natural food plant in Vietnam is unknown, this species is able to feed on a large variety of plants in captivity such as brambles and raspberries (Rubus spp. (L. 1753)), hazel (Corylus maxima (Mill. 1768)) for the most common. When current food shortages (bramble, raspberry and hazel), it has been demonstrated that some specimens of the species M. extradentata are able to survive on other food resources (1). Mentha spicata var. spicata does not seem to pose adaptation problem, but survival on Raphanus sativus var. sativus is obviously accessible to a limited number of specimens (3 out of 11 in the cited experiment). This was the first time that it was observed that M. extradentata is able to feed on spearmint and radish. New experiments, over a longer period in order to study if specimens living on one of the cited plants have the capacity to perform a complete cycle, if their eggs are viable, are described here.

Conclusion

The selection of food for this species has been slightly expanded. Indeed, only M. spicata can be used as food for M. extradentata, as R. sativus allows only the survival of the specimens but not of the M. extradentata species.

Experimental and Results

(1) Olive Gabriel, Zimmer Jean-Yves, Olive Gilles (2016 Two specimens living on spearmint were followed during one year.

Two specimens living on radish plants were followed during ten months.

Mentha spicata var. spicata

Raphanus sativus var. sativus

The two had a normal development.

They did not develop normally, as they did not exceed in size the fourth instar.

They are adult with their offspring at different instars.

The one who lived on the radish is 8 months old, and it is much smaller than another who was fed classically and who was only 7 months old. And the second specimen has molted for nothing, as it has not grown and this moult has been fatal to it.

  Mentha spicata var. spicata (L. 1753) and Raphanus sativus var. sativus (L. 1753): meal for Medauroidea extradentata (Brunner von Wattenwyl 1907) (Phasmatodea: Phasmatidae) Gabriel OLIVE and Gilles OLIVE a Ecole Industrielle et Commerciale de la Ville de Namur, Laboratoire C 2 A, Rue Pépin, 2B, 5000 Namur, Belgium, email: gilles.olive@eicvn.be


Amelia Carolina Sparavigna

A method for the segmentation of images based on thresholding and applied to vesicular textures

Keywords: Segmentation, Edge Detection, Image Analysis, 2D Textures, Texture Functions

In image processing, a segmentation is a process of partitioning an image into multiple sets of pixels, that are defined as super-pixels. Each super-pixel is characterized by a label or parameter. Here, we are proposing a method for determining the super-pixels based on the thresholding of the image. This approach is quite useful for studying the images showing vesicular textures.

Introduction

In image processing, a segmentation is a process of partitioning an image into multiple sets of pixels, defined as super-pixels, in order to have a representation which is simpler than the original one and more useful to the following desired analyses [START_REF] Shapiro | Computer vision[END_REF]. For this reason, the segmentation of images is often used in many applications of the image processing, and in particular in the medical image processing, where the aim is that of determining the presence of pathologies, and for the stacking of the maps coming from tomography to have the 3D reconstructions [START_REF] Pham | Current methods in medical image segmentation[END_REF][START_REF] Forghani | Parameter optimization of improved fuzzy c-means clustering algorithm for brain MR image segmentation[END_REF][START_REF] Vv | Wikipedia[END_REF].

The typical use of the image segmentation is that of locate objects, or domains, and boundaries among them. Specifically, the segmentation is a process of assigning a label to every pixel in an image, such that the pixels having the same label share certain characteristics [START_REF] Vv | Wikipedia[END_REF]. As a consequence, the result of the segmentation is a set of "segments", or "super-pixels", that are covering the whole image, or a set of contours, that is "edges", extracted from the image. In this case, the segmentation gives the "edge detection".

Several methods exist for segmentation, as we can appreciate from [START_REF] Vv | Wikipedia[END_REF]. A discussion of these methods is not the subject of this paper. Here in fact, we want to address this method for applying it to the analysis of the vesicular textures, that we can encounter in geology, materials science and physics. The vesicular textures in images are features that evidence the presence of cavities or holes in the samples; these textures look like those displayed by the volcanic rocks when are pitted with many cavities (known as vesicles) at their surfaces and inside. In such cases, the vesicles are made by gas escaping from cooling lava.

From macrophotography or microscopes (optical, SEM and AFM), or from tomographic devices, we can have 2D maps of pixels representing distributions of vesicular domains. In these cases, it could be interesting to determine the numbers and the size of such domains: this can be obtained by means of segmentation. After some examples illustrating the approach by thresholding to the segmentation, we will consider some studies of the vesicular textures.

Brightness matrix

Before discussing the segmentation, let us remember something about images and image processing. Let us suppose that our starting point is a RGB source image of N x x N y pixels, reppresented by the three-channel brightness function:

3 3 2 ] 255 , 0 [ , ] , 1 [ ] , 1 [ , : N N ⊂ = ⊂ × = → B N N I B I b y x c
From this function, a grey-tone map can be obtained by giving:

∑ = = 3 1 ) , ( 3 1 )
, ( ~c c j i b j i β . Index c corresponds to the three channels R, G, B. The integer indeces i and j are ranging in the x and y directions of the cartesian frame corresponding to the image frame. In this manner, we have, from a RGB image, a brightness map of its grey-tone pixels.

Of course, we could give some statistical parameters of the whole image, such as average brightness M 0 and standard deviation Σ 0 :

∑∑ = = x N i y N j y x j i b N N M 1 1 0 ) , ( 1 = , ( ) ∑∑ = = - Σ x N i y N j o y x M j i b N N 1 1 2 2 0 ) , ( 1 =
From them, many statistical methods of image processing had been developed [START_REF] Haralick | Statistical and structural approach to textures[END_REF]. The author (ACS) for instance, proposed a statistical approach based on the Coherence Length Diagrams [START_REF] Montrucchio | A new image processing method for enhancing the detection sensitivity of smooth transitions in liquid crystals[END_REF][START_REF] Sparavigna | Texture transitions in the liquid crystalline alkyloxybenzoic acid 6OBAC[END_REF][START_REF] Sparavigna | An image processing analysis of skin textures[END_REF], for investigating the texture transitions in liquid crystals, evidenced by polarized light microscopy.

Thresholding and segmentation

It is true that for several physical analysis, the requested measures, which are concerning the domains in the image, are those of simple quantities such as size and area and number of domains. Let us therefore move on with a simple method based on the thresholding of the brightness map. Thresholding is using a clip-level (the threshold value τ), according to which a grey-scale image is turned into a binary image T.

white j i T j i black j i T j i 255 ) , ( ) , ( ~0 ) , ( ) , ( ~= → > = → ≤ τ β τ β
The clip-level has a crucial role in the rendering of the binary image; often it is determined by means of the entropy, evaluated on the histogram of grey-tones of the pixels [START_REF] Gull | Maximum entropy method in image processing[END_REF][START_REF] Sahoo | Image thresholding using two-dimensional Tsallis -Havrda -Charvát[END_REF][START_REF] Sparavigna | Tsallis entropy in bi-level and multi-level image thresholding[END_REF]. A simple method is that of using GIMP (GNU Image Manipulation Program), for X Windows systems, and make a visual choice of thresholding.

Once we have the binary image, we have a matrix of pixels containing black and white domains, or segments. Moving from the left/upper corner of this matrix, we focus on black pixels, and characterize each of them by an integer number k, acting as a label which will be also the label identifying the segment (super-pixel) to which the pixel belongs. The label is determined according to the labels k of the nearest pixels above (A) and on the left (L) of the considered pixel. If the labels k A and k L are the same, their value is the label of the pixel. If the labels are different, the pixel assumes as label the lower value among them. Then, all the pixels having the label with the larger value change their labels into the value of the smaller one. This approach can be easily obtained by logic instructions in any programming language (in the examples here proposed we use Fortran 77). It gives to each of the super-pixels a different label. After this procedure, we have the matrix of labels:

( ) N ⊂ ≠ = → = = → = k k k j i K j i T j i K j i T , 0 , , 0 ) , ( 0 ) , ( 255 ) , (
Then, a new map can be proposed, where a grey tone is associated to the label and then to each super-pixel. Let us see an example based on a detail from an image of a honeycomb structure (Courtesy: Audrius Meskauskas, Wikipedia). In the Figure 1, the steps of segmentation are shown. We start from A, the original image. Then we obtain the grey-tone image B. After, we use GIMP for a simple thresholding to have the black and white image C. After some small adjustments, we obtain the image D, on which we apply the Fortran program for segmentation. In the panel E, we show the super-pixels having different grey tones. Since some are very dark, the panel F shows the output of GIMP Sobel filter for edge detection.

Since each black pixel of the original grey-tone image is labelled by the tone of the super-pixel to which it belongs, we can easily do some calculations. For instance, we can give the distribution of the area (in pixels) of the super-pixels. Since each super-pixel has a different label, we simply count the pixels having the same label. In this manner, we have the areas of the cells of the honeycomb structure. The result is proposed in the Figure 2. In the following example (Figure 5), the original image is showing some sponge borings (Entobia made by the genus Cliona). The photograph was taken by Mark A. Wilson (Department of Geology, The College of Wooster). In this case, we show also the areas of the super-pixels, given in the plot of Figure 6.

Vesicular textures

As told previously, the vesicular textures are those containing domains which look like cavities or holes. In fact, in the previous examples, we have already investigated images which are showing cavities, and we have seen that the approach can be very useful to measure the number and the size of the cavities. Let us continue proposing specific examples.

In the Figure 7, the original image is a detail of a photograph taken by Siim Sepp. It is a picture of vesicular basalt with olivine crystals. In the Figure 8, a volcanic sand grain with many vesicles, is viewed with a petrographic microscope (Courtesy: Qfl247, Wikipedia).

Of course other materials, besides the volcanic rocks, have a vesicular structure. In the Figure 9, we see a detail of the surface of a sponge, and in the Figure 10 the surface of a crisp toast. As previously told, we can find several cases of materials, having a vesicular structure. The example of the Figure 9, involves the surface of a sponge, and then all such cases can be studied by the proposed segmentation. In the Figure 10, we have used the surface of a crisp toast. Again, all the surfaces of such products and others similar, can be studied. Then, the segmentation we proposed seems being suitable for studying several natural samples and artificial products. The examples given above are coming from photography and macro-photography, but the same approach can be used for images obtained from optical microscopes, SEM and AFM microscopes.

Figure 1 :

 1 Figure 1: A is the original image (240 x 240 pixels). B is the corresponding image in grey tones. C is after thresholding. D is the same as C after some smoothing. E is the result of segmentation according to the Fortran program. The super-pixels are given in grey-tones. Since some of these super-pixels are very dark, they are shown in F by an edge detection (Sobel) obtained using GIMP.

Figure 2 :Figure 3 :Figure 4 (GFigure 4 :

 2344 Figure 2: Areas of the super-pixels.

Figure 5 :

 5 Figure 5: A is the original image (240 x 240 pixels). B is its grey-tone image. C is after a thresholding. D is the result of segmentation according to the Fortran program discussed above.

Figure 6 :

 6 Figure 6: Areas of the super-pixels.

Figure 7 (Figure 7 :Figure 8 :Figure 9 :Figure 10 :

 778910 Figure 7 (continues in the next page)

Figure 11 :

 11 Figure 11: Areas of the super-pixels.


Corrigenda to

Essays on Gödel's Reception of Leibniz, Husserl, and Brouwer Mark van Atten November 8, 2016 Please send further corrections to vanattenmark@gmail.com for inclusion in later versions of this list.

  All the lines I quote from Hill's article here are actually translations of sentences written by Husserl. Hill presents these without quotation marks or indentation, but at the end of her paragraph there is a reference to the corresponding pages in Husserliana xxiv(411, 422, 423; and 425 must be added). I thank Dr. Hill for bringing this to my attention, and apologise for this mistaken attribution to her. The reason my argument is not affected is that the sentences Hill quotes come from a group of texts of 1908, and what I document on pages 241-242 is precisely how, as Husserl developed his transcendental phenomenology over the following years, he came to oppose the view that a priori ontology is not part of transcendental phenomenology.

	• p.46 line -4 of main text
	AFTER axiom INSERT the latter collection is itself a set. It is this set the
	existence of which Gödel's
	• p.50 line -1 of main text
	AFTER Gödel's INSERT assertion to Paul Benacerraf
	• p.52 line 20
	AFTER principle INSERT of
	• p.53 line 4
	AFTER according INSERT to
	• p.59 line -3 of main text
	INSERT in BEFORE intension
	• p.36 line 16 • p.126 line -2 of main text AFTER Leibniz INSERT metaphysics itself. Leibniz calls READ 050191 FOR 050120.1
	• p.37 line 5 • p.242 From line 11 onward AFTER Cantor's INSERT Cantor's set theory, then, for Leibniz would be Even though it does not affect the content of my argument, here I com-
	• p.39n.20 mitted a howler.
	FOR see (2002) READ see Roth (2002)
	• p.40 line 14
	AFTER Wang INSERT reports, Gödel
	• p.40 line -2 of main text
	AFTER Cantor's INSERT intentions; and, although Ackermann does not
	point this out, this is indeed the principle that Cantor
	• p.42 line -7 of main text
	FOR 8 READ 58
	• p.43 line -6 of main text
	AFTER Gödel INSERT presented to Wang
	• p.45 line 5
	AFTER Wang INSERT recorded Gödel's
	• p.45 line -4 of main text
	FOR monad'. READ monad',