Segmentation

“ By this stage the three layers of the embryo are definitely established. The epiblast, consisting from the first of two strata, arises from the small cells forming the roof of the segmentation-cavity. It becomes continuous at the lip of the blastopore with cells intermediate in size between the cells of which it is formed and the yolk-cells. These latter, increasing in number by additions from the yolk-cells, give rise to the mesoblast and to part of the hypoblast ”

“ Within thresholding methods, a number of approaches have already been described [7] , including: (i) histogram shape-based methods which function by analyzing histogram peaks and curves; (ii) clustering based methods that divide pixels into two groups, foreground and background, via analysis of global intensity values, to create a segmented image (iii) entropy based methods which utilize the entropic properties of the image foreground and background to segment the image, (iv) object attribute methods that look for commonalities among certain object features for image segmentation ”

“ In the first place, the reader should fix in his mind the nature of these distribution areas. Our analyses show that each is a more or less illy-defined area in which there are many trait differences, but that these show a gradation outward from a center, or nucleus. While, by comparative study, one arrives at the generalization of a type for the various social groups making up such a center, the result is, nevertheless, strongly grounded in empirical methods, and is not the work or interpretation of a single individual. ”

“ Let us confine ourselves to cuts in which the lower section has no maximum; in this case we will call the lower section a "segment." Then those segments that correspond to ratios are those that consist of all ratios less than the ratio they correspond to, which is their boundary; while those that represent irrationals are those that have no boundary. Segments, both those that have boundaries and those that do not, are such that, of any two pertaining to one series, one must be part of the other; hence they can all be arranged in a series by the relation of whole and part. ”

“ In many cases where all essential items are happily arranged, but, as a whole, refuse to compose, the addition of some element or the readjustment of a part which will produce circular observation, will ofttimes prove the solution of the difficulty.
Just as progression in a straight line will soon carry us out of the picture, will circular progression keep us within its bounds. If then, circular observation affords the best means of appreciation, [pg 103] it follows that circular composition is the most telling form of presentation. ”

“ In the case of the colored balls we have no difficulty in making the enumeration, because we ourselves determine what the possibilities shall be. But suppose a case more analogous to those which occur in nature: instead of three colors, let there be in the box all possible colors, we being supposed ignorant of the comparative frequency with which different colors occur in nature, or in the productions of art. How is the list of cases to be made out? Is every distinct shade to count as a color? If so, is the test to be a common eye, or an educated eye—a painter's, for instance? ”

“ In counting the all of the kind is the all of our purpose; in classification the all is the all of nature. Then we must remember that in mathematics, number is taken as the representative of the other concomitant properties of quantity and that they are reduced to number by measurement, while in classification kinds are used to represent the other properties and they are reduced to kinds by logical convention. While in conventional counting we consider kinds in series, so in classifying the bodies and properties of nature we are compelled to consider kinds in series. ”

“ Not only is this true, but the further interesting fact may be discovered that social statistics of every category employed or known are based upon a frank recognition of that coefficient of resemblance, physical or mental, which I have contended is a mark of social phenomena. The first step in statistical tabulation is classification, and classification invariably starts from an assumption of real or supposed resemblance. ”

“ But let us assume you are to be called upon to explain a sector to some one who has no idea of terms and their definitions. How would you describe it? While it is true it is wedge-shaped, you will see by examining the drawing that it is not like a wedge. The sector has two sides running from a point like a wedge, but the large end of the sector is curved.
If you were called upon to define a segment you might say it had one straight line and one curve, but this would not define it very lucidly. ”

“ Let us suppose that we desire to find the degree of correlation in variation, or deviation from the mean, between an organ A, called subject, and a second organ B, called relative. We first take all the individuals of one (subject) class; that is, individuals whose subject organ deviates from the mean by a constant quantity, p. We next find for those individuals the average deviation-from-the-mean of the organ B, and call it q. We then find the ration q/p; this is the partial index of correlation. ”

“ Beginning with the most extreme judgments on either side the center, I have erected modes to represent the number of judgments made within each ensuing five millimeters, the number in each case being denoted by the figure at the top of the mode. The two vertical dot-and-dash lines represent the means of the several averages of all the subjects, or the total averages. The short lines, dropped from each of the horizontals, mark the individual averages of the divisions [546] either side the center, and at X these have been concentrated into one line. ”

“ No statistician dreams of combining objects into the same generic group that do not cluster towards a common centre; no more should we attempt to compose generic portraits out of heterogeneous elements, for if we do so the result is monstrous and meaningless. ”

“ This discovery is made by means of comparison and classification. We cease to study each flower for its own sake; and by continually enlarging the sphere of our observation, we try to discover what is common to many and offers those essential points on which groups or natural classes may be established. These classes again, in their more general features, are mutually compared; new points of difference, or of similarity of a more general and higher character, spring to view, and enable us to discover classes of classes, or families. ”

“ Passing over the most abstract science, Logic, on the due guidance by which, however, the large producer or distributor depends, knowingly or unknowingly, for success in his business-forecasts, we come first to Mathematics. Of this, the most general division, dealing with number, guides all industrial activities; be they those by which processes are adjusted, or estimates framed, or commodities bought and sold, or accounts kept. No one needs to have the value of this division of abstract science insisted upon. ”

“ We get it when we pass from a short vertical line to a long horizontal one, from a small square to a large circle, as well as when we pass between those figures whose shapes are congruous. But when the shapes are congruous our consciousness of the relation is a good deal more distinct, and it is most distinct of all when, in the exercise of our analytic attention, we notice, first, a part, and then the whole, of a single line or shape. ”

“ If the names of the groups had been simply written down in a linear series the representation would have been still less natural; and it is notoriously not possible to represent in a series, on a flat surface, the affinities which we discover in nature among the beings of the same group. ”

“ If we formed our groups, not by equal numbers, but by equal amount of variation, we should probably find, in accordance with the law of averages, that the central group in which the mean characteristics prevailed was much more numerous than the extremes, perhaps twice, or even three times, as great as either of them, and forming such a series as the following—10 maximum, 30 mean, 10 minimum development. ”

“ If an observer is clever, then, he can use a series of measurements on part of his data-set to ground a guess about a pattern that holds in that data set, and then use that pattern to ground a guess about the values of unmeasured parts of the data set. ”

“ The method of representation, in which the co-ordinates of the point in the diagram are made equal to the volume and entropy of the body, presents certain characteristics which entitle it to a somewhat detailed consideration, and for some purposes give it substantial advantages over any other method. ”

“ The geometer, with his one definite figure before him, knows perfectly that his thoughts apply to countless other figures as well, and that although he sees lines of a certain special bigness, direction, color, etc., he means not one of these details. When I use the word man in two different sentences, I may have both times exactly the same sound upon my lips and the same picture in my mental eye, but I may mean, and at the very moment of uttering the word and imagining the picture, know that I mean, two entirely different things. ”

“ The index would be classified primarily by some unchanging physical characteristic, such as we are told the thumb-mark and finger-mark afford, and to these would be added any other physical traits that were of material value. The classification of thumb-marks and of inalterable physical characteristics goes on steadily, and there is every reason for assuming it possible that each human being could be given a distinct formula, a number or “scientific name,” under which he or she could be docketed. ”

“ While a nicer artificial analysis, or more accurate observation, is detecting unsuspected resemblances, and, still more frequently, unsuspected diversities, there is hence no fixed point nor regular advance, but a sort of ebb and flow of wider and narrower divisions and subdivisions ”

“ But let me plunge at once in medias res; and let me mention, before we proceed further, that my statistics will be illustrated by scientific diagrams, invented by myself without the assistance of any man, woman, or child whatsoever.
Any ordinary intelligent person must have observed that human beings differ in many things, and especially in personal appearance. This is an absolute fact. And here is a terrible field for the fiend aforementioned. I begin at once, and I herewith give a diagram, which I am able to produce after years of observation. ”

“ The word is not limited to a circle; we have long spoken of a spherical segment, and it is common to-day to speak of a line segment, to which some would apply a new name "sect." There is little confusion in the matter, however, for the context shows what kind of a segment is to be understood, so that the word "sect" is rather pedantic than important. It will be noticed that Euclid here uses "circumference" to mean "arc."
7. Angle of a Segment. An angle of a segment is that contained by a straight line and a circumference of a circle. ”

“ When the word "significantly" is used in comparisons, it is meant to show that there is a significant statistical difference between two or more samples. Whenever eight or more specimens from one locality were available, the mean, range, standard deviation, standard error of the mean, and coefficient of variability were calculated. ”

“ The phrase Natural Classification seems most peculiarly appropriate to such arrangements as correspond, in the groups which they form, to the spontaneous tendencies of the mind, by placing together the objects most similar in their general aspect; in opposition to those technical systems which, arranging things according to their agreement in some circumstance arbitrarily selected, often throw into the same group objects which in the general aggregate of their properties present no resemblance, and into different and remote groups, others which have the closest similarity. ”

“ We call a series the more variable, the more frequently deviating types occur in it; so that the average amount of differences between the individuals constituting the series and the most common type may be used as a measure of the variability of the series. ”

“ When the number of segments is very large, the youngest ones are, as a rule, transversely oblong, the middle ones are squarish, and the mature ones longitudinally oblong. The posterior border of the segments, as a rule, carries a longitudinal groove for the reception of the shorter anterior border of the following proglottis. ”

“ If we represent the corresponding value of u by an ordinate drawn from the line, the extremities of all such ordinates will lie on a curve which will be the graph of u with regard to x. Interpolation therefore consists in determining the length of the ordinate of a curve occupying a particular position, when the lengths of ordinates occupying certain specified positions are known. If u is a function of two variables, x and y, we may similarly represent it by the ordinate of a surface, the position of the ordinate being determined by the values of x and of y jointly. ”

“ Mere varieties from a common typical centre blend freely in the offspring, and the offspring of every race whose statistical characters are constant, necessarily tend, as I have often shown, to regress towards their common typical centre. ”

“ Every work should have one index to the whole set, and not an index to each volume.
An index to each volume of a set is convenient if a general amalgamated index to the whole set is given as well; but a work with several indexes and no general one is most inconvenient and irritating, while to have both seems extravagant. If, however, the author or publisher is willing to present both, it is not for the user of the book to complain.
2. Indexes to be arranged in alphabetical order, proper names and subjects being united in one alphabet. ”