ImageJ中的曲線擬合功能并不很強,但通過定制應該遠強于Excel,部分地接近少數一些專門工具,例如Logger Pro的水平。我們知道,Excel里面的曲線擬合功能沒有幾種,簡單湊合還可以,稍復雜點的就很無力了;Tracker里的曲線擬合功能也不太行,盡管它能自定義一些函數,但也沒好哪里去。 ImageJ的不少中英文網頁上都建議不要直接使用ImageJ的曲線擬合功能,但也有較少的卻在建議。說明它的曲線擬合尚可一用,特別是在不太奇怪的范圍里使用,完全可以一搏的。 ImageJ的曲線擬合在Analyze/Tools/Curve Fittings菜單下,探索英文網站的關鍵詞ImageJ Analyze Tools CurveFittings function,會給出一大批介紹,基本夠用了。 利用Math函數集合進行簡單的自定義函數擬合:
直接線性擬合,在一個畫布上可以同時畫兩個擬合曲線: 能通過擬合曲線反向列出擬合數據表: ImageJ默認也存在一些數學函數、類型轉換函數等,這些函數在編寫macro時使用,但適用于曲線擬合時期: 在https://imagej./ij/developer/macro/functions.html列出的大部分數學函數和類型轉換函數,約45個: abs(n):Returns the absolute value of n. acos(n):Returns the inverse cosine (in radians) of n. asin(n):Returns the inverse sine (in radians) of n. atan(n):Calculates the inverse tangent (arctangent) of n. Returns a value in therange -PI/2 through PI/2. atan2(y, x):Calculates the inverse tangent of y/x and returns an angle in the range -PIto PI, using the signs of the arguments to determine the quadrant. Multiply theresult by 180/PI to convert to degrees. cos(angle):Returns the cosine of an angle (in radians). exp(n):Returns the exponential number e (i.e., 2.718...) raised to the power of n. floor(n):Returns the largest value that is not greater than n and is equal to aninteger. See also: Math.ceil and round. log(n):Returns the natural logarithm (base e) of n. Note that log10(n) =log(n)/log(10). See also: Math.log10. Math.abs(n):Returns the absolute value of n. Math.acos(n):Returns the inverse cosine (in radians) of n. Math.asin(n):Returns the inverse sine (in radians) of n. Math.atan(n):Returns the inverse tangent (arctangent) of n, a value in the range -PI/2through PI/2. Math.atan2(y, x):Calculates the inverse tangent of y/x and returnsan angle in the range -PI to PI, using the signs of the arguments to determinethe quadrant. Multiply the result by 180/PI to convert to degrees. Math.ceil(n):Returns the smallest (closest to negative infinity) value that is greaterthan or equal to n and is an integer. Math.cos(angle):Returns the cosine of an angle (in radians). Math.erf(x):Returns an approximation of the error function. Math.exp(n):Returns the exponential number e (i.e., 2.718...) raised to the power of n. Math.floor(n):Returns the largest value that is not greater than n and is equal to aninteger. Math.log(n):Returns the natural logarithm (base e) of n. Math.log10(n):Returns the base 10 logarithm of n. Math.min(n1, n2):Returns the smaller of two values. Math.max(n1, n2):Returns the larger of two values. Math.pow(base, exponent):Returns the value of base raised to the power ofexponent. Math.round(n):Returns the closest integer to n. Math.sin(angle):Returns the sine of an angle (in radians). Math.sqr(n):Returns the square of n. Math.sqrt(n):Returns the square root of n, or NaN if n is less than zero. Math.tan(n):Returns the tangent of an angle (in radians). Math.tan(n):Returns the tangent of an angle (in radians). Math.toRadians(degrees):Converts an angle in degrees to an equivalent anglein radians. Requires 1.53f. Math.toDegrees(radians):Converts an angle in radians to an equivalent anglein degrees. Requires 1.53f. Math.constrain(n, min, max):Limits 'n' to the range 'min'-'max'. Requires1.53n. Math.map(n, low1, high1, low2, high2):Maps thevalue 'n' in the input range 'low1'-'high1' to the output range 'low2'-'high2'.Requires 1.53n. maxOf(n1, n2):Returns the greater of two values. See also: Math.max. minOf(n1, n2):Returns the smaller of two values. See also: Math.min. parseFloat(string):Converts the string argument to a number andreturns it. Returns NaN (Not a Number) if the string cannot be converted into anumber. Use the isNaN() function to test for NaN. For examples, seeParseFloatIntExamples. parseInt(string):Converts string to an integer and returns it.Returns NaN if the string cannot be converted into a integer. parseInt(string, radix):Converts string to an integer and returns it. Theoptional second argument (radix) specifies the base of the number contained inthe string. The radix must be an integer between 2 and 36. For radixes above10, the letters of the alphabet indicate numerals greater than 9. Set radix to16 to parse hexadecimal numbers. Returns NaN if the string cannot be convertedinto a integer. For examples, see ParseFloatIntExamples. PI:Returns the constant π (3.14159265), the ratio of the circumference to thediameter of a circle. pow(base, exponent):Returns the value of base raised to the power ofexponent. round(n):Returns the closest integer to n. See also: floor. sin(angle):Returns the sine of an angle (in radians). sqrt(n):Returns the square root of n. Returns NaN if n is less than zero. tan(angle):Returns the tangent of an angle (in radians). |
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