Photo Background Remover Biography
source(google.com.pk)Andrew Jackson (March 15, 1767 – June 8, 1845) was the seventh President of the United States (1829–1837). He was born into a recently immigrated Scots-Irish farming family of relatively modest means, near the end of the colonial era. He was born somewhere near the then-unmarked border between North and South Carolina. During the American Revolutionary War Jackson, whose family supported the revolutionary cause, acted as a courier. He was captured, at age 13, and mistreated by his British captors. He later became a lawyer, and in 1796 he was in Nashville and helped found the state of Tennessee. He was elected to the U.S. House of Representatives, and then to the U. S. Senate. In 1801, Jackson was appointed colonel in the Tennessee militia, which became his political as well as military base. Jackson owned hundreds of slaves who worked on the Hermitage plantation which he acquired in 1804. Jackson killed a man in a duel in 1806, over a matter of honor regarding his wife Rachel. Jackson gained national fame through his role in the War of 1812, where he won decisive victories over the Indians and then over the main British invasion army at the Battle of New Orleans. Jackson's army was sent to Florida where, without orders, he deposed the small Spanish garrison. This led directly to the treaty which formally transferred Florida from Spain to the United States.
Nominated for president in 1824, Jackson narrowly lost to John Quincy Adams. Jackson's supporters then founded what became the Democratic Party. Nominated again in 1828, Jackson crusaded against Adams and the "corrupt bargain" between Adams and Henry Clay he said cost him the 1824 election. Building on his base in the West and new support from Virginia and New York, he won by a landslide. The Adams campaigners called him and his wife Rachel Jackson "bigamists"; she died just after the election and he called the slanderers "murderers," swearing never to forgive them. His struggles with Congress were personified in his personal rivalry with Henry Clay, whom Jackson deeply disliked, and who led the opposition (the emerging Whig Party). As president, he faced a threat of secession from South Carolina over the "Tariff of Abominations" which Congress had enacted under Adams. In contrast to several of his immediate successors, he denied the right of a state to secede from the union, or to nullify federal law. The Nullification Crisis was defused when the tariff was amended and Jackson threatened the use of military force if South Carolina (or any other state) attempted to secede.
Congress attempted to reauthorize the Second Bank of the United States several years before the expiration of its charter, which he opposed. He vetoed the renewal of its charter in 1832, and dismantled it by the time its charter expired in 1836. Jackson's presidency marked the beginning of the ascendancy of the "spoils system" in American politics. Also, he supported, signed, and enforced the Indian Removal Act, which relocated a number of native tribes to Indian Territory (now Oklahoma). He faced and defeated Henry Clay in the 1832 Presidential Election, and opposed Clay generally. Jackson supported his vice president Martin Van Buren, who was elected president in 1836. He worked to bolster the Democratic Party and helped his friend James K. Polk win the 1844 presidential election.
The signal-to-noise ratio (SNR) is used in imaging as a physical measure of the sensitivity of a (digital or film) imaging system. Industry standards measure SNR in decibels (dB) of power and therefore apply the 20 log rule to the "pure" SNR ratio (a ratio of 1:1 yields 0 decibels, for instance). In turn, yielding the "sensitivity." Industry standards measure and define sensitivity in terms of the ISO film speed equivalent; SNR:32.04 dB = excellent image quality and SNR:20 dB = acceptable image quality.[1]
Contents
1 Definition of SNR
2 Calculations
2.1 Explanation
2.2 Polynomial and coefficients
2.3 Net signal, signal, and background
2.4 RMS noise and SNR
3 See also
4 References
5 Further reading
Definition of SNR
An operator arbitrarily defines a box area in the signal and background regions of a back-illuminated half moon or knife-edge test target. The data, (such as pixel intensity), is used to determine the average signal and background values.
Traditionally, SNR has been defined as the ratio of the average signal value \mu_\mathrm{sig} to the standard deviation \sigma_\mathrm{bg} of the background:
\mathrm{SNR} = \frac{\mu_\mathrm{sig}}{\sigma_\mathrm{bg}}
However, when presented with a high-contrast scene, many imaging systems clamp the background to uniform black, forcing \sigma_\mathrm{bg} to zero, artificially making the SNR infinite.[2] In this case a better definition of SNR is the ratio of the average signal value \mu_\mathrm{sig} to the standard deviation of the signal \sigma_\mathrm{sig}:
\mathrm{SNR} = \frac{\mu_\mathrm{sig}}{\sigma_\mathrm{sig}}
which gives a meaningful result in the presence of clamping.
Calculations
Explanation
The line data is gathered from the arbitrarily defined signal and background regions and input into an array (refer to image to the right). To calculate the average signal and background values, a second order polynomial is fitted to the array of line data and subtracted from the original array line data. This is done to remove any trends. Finding the mean of this data yields the average signal and background values. The net signal is calculated from the difference of the average signal and background values. The RMS or root mean square noise is defined from the signal region. Finally, SNR is determined as the ratio of the net signal to the RMS noise.
Polynomial and coefficients
The second order polynomial is calculated by the following double summation.
f_i = \sum_{j=0}^m \sum_{i=1}^n a_j x_i^j
f\, = output sequence
m\, = the polynomial order
x\, = the input sequence (array/line values) from the signal region or background region, respectively.
n\, = the number of lines
a_j\, = the polynomial fit coefficients
The polynomial fit coefficients can thus be calculated by a system of equations.[3]
\begin{bmatrix} 1 & x_1 & x_1^2 \\ 1 & x_2 & x_2^2 \\ \vdots & \vdots & \vdots \\ 1 & x_n & x_n^2 \end{bmatrix} \begin{bmatrix} a_2 \\ a_1 \\ a_0 \\ \end{bmatrix} = \begin{bmatrix} f_1 \\ f_2 \\ \vdots \\ f_n \end{bmatrix}
Which can be written...
\begin{bmatrix} n & \sum x_i & \sum x_i^2 \\ \sum x_i & \sum x_i^2 & \sum x_i^3 \\ \sum x_i^2 & \sum x_i^3 & \sum x_i^4 \end{bmatrix} \begin{bmatrix} a_2 \\ a_1 \\ a_0 \end{bmatrix} = \begin{bmatrix} \sum f_i \\ \sum f_i x_i \\ \sum f_i x_i^2 \end{bmatrix}
Computer software or rigorous row operations will solve for the coefficients.
Net signal, signal, and background
The second-order polynomial is subtracted from the original data to remove any trends and then averaged. This yields the signal and background values[clarification needed]:
\mu_\text{sig} = \frac{\sum_{i=1}^n (X_i - f_i)}{n} \qquad \qquad \mu_\text{bkg} = \frac{\sum_{i=1}^n (X_i-f_i)}{n}
where
\mu_\text{sig} = average signal value
\mu_\text{bkg} = average background value
n\, = number of lines in background or signal region
X_i\, = value of the ith line in the signal region or background region, respectively.
f_i\, = value of the ith output of the second order polynomial.
Hence, the net signal value is determined by[citation needed]:
\text{signal} = \mu_\text{sig} - \mu_\text{bkg}.
RMS noise and SNR
The RMS Noise is defined as the square root of the sum of variances from the background region.[2]
\text{RMS noise} = \sqrt{\frac{\sum_{i=1}^n (X_i-\frac{\sum_{i=1}^n X_i}{n})^2}{n}}
The SNR is thus given by
\text{SNR} = \frac{\text{signal}}{\text{RMS noise}}
Using the industry standard 20 log rule[4]...
\text{SNR} = 20 \log_{10} \frac{\text{signal}}{\text{RMS noise}}\,\mbox{dB}
See also
Coefficient of variation
Minimum resolvable contrast
Minimum resolvable temperature difference
Optical transfer function
Signal transfer function
References
ISO 12232: 1997 Photography – Electronic Still Picture Cameras – Determining ISO Speed here
Mazzetta, J.; Caudle, Dennis; Wageneck, Bob (2005). "Digital Camera Imaging Evaluation" (PDF). Electro Optical Industries. p. 8. Retrieved 28 March 2010.
Aboufadel, E.F., Goldberg, J.L., Potter, M.C. (2005).Advanced Engineering Mathematics (3rd ed.).New York, New York: Oxford University Press
Test and Measurement World (2008). SNR. In Glossary and Abbreviations.http://www.tmworld.com/info/CA6436814.html?q=SNR
Further reading
ISO 15739:2003, Photography -- Electronic still-picture imaging -- Noise measurements: specifies methods for measuring and reporting the noise versus signal level and dynamic range of electronic still-picture cameras. It applies to both monochrome and colour electronic still-picture cameras.
ISO 12232:2006, Photography -- Digital still cameras -- Determination of exposure index, ISO speed ratings, standard output sensitivity, and recommended exposure index: specifies the method for assigning and reporting ISO speed ratings, ISO speed latitude ratings, standard output sensitivity values, and recommended exposure index values, for digital still cameras. ISO 12232:2006 is applicable to both monochrome and colour digital still cameras. It revises ISO 12232:1998.
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