INTERPLOATION:
Interpolation is a method of constructing new data points within the range of a discrete set of known data points. In engineering and science one often has a number of data points, as obtained by sampling or experimentation, and tries to construct a function which closely fits those data points. This is called curve fitting or regression analysis. Interpolation is a specific case of curve fitting, in which the function must go exactly through the data points.
DIGITAL IMAGE INTERPLOATION:
Digital image interpolation is the recovery of a continuous intensity surface from discrete image data samples. It is a link between the discrete world and the continuous one. In general, almost every geometric transformation requires interpolation to be performed on an image, e.g. translating, rotating, scaling, warping or other applications. Interpolation works by using known data to estimate values at unknown points.
For example: if you wanted to know the temperature at noon, but only measured it at 11AM and 1PM, you could estimate its value by performing a linear interpolation.If you had an additional measurement at 11:30AM, the bulk of the temperature rise occurred before noon, and could use this additional data point to perform a quadratic interpolation.
Image interpolation works in two directions, and tries to achieve a best approximation of a pixel's color and intensity based on the values at surrounding pixels.
TYPES OF INTERPOLATION ALGORITHMS
Common interpolation algorithms can be grouped into two categories: adaptive and non-adaptive. Adaptive methods change depending on what they are interpolating (sharp edges vs. smooth texture), whereas non-adaptive methods treat all pixels equally
Non-adaptive algorithms include: nearest neighbor, bilinear, bicubic, spline and others. Depending on their complexity, these use anywhere from 0 to 256 (or more) adjacent pixels when interpolating. The more adjacent pixels they include, the more accurate they can become, but this comes at the expense of much longer processing time. These algorithms can be used to both distort and resize a photo
NEAREST NEIGHBOR INTERPOLATION
Nearest neighbor is the most basic and requires the least processing time of all the interpolation algorithms because it only considers one pixel-- the closest one to the interpolated point. This has the effect of simply making each pixel bigger
BILINEAR INTERPOLATION
Bilinear interpolation considers the closest 2x2 neighborhood of known pixel values surrounding the unknown pixel. It then takes a weighted average of these 4 pixels to arrive at its final interpolated value. This results in much smoother looking images than nearest neighbor
The diagram to the left is for a case when all known pixel distances are equal, so the interpolated value is simply their sum divided by four
BICUBIC INTERPOLATION
Bicubic goes one step beyond bilinear by considering the closest 4x4 neighborhood of known pixels-- for a total of 16 pixels. Since these are at various distances from the unknown pixel, closer pixels are given a higher weighting in the calculation. Bicubic produces noticeably sharper images than the previous two methods, and is perhaps the ideal combination of processing time and output quality. For this reason it is a standard in many image editing programs, printer drivers and in-camera interpolation
HIGHER ORDER INTERPOLATION
There are many other interpolators which take more surrounding pixels into consideration, and are thus also much more computationally intensive. These algorithms include spline and sinc, and retain the most image information after an interpolation. They are therefore extremely useful when the image requires multiple rotations / distortions in separate steps. However, for single-step enlargements or rotations, these higher-order algorithms provide diminishing visual improvement as processing time is increased
Interpolation is a method of constructing new data points within the range of a discrete set of known data points. In engineering and science one often has a number of data points, as obtained by sampling or experimentation, and tries to construct a function which closely fits those data points. This is called curve fitting or regression analysis. Interpolation is a specific case of curve fitting, in which the function must go exactly through the data points.
DIGITAL IMAGE INTERPLOATION:
Digital image interpolation is the recovery of a continuous intensity surface from discrete image data samples. It is a link between the discrete world and the continuous one. In general, almost every geometric transformation requires interpolation to be performed on an image, e.g. translating, rotating, scaling, warping or other applications. Interpolation works by using known data to estimate values at unknown points.
For example: if you wanted to know the temperature at noon, but only measured it at 11AM and 1PM, you could estimate its value by performing a linear interpolation.If you had an additional measurement at 11:30AM, the bulk of the temperature rise occurred before noon, and could use this additional data point to perform a quadratic interpolation.
Image interpolation works in two directions, and tries to achieve a best approximation of a pixel's color and intensity based on the values at surrounding pixels.
TYPES OF INTERPOLATION ALGORITHMS
Common interpolation algorithms can be grouped into two categories: adaptive and non-adaptive. Adaptive methods change depending on what they are interpolating (sharp edges vs. smooth texture), whereas non-adaptive methods treat all pixels equally
Non-adaptive algorithms include: nearest neighbor, bilinear, bicubic, spline and others. Depending on their complexity, these use anywhere from 0 to 256 (or more) adjacent pixels when interpolating. The more adjacent pixels they include, the more accurate they can become, but this comes at the expense of much longer processing time. These algorithms can be used to both distort and resize a photo
NEAREST NEIGHBOR INTERPOLATION
Nearest neighbor is the most basic and requires the least processing time of all the interpolation algorithms because it only considers one pixel-- the closest one to the interpolated point. This has the effect of simply making each pixel bigger
BILINEAR INTERPOLATION
Bilinear interpolation considers the closest 2x2 neighborhood of known pixel values surrounding the unknown pixel. It then takes a weighted average of these 4 pixels to arrive at its final interpolated value. This results in much smoother looking images than nearest neighbor
The diagram to the left is for a case when all known pixel distances are equal, so the interpolated value is simply their sum divided by four
BICUBIC INTERPOLATION
Bicubic goes one step beyond bilinear by considering the closest 4x4 neighborhood of known pixels-- for a total of 16 pixels. Since these are at various distances from the unknown pixel, closer pixels are given a higher weighting in the calculation. Bicubic produces noticeably sharper images than the previous two methods, and is perhaps the ideal combination of processing time and output quality. For this reason it is a standard in many image editing programs, printer drivers and in-camera interpolation
HIGHER ORDER INTERPOLATION
There are many other interpolators which take more surrounding pixels into consideration, and are thus also much more computationally intensive. These algorithms include spline and sinc, and retain the most image information after an interpolation. They are therefore extremely useful when the image requires multiple rotations / distortions in separate steps. However, for single-step enlargements or rotations, these higher-order algorithms provide diminishing visual improvement as processing time is increased
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