Depth articles - image processing methods (d) elaborate pyramid image

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In this section, elaborate pyramid image

VII. Image pyramid

The image pyramid is an effective but simple concept of multi-classification structure to explain the resolution of the image. It applied to image segmentation, machine vision and image compression. An image pyramid is a series arrangement of pyramid shape gradually reduce the resolution, and the one derived from the same set of original images. Downsampling obtained by echelon, until it reaches a termination condition did not stop sampling. Bottom of the pyramid is a high resolution representation of the image to be processed, and the top is the low resolution approximation. Here the layers of the image pyramid metaphor, the higher the level, the image, the lower the resolution.

Depth: $\large J = log_{2} N$ , $\large N$ represents the width or length.

1. The common types of image pyramid

(1). Gaussian pyramind Gaussian pyramid

For down-sampling, the main image pyramid

(2). Laplacian pyramind Laplacian pyramid

From the upper layer to the lower layer reconstructed image pyramid be sampled image, the digital image processing, that is, a prediction residual, the maximum degree of reduction may be performed on the image, together with the use of Gaussian pyramid.

(3) The difference between the two

Gaussian pyramid is used to decrease the sample image, and can be used for the Laplacian pyramid images from the pyramid image is up sampled a reconstructed.

(4) The down sampling up here, is of (and the direction opposite to the pyramid) for the image size, the image size is doubled up, down image size is halved.

(5) When the image is moved to the upper pyramid, reduces size and resolution. In opencv in an image from the pyramid image generation can be used at a pyrDown. PyrUp through the conventional image enlarged twice in each dimension. Pyramid upward and downward, respectively, is achieved by sampling and opencv function pyrUp pyrDown.

(6). Note that, pyrUp and pyrDown not reciprocal, i.e. the inverse operation pyrUp than down-sampled. In this case, the image is first expanded to twice the original in each dimension, the new lines (even lines) filled with zeros. Then convolution (actually a filter will expand to twice the original in each dimension) to estimate the approximate value of the "missing" pixels to the specified filter. pyrDown () is a function of information will be lost. In order to restore the original image resolution is higher, it is necessary to obtain the missing information by the down-sampling operation, these data and Laplace Pyramid relationship.

2. Gaussian pyramid

(1). Gaussian pyramid by Gaussian smoothing and sub-sampling the sampled image to obtain a series, that is to say the k-th Gaussian pyramid by smoothing floors, sub-sampling k + 1 can be obtained as storey Stuttgart, Gaussian pyramid contains a series of low -pass filter cutoff frequency from the upper layer to the next is a factor of 2 gradually increases, the Gaussian pyramid can span a large frequency range.

(2) For image downsampling

In order to obtain a level of $\large G_{i + 1}$ the pyramid image, by the following method:

①. Image $\large G_{i}$ layer Gaussian convolution kernel

②. The removal of all even rows and columns

The resulting image is the $\large G_{i + 1}$ image layer, which is an image area of $\large G_{i}$ layer $\large \frac{1}{4}$ size. By the image $\large G_{i}$ (original image) kept above step iteration can get the whole pyramid. Down sampling information will gradually lose the image.

(3) For samples up image

To enlarge the image, it is necessary to give up through the sampling operation, Specifically, the following:

①. The image is expanded to twice the original in each direction, add rows and columns filled with zeros

②. Previously used the same core (multiplied by 4) and the enlarged image after convolution, an approximation to obtain "new pixels".

The resulting image after image that is magnified, but will find that compared with the original image is vague, because the scaling process has lost some information, if you want to reduce the loss of information in zoom in and out throughout the process, these data You can use Laplace pyramid.

3. Laplace pyramid (used in image fusion)

(1) Laplace pyramid is a modified version of the Gaussian pyramid, in order to revert to the original. FIG achieved by calculating the residual reduction.

(2) the formula is the mathematical definition of a Laplacian pyramid i-th layer:

opencv are available: $\large L_{i} = G_{i} - pyrUp(G_{i+1})$

Downsampling the image after the re-sampling operation, then the previous picture do not downsampled residual difference obtained in FIG. This is done in order to restore the image information ready. In other words, Laplacian pyramid is reduced by subtracting the original image and then zoom in a series of images composed. It retained residuals, to prepare for image reproduction.

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