Gaussian pyramid is the first step SIFT feature extraction, after determining the extreme points of the feature space, are based on the Gaussian pyramid, so the first step SIFT features to learn is how to build a Gaussian pyramid.
Octave (octave) Briefly octave is in a particular size (length and width), the fuzzy images of different Gaussian kernel of collection. Octave is a collection of Gaussian pyramid.
Why build a Gaussian pyramid:
Throughout the Gaussian pyramid, or a differential Gaussian pyramid is the foundation we identified SIFT features, let's think about what the Gaussian pyramid in the end did a thing, in the end imitating what he is? The answer is easy to determine, Gaussian pyramid mimic how different scales, the scale of the image to be understood? For an image, a close look at your image, and you observe a meter outside, you can see the image effect is different, the former is relatively clear, the latter is more vague, the former is relatively large, which is relatively small by the former can see some details of the image, through the latter to see some outline of the image information, which is scale-scale image, the image is a naturally occurring, not man-made creation. Well, here we see, in fact, before the processing of an image is quite monotonous, because we only focus falls on the two-dimensional space, and does not take into account the concept of a "depth image", if these content is not taken into account we'll get more info before in two-dimensional space does not get it? So Gaussian pyramid turned out, it is the basis for the two-dimensional image on, squeeze out the other dimensions of the image naturally present: scale. Because the Gaussian kernel is the only linear kernel, that is to say a Gaussian blur checking image without introducing other noise, and therefore chose to build scale Gaussian kernel image.
FIG two images is the image of a typical Gaussian pyramid, which is imitated image on your retina imaging, the image representing a distance away you are in a dynamic manner.
Gaussian pyramid build steps:
According to Lowe papers, Gaussian pyramid building is relatively simple, the only nuclear Gaussian linear convolution and is the scale transformation.
Construction of a pyramid as shown below:
figure 1
It is different to ó Gaussian convolution Gaussian blur ó1 Octave1 for performing down-sampling the resulting image; obtained Octave2 bottom (as in FIG ... picture number), the Gaussian blur image to obtain ó2 the picture during downsampling; so the cycle; get Gaussian pyramid;
Refers pyramid model image, the original image is sampled continuously reduced order to obtain a series of images of different sizes, from large to small, tower model configuration from bottom to top. Original image pyramid of the first layer, each time a new image is obtained by sampling down pyramid layer (an image of each layer), an n-layer were each pyramid. In order to reflect the scale of its continuity, Gaussian pyramid on the basis of a simple down-sampling of the added Gaussian filter. Gaussian pyramid initial image (bottom image) on a set of images is obtained as the inverse of the third set of images of the previous images compartment sampled points.
DETAILED Visible: sampling and down sampling the image opencv-
In the same group, the size of the different layers of the same image, the image layer of the Gaussian smoothing factor σ is k times that of the previous layer image smoothing factor;
In different groups, the first image is a group of one-half the previous set antepenultimate sampling image, the image size is half of the previous group;
The foregoing has from human visual perception point of view so that we perceptions of the "scale", also mentioned above, using a Gaussian kernel to achieve the scale of the transformation, the implementation process, the scale is reflected in where? It is how to quantify it? How to determine the Gaussian kernel ó it?
In Figure 1, S indicates how much each extracted layer, s represents the first layers, o the first of several octaves;
Octave (octave) Briefly octave is in a particular size (length and width), the fuzzy images of different Gaussian kernel of collection. Octave is a collection of Gaussian pyramid.
In the Gaussian pyramid, the two variables is important that the first few octaves (o) and layers (s) of the octaves, the two amounts together (o, s) constitute the Gaussian pyramid of scale space. Scale space will also be appreciated, a first image octave width and length are equal, i.e., the control variable o is the size of the column dimension; distinguishing image at the same size scale, the need to s, s control a different octave blur. Thus (o, s) can be determined uniquely in a Gaussian pyramid of the image, which is a three-dimensional, two-dimensional coordinates, it is a one-dimensional image.
The lowe paper, (o, s) is applied to an image by the formula
definite. Can also be seen by the equation, the scale space is continuous, two variables control the value of δ, in which there are 1 <(o + s / S) <= 2 in the first octave, in the same way a second there octave 2 <(o + s / S) <= 3, and so on, the key portion (o + s / S) δ portion is in the (gradually increasing the specific implementation, this value in some Gaussian pyramid It is increased gradually but not uniformly increases can only be said to be continuous).
Scale image in the figure above the first octave are δ, kδ, k ^ 2δ ......, the second octave scale are 2δ, 2kδ, 2k ^ 2δ ..... ..., empathy third octave scale are 4δ, 4kδ, 4k ^ 2δ ......... This sequence is determined by the following formula:
Therefore, each additional one octave, to be amplified by 2 [delta], in one octave, k is the subscript s to distinguish different Gaussian kernels.
So far, the scale of the Gaussian pyramid space has been said about it, including what the dimensions are, including the Gaussian pyramid scale continuity, continuity of scale space will later be described in detail.
Difference of Gaussian pyramid
The above can know the Gaussian pyramid building process in general, the image is first doubled, to build a Gaussian pyramid basis image enlarged on, and then Gaussian blur the image at size, after collection of images of the pieces make up an eight-blur degree , course and then an image of the vaguest under octave sampling in length and width, respectively, decreased a half , a quarter of the original image area becomes. This image is the original image of the next octave, completed on the basis of the initial image belongs to the Gaussian blur octave, and so do all octaves needed to build the entire algorithm, so that the Gaussian pyramid to build out a.
So that each group had the pieces of the Gaussian pyramid images;
Construct a Gaussian pyramid is constructed for subsequent differential Gaussian pyramid. For the same octave difference between two adjacent images do get interpolated image, all octave set of these interpolated images, constitute the differential Gaussian pyramid. Process is shown below, the benefits of the differential Gaussian pyramid is to provide a convenient subsequent extraction of feature points.
Scale space []
Scale space images to resolve the problem is how to describe images in all scales.
Generating a total Gaussian pyramid images in different scales of layers O L groups, together these two quantities (O, L) to form a scale space pyramid of Gaussian, Gaussian pyramid group that is a two-dimensional coordinate system O a coordinate, a further different layer L as coordinates, given a set of coordinates (O, L), uniquely identifies an image in the Gaussian pyramid.
Image scale-space representation:
Figure above coefficient K scale space before the first set of n represents the image size is n times the currently set image size.
Corner Detection] [DoG
DoG (Difference of Gaussian) is a gray scale image enhancement and corner detection, which is relatively simple approach proves more complex, specifically explained as follows: Difference of Gaussian (DOG) is a differential Gaussian function. We already know that the results may be low-pass filtering an image obtained by convolution of the image with a Gaussian function, i.e. denoising process, where the Gaussian and Gaussian Gaussian low-pass filter, is a function, i.e. normal function.
Then the difference of Gaussian i.e. the difference between two Gaussian function is a Gaussian differential image,
One-dimensional representation:
Two-dimensional representation:
Specific terms of the image processing, the image subtraction is Gaussian filtering result with different parameters, to obtain DoG FIG.
Reference article:
DoG (Difference of Gaussian) corner detection
Sift in the scale space, Gaussian pyramid, pyramid difference (DOG pyramid), the image pyramid