Normalization in image processing

image processingnormalization

What is the correct mean of normalization in image processing? I googled it but i had different definition. I'll try to explain in detail each definition.

Normalization of a kernel matrix

If normalization is referred to a matrix (such as a kernel matrix for convolution filter), usually each value of the matrix is divided by the sum of the values of the matrix in order to have the sum of the values of the matrix equal to one (if all values are greater than zero). This is useful because a convolution between an image matrix and our kernel matrix give an output image with values between 0 and the max value of the original image. But if we use a sobel matrix (that have some negative values) this is not true anymore and we have to stretch the output image in order to have all values between 0 and max value.

Normalization of an image

I basically find two definition of normalization. The first one is to "cut" values too high or too low. i.e. if the image matrix has negative values one set them to zero and if the image matrix has values higher than max value one set them to max values. The second one is to linear stretch all the values in order to fit them into the interval [0, max value].

Best Answer

I will extend a bit the answer from @metsburg. There are several ways of normalizing an image (in general, a data vector), which are used at convenience for different cases:

Data normalization or data (re-)scaling: the data is projected in to a predefined range (i.e. usually [0, 1] or [-1, 1]). This is useful when you have data from different formats (or datasets) and you want to normalize all of them so you can apply the same algorithms over them. Is usually performed as follows:
```
Inew = (I - I.min) * (newmax - newmin)/(I.max - I.min)  + newmin
```
Data standarization is another way of normalizing the data (used a lot in machine learning), where the mean is substracted to the image and dividied by its standard deviation. It is specially useful if you are going to use the image as an input for some machine learning algorithm, as many of them perform better as they assume features to have a gaussian form with mean=0,std=1. It can be performed easyly as:
```
Inew = (I - I.mean) / I.std
```
Data stretching or (histogram stretching when you work with images), is refereed as your option 2. Usually the image is clamped to a minimum and maximum values, setting:
```
Inew = I
Inew[I < a] = a
Inew[I > b] = b
```
Here, image values that are lower than a are set to a, and the same happens inversely with b. Usually, values of a and b are calculated as percentage thresholds. a= the threshold that separates bottom 1% of the data and b=the thredhold that separates top 1% of the data. By doing this, you are removing outliers (noise) from the image. This is similar (simpler) to histogram equalization, which is another used preprocessing step.
Data normalization, can also be refereed to a normalization of a vector respect to a norm (l1 norm or l2/euclidean norm). This, in practice, is translated as to:
```
Inew = I / ||I||
```
where ||I|| refeers to a norm of I.

If the norm is choosen to be the l1 norm, the image will be divided by the sum of its absolute values, making the sum of the whole image be equal to 1. If the norm is choosen to be l2 (or euclidean), then image is divided by the sum of the square values of I, making the sum of square values of I be equal to 1.

The first 3 are widely used with images (not the 3 of them, as scaling and standarization are incompatible, but 1 of them or scaling + streching or standarization + stretching), the last one is not that useful. It is usually applied as a preprocess for some statistical tools, but not if you plan to work with a single image.

Related Solutions

Python – Peak detection in a 2D array

I detected the peaks using a local maximum filter. Here is the result on your first dataset of 4 paws: Peaks detection result

I also ran it on the second dataset of 9 paws and it worked as well.

Here is how you do it:

import numpy as np
from scipy.ndimage.filters import maximum_filter
from scipy.ndimage.morphology import generate_binary_structure, binary_erosion
import matplotlib.pyplot as pp

#for some reason I had to reshape. Numpy ignored the shape header.
paws_data = np.loadtxt("paws.txt").reshape(4,11,14)

#getting a list of images
paws = [p.squeeze() for p in np.vsplit(paws_data,4)]


def detect_peaks(image):
    """
    Takes an image and detect the peaks usingthe local maximum filter.
    Returns a boolean mask of the peaks (i.e. 1 when
    the pixel's value is the neighborhood maximum, 0 otherwise)
    """

    # define an 8-connected neighborhood
    neighborhood = generate_binary_structure(2,2)

    #apply the local maximum filter; all pixel of maximal value 
    #in their neighborhood are set to 1
    local_max = maximum_filter(image, footprint=neighborhood)==image
    #local_max is a mask that contains the peaks we are 
    #looking for, but also the background.
    #In order to isolate the peaks we must remove the background from the mask.

    #we create the mask of the background
    background = (image==0)

    #a little technicality: we must erode the background in order to 
    #successfully subtract it form local_max, otherwise a line will 
    #appear along the background border (artifact of the local maximum filter)
    eroded_background = binary_erosion(background, structure=neighborhood, border_value=1)

    #we obtain the final mask, containing only peaks, 
    #by removing the background from the local_max mask (xor operation)
    detected_peaks = local_max ^ eroded_background

    return detected_peaks


#applying the detection and plotting results
for i, paw in enumerate(paws):
    detected_peaks = detect_peaks(paw)
    pp.subplot(4,2,(2*i+1))
    pp.imshow(paw)
    pp.subplot(4,2,(2*i+2) )
    pp.imshow(detected_peaks)

pp.show()

All you need to do after is use scipy.ndimage.measurements.label on the mask to label all distinct objects. Then you'll be able to play with them individually.

Note that the method works well because the background is not noisy. If it were, you would detect a bunch of other unwanted peaks in the background. Another important factor is the size of the neighborhood. You will need to adjust it if the peak size changes (the should remain roughly proportional).

C++ – Image Processing: Algorithm Improvement for ‘Coca-Cola Can’ Recognition

An alternative approach would be to extract features (keypoints) using the scale-invariant feature transform (SIFT) or Speeded Up Robust Features (SURF).

You can find a nice OpenCV code example in Java, C++, and Python on this page: Features2D + Homography to find a known object

Both algorithms are invariant to scaling and rotation. Since they work with features, you can also handle occlusion (as long as enough keypoints are visible).

Enter image description here

Image source: tutorial example

The processing takes a few hundred ms for SIFT, SURF is bit faster, but it not suitable for real-time applications. ORB uses FAST which is weaker regarding rotation invariance.

Best Answer

Related Solutions

Python – Peak detection in a 2D array

C++ – Image Processing: Algorithm Improvement for ‘Coca-Cola Can’ Recognition

The original papers

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