Image processing

dilatation: $𝚍𝚜𝚝(x,y)=max_{(x′,y′):𝚎𝚕𝚎𝚖𝚎𝚗𝚝(x′,y′)≠0}𝚜𝚛𝚌(x+x′,y+y′)$​

erosion: $𝚍𝚜𝚝(x,y)=min_{(x′,y′):𝚎𝚕𝚎𝚖𝚎𝚗𝚝(x′,y′)≠0}𝚜𝚛𝚌(x+x′,y+y′)$​

Opening Useful for removing small objects (it is assumed that the objects are bright on a dark foreground) $dst=open(src,element)=dilate(erode(src,element))$​

Closing Useful to remove small holes (dark regions).

Morphological gradiant It is useful for finding the outline of an object as can be seen below

Blackhat $dst=blackhat(src,element)=close(src,element)−src$​

The Hit-or-Miss transformation is useful to find patterns in binary images.

In particular, it finds those pixels whose neighbourhood matches the shape of a first structuring element B1 while not matching the shape of a second structuring element B2 at the same time

Opening images with h or v vectors

Gaussian pyramid: Used to downsample images

Laplacian pyramid: Used to reconstruct an upsampled image from an image lower in the pyramid (with less resolution)

To produce layer (i+1) in the Gaussian pyramid, we do the following:

How to upsample the image instead?

The simplest segmentation method

Hue channel models the color type, it is very useful in image processing tasks that need to segment objects based on its color

Variation of the saturation goes from unsaturated to represent shades of gray and fully saturated

Value channel describes the brightness or the intensity of the color.

HSV is useful since colors in the RGB colorspace are coded using the three channels, so it is more difficult to segment an object in the image based on its color.

One of the most important convolutions is the computation of derivatives in an image (or an approximation to them)

A method to detect edges in an image can be performed by locating pixel locations where the gradient is higher than its neighbors (or to generalize, higher than a threshold).

The Sobel Operator combines Gaussian smoothing and differentiation.

When the size of the kernel is 3, the Sobel kernel shown above may produce noticeable inaccuracies (after all, Sobel is only an approximation of the derivative). OpenCV addresses this inaccuracy for kernels of size 3 by using the Scharr() function.

Getting the first derivative of the intensity, we observed that an edge is characterized by a maximum

You can observe that the second derivative is zero!

So, we can also use this criterion to attempt to detect edges in an image. However, note that zeros will not only appear in edges (they can actually appear in other meaningless locations); this can be solved by applying filtering where needed.

Trees and the silhouette of the cow are approximately well defined (except in areas in which the intensity are very similar, i.e. around the cow's head).

The roof of the house behind the trees (right side) is notoriously marked. This is due to the fact that the contrast is higher in that region.

Low error rate: Meaning a good detection of only existent edges.

Good localization: The distance between edge pixels detected and real edge pixels have to be minimized.

Minimal response: Only one detector response per edge.

Steps

The Hough Line Transform is a transform used to detect straight lines.

To apply the Transform, first an edge detection pre-processing is desirable.

Line equation can be written as: $y=(−\frac{cosθ}{sinθ})x+(\frac{r}{sinθ})$​

Arranging the terms: $r_θ=x⋅cosθ+y⋅sinθ$​

If for a given (x0, y0) we plot the family of lines that goes through it, we get a sinusoid.

If the curves of two different points intersect in the polar plane, that means that both points belong to a same line.

It means that in general, a line can be detected by finding the number of intersections between curves.

This is what the Hough Line Transform does.

It keeps track of the intersection between curves of every point in the image.

If the number of intersections is above some threshold, then it declares it as a line with the parameters (θ,rθ) of the intersection point.

The Standard Hough Transform output a vector of couples (θ,rθ)

The Probabilistic Hough Line Transform output the extremes of the detected lines (x0,y0,x1,y1)

src: output of edge detector

rho: resolution of the parameter r, in pixels (default is 1)

theta: resolution of the parameter theta, in degrees (default is 1)

threshold: the minimum number of intersections to detect a line

same parameters than houghlines, plus:

minLineLength: The minimum number of points that can form a line. Lines with less than this number of points are disregarded.

maxLineGap: The maximum gap between two points to be considered in the same line.

In the circle case, we need three parameters to define a circle

To accomplish the mapping process, it might be necessary to do some interpolation for non-integer pixel locations, since there will not always be a one-to-one-pixel correspondence between source and destination images.

Used for:

$X=[x, y]^T$​

$T=A⋅[x,y]^T+B \;or \\T=M⋅[x,y,1]^T$​

2 ways to express an affine relation

Image Histogram = intensity distribution

Histogram Equalization improves the contrast in an image, in order to stretch out the intensity range

Equalization implies mapping one distribution (the given histogram) to its cumulative distribution (more details needed)

use 4 different metrics to express how well two histograms match with each other.

Method

Calculate the histogram model of a feature and then use it to find this feature in an image

If you have a histogram of flesh color (say, a Hue-Saturation histogram ), then you can use it to find flesh color areas in an image:

After applying some mask to capture the skin area in T0 image, we computed the H-S histogram.

We also computed the entire H-S histogram for T2.

Method

match method

Possible use case: fix templates, like stop signs ?

The most important practical difference is that findContours gives connected contours, while Canny just gives edges, which are lines that may or may not be connected to each other.

To choose, I suggest that you try both on your sample application and see which gives better results.

2nd argument is contour retrieval mode: a shape(or a contour) may be present inside another shape(or contour). The retrieval mode argument decides if want the output of the contours list in a hierarchical(parent-child) manner or we simply want them as a list(having no hierarchy, cv2.RETR_LIST).

3rd argument is contour approximation, it specifies how many points should be stored so that the contour shape is preserved and can be redrawn (cv2.CHAIN_APPROX_NONE store all the points)

Operations on contours include moments (extract important contour’s physical properties like the center of mass of the object, area of the object)

Minimum boundary that completely wrap a contour

Any deviation of the contour from its convex hull is known as the convexity defect

moment m00 is the area

PointPolygonTest computes distance between a point and a contour