CNN 003

Image Gradient

• It is a directional change in the intensity or color in an image.
• can be used to extract valuable information from images.
• commonly used in edge detection.
• ➡️ Change is X-directions, ⬇️ Change is Y-directions.
• Combining both X and Y diretion to estimate if changes are in both directions.

HoG, Histogram of Oriented Gradient

To find edge and shape of the object in the image

• Computing Image Gradient
  • Use the horizontal and vertical filters to compute gradient values
• Compute the strength/magnitude and direction of gradient
  • Strength/Magnitude(g): $\sqrt{g_x^2 + g_y^2}$
  • Direction($\theta$): $\tan^{-1}(g_y / g_x)$
• Create orientation histogram
  • Divide the image into small connected regions called Cells which is a 8x8 patch
  • Create cell histogram based on gradient direction and magnitude
  • 64 (8x8) gradient vectors are put into a 9-bin histogram.
  • The bins are the gradient directions ($\theta$) quantized into 9-bins
• Block Normalization
  • 16x16 pixels blocks or 22 cells are used for normalization, which has 4 histograms.
  • Normalization will make it scale/multiplication invariant
  • Each block will represent 36x1 element vector
• Intensity: brightness of the pixel
• Saturation: HSV color space, the amount of gray in the color
• Calculate the HoG feature vector
  • Each of the 36x1 vectors in each blocks are concatenated into one big vector
  • Size of the vector will be 36xN, where N is the number of blocks in the image
• Hog feature extractor

LBP, Local Binary Pattern

To describe the image textures

$LBP_{P,R}(x_c, y_c) = \sum_{p=0}^{P-1} s(g_p - g_c) \cdot 2^p$

• An eifficient texture operator which labels each pixels of an image by thresholding their neighbours.
• A powerful feature for texture classification
• LBP operator is to describe the image textures using two measures namely, local spatial patterns and the gray scale constract of its strength.
• $S(x)$ is a thresholding function
• $(x_c, y_c)$ is the center pixel in the 8 pixel neighbourhood
• $g_c$ is gray level of the center pixel
• $g_p$ is gray value of a smpling point in an equally spaced circular neighbourhood of P sampling points and radius R around the point $(x_c, y_c)$

1. Sample pixel neighbourhood
2. Difference result
3. Thresholding result

ANN

$L(a, y) = -(y \log a + (1-y) \log (1-a))$ $GD(w, b) = x = \frac{1}{m} \sum_{i=1}^{m} L(a^{(i)}, y^{(i)})$