Summary Template matching is a type of object recognition in a scene. It works if and only if the patterns compared are exactly identical. Performing convolution, which deals with Fourier transforms (FT), of an object image and conjugate of a scene, one obtains an inverse Fourier transform that gives you the “digital identity” of the […]

Summary Edge detection is executed on an image by computing the gradient of the location of each of its pixel. Edge detection, as a gradient operator, applies lter mask on the digital image of interest. Fig. 1 shows two kinds of filter masks utilized, i.e., Prewitt and Sobel lter. The center pixel, of both two-dimensional […]

Summary Sample image, 8-bit RGB color and in PNG format, was used. Two color balancing techniques were utilized to enhance the colored image. Succeeding discussions will determine which technique performs the best image enhancement. The first technique used is the automatic white balancing (gray world  algorithm). Average value of each color channel, figs. 1b-1d, was […]

Brief introduction Signals can be processed by dwelling on their Fourier transform (FT). Theorem tells us that signals/images can be expressed as a superposition of sinusoids. Filtering out spatial frequency components of “unwanted repetitive” patterns in an image can be performed by noting that: (i) convolution of two functions is just multiplication of their FTs […]

Brief introduction Fourier series and transforms are widely used due to their ability to describe complicated functions as summation of sine and cosine functions. One advantage of this concept is that it lets us tap/fix the Fourier domain (inverse space domain), and return to the direct space domain without losing vital information. Their applicability extends up […]

Brief introduction    Figure 1: Region enclosed by a contour running in counter-clockwise direction [1].   Area of region in fig. 1 can be calculated using Green’s Theorem which uses line integral of the contour to calculate the area of the region it encloses. The expression is given by where there exists two continuous functions, […]

I. Synthesizing the hologram Figure 1: Synthesizing a hologram. Phase relations.   II. Binarizing the hologram Figure 2: Binarized form of the hologram from fig. 1c   III. Applying Fourier transform Figure 3: Fourier transform of the unbinarized and binarized holograms (click images to look closer).

I. Phase Figure 1: Simulation of HG beams. Each intensity pattern in the left column corresponds to a phase mask in the right column. Figure 2: Simulation of LG beams (intensity pattern only).   II. Phase x Amplitude Figure 3: Superposition of HG(1,0) and HG(0,1) beams.   Figure 4: Superposition of LG beams.   III. Phase […]

Intensity transformations Figures 1b-1g below are the results obtained when intensity transformations were applied on a digital image in grayscale.   Figure 1: Intensity transformations applied on a grayscaled digital image of Vincent Van Gogh’s “Starry Night.”   Negative of the the original image, which has gray level values in the range , was operated using […]

This experiment aims to simulate and analyze the intensity behaviour of beams, within the near field (Fresnel region), of selected apertures.   propTF vs. propIR Propagation of beams, with different shapes, were studied by simulation. Two different types of propagator functions were used, i.e, the Fresnel transfer function (TF) propagator, and the impulse response (IR) […]