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### Measures of edge image continuity and connectivity

Suppose I have a scalar image $I:\mathbb{Z}_{1,m} \times \mathbb{Z}_{1,n}\rightarrow [0,1]\subset \mathbb{R}$, where $\mathbb{Z}_{1,m} = \{1,\ldots, m\}$. (For instance, computed as the (scaled) ...
70 views

### Calculating the numerical gradient of a volume in one direction at a time

I want to calculate the gradient of an image volume in one direction at a time. Using the built-in function of Matlab gradient() I can get the ...
157 views

### Optimal trade-off between oversampling and filter length

For some sampling-frequency-preserving operations on Nyquist–Shannon sampled signals, such as: a shift a.k.a. translation, and differentiation by applying a derivative filter a.k.a. gradient filter, ...
69 views

### The Gradient of Least Squares of 2D Image Convolution

Given the objective function: $$\frac{1}{2} {\left\| h \ast x - y \right\|}_{2}^{2}$$ Where $h$ is the 2D convolution kernel and $x$ is the 2D convolution image and $y$ is a given 2D image. ...
22 views

### What is meant by peak value of gradient magnitude?

I am trying to write MATLAB code for the research paper entitled Echocardiography Image Enhancement Using Adaptive Fractional Order Derivatives. The two thresholds are given by a=(peak+min(Gmag))/2 ...
20 views

### Expression related to Tellegen's theorem and signal flow graphs

I'm reading the paper "Signal Flow Graphs-Computer-Aided System Analysis and Sensitivity Calculations" by Arnold Y Lee and my question in about expression/equality (59) in the paper. The expression ...
162 views

### Is discrete cosine transform differentiable?

Is DCT differentiable? I.e. is $\frac{\mathrm{d}\mathrm{DCT}(x)}{\mathrm{d} x}$ defined? I've seen a few implementations in automatic differentiation software packages, so I suppose the answer is ...
123 views

126 views

### Contour sharpening: Optimal direction for derivation

Talking about sharpening a contour in an image. What's the optimal direction for derivation? What's the maximum value of derivative? I think that the optimal direction for derivation is the direction ...
104 views

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853 views

### Measuring spectral tilt

I have quite a few noisy signals and I want to calculate their spectral tilt over time, preferably using a method from literature. So far, I can only come up with the slope of the line between the F0 ...
79 views

### Iterative Blind Sinus Signal Suppression

There are two real signals in the form of $A_i sin(wt+p_i), i=1,2$. Suppose frequency $w$ of both the signals is the same and amplitude $A_i$ and phase $p_i$ are different. The first signal has ...
154 views

### Encoding the HOG features

I have got a video containing 200 frames and i am extracting low level features at pixel level. Then i am dividing the entire frame in to small spatial patches (say of size 7x7) and creating a feature ...
381 views

I have an array $A$ having the next 145 values I would like to calculate the $\frac{dA}{dX}$, having a 1D grid, $x$: 1:286:41468 I use the function gradient: ...
133 views

### How to estimate gradient orientation?

I have a general task of discriminating images of shaded cylinders that significantly vary in 3d orientation, and almost insignificantly in size and shape. I have treated it as a regression problem ...
9k views

### kernels to compute second order derivative of digital image

For an image $I$, its first order derivatives can be computed using several oprators, such as K_{sobel} = \left[ \begin{array}{ccc} -1 &0 &1 \\ -2 &0 &2 \\ -1 &0 &1 \end{...
12k views

### How to Compute Image Gradients?

How to compute Image gradients? In X Direction - Kernel : -1 0 1 In Y Direction - Kernel : -1 0 1 Let's assume my input image is: unsigned char* imgImage; ...
283 views

### Banding in the derivative of a lock-in amplifier signal

I'm analysing several measurements taken with a SR830 lockin amplifier. These measurements look similar to this one. Since I'm interrested in the derivative of the signal I took the numerical ...
17k views

### How Does a Convolution Can Be Expressed as a Matrix Multiplication (Matrix Form)?

I know this question may not be very relevant to programming, but if I don't understand the theory behind image processing I'll never be able to implement something in practice. If I got it right ...
454 views

Are the following sequence of operations the same - Down-sampling filtering followed by gradient filtering with kernel [-1 0 1] Gradient filtering with kernel [-1 0 1] followed by down-sampling ...
904 views

### Gradient of Total Variation of Magnitude of Complex Function for Denoising

Say I have a complex function $f^*$ (e.g. a MRI image) that has a near piece-wise constant magnitude, but a non constant phase. If I have an optimization problem to find $f^*$ and set up an objective ...