The computational time for most applications is less than 0.5 s in original sizes (without downsampling).įor toy problem, I developed two versions with and without using for loops.
I developed a fast MATLAB implementation without using any for loop during the generation of A and b.įurther, I use parfor to parallelize the gradient domain optimization problems in three channels. We could solve linear equations as the form of Ax=b where A is a sparse matrix. Since E(f) is a standard least square cost function, For Salience-Preserving Color Removal,Īnd Gradient Domain Image Filtering, we use both two terms and set the parameter lambda to balance the tradeoffīetween fidelity to data versus gradient constraints. We set w_d, w_x and w_y as uniform weights.įor Poisson Blending and Mixed Gradient, we only use gradient cost function. To keep things simple, we do not use weighting scheme described in "Gradient Shop". The desired values (the guidance intensity image d and guidance gradient field g), and the actual values The energy terms E_d and E_g are the squared errors between Terms E_d and E_g are quadratic functions defined as follows: Where p is a pixel in f, E_d is intensity cost function, and E_g is The result image f is generated by minimizing the following function: The gradient domain framework could be viewed as a energy function optimization problem, While "Gradient Shop" provided a gradient domain optimization framework for defining perceptually motivated image and video filters The "Gradient Brush" system presented a friendly user interface to paint in gradient domain with real-time feedback on large images Gradient domain methods have been applied to many problems in both computer vision and computer graphics. gradient) is much more noticeable for our human vision system.Ģ) High-level control over images: A local change in gradient field could affect the global image. This new perspective gives us two advantages :ġ) Great for human perception: The difference between intensities (i.e. Instead of considering and changing the image intensity, we could manipulate the gradient field. This powerful idea provides a different perspective to look at images. Gradient Domain Fusion was first introduced in high dynamic range compression Īnd image composition. Salience-Preserving Color Removal, Gradient Domain Sharpen Filtering and Non-Photorealistic Rendering. In this project, I use gradient domain methods to address computational photography problems including Poisson Image Blending,
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