Playful palette: an interactive parametric color mixer for artists

Playful Palette: An Interactive Parametric Color Mixer for Artists Published in TOG 2017, This paper presents a new palette called ：Playful Palette. Like the previous palette, for example [Chang 2013] Clustering based palette and [Tan 2017] The difference between convex hull based palettes is , The previous palette can only modify the colors of existing images . But this article has really generated the color palette that can be used by painters , That is, multiple colors can be generated （ Pigment ） Blend gradient colors for .

The customary , Take the last one teaser.（a） Inside the middle circle is the palette generated by several colors currently used , You can see that there is a smooth gradient effect . On the circle are historical color records , And the palette of the moment corresponding to each color outside the circle , This is mainly used to go back to a certain step or change the color .（b） Select a color painting in the palette ;（c） Painting effect ,（d） Modify image colors through palette history .

Paper points out Color Picker The research of has not been paid attention to , The current color user interface has been unable to meet the needs of digital painting . At first, the paper makes a preliminary user survey on the problems of digital painting . Research indicates that there are Color Picker The most obvious drawback is the inability to mix multiple colors , But real painting often needs to make a variety of pigments into new colors to meet the demand . therefore , The most important contribution of this paper is to propose a new palette that can mix multiple colors and generate smooth color gradient effects .

One 、Playful Palette principle

The palette consists of a plurality of circular color drops （Blob） Generate , Each color drop can be represented as a Yuanzu ：$B_i=(r_i,g_i,b_i,x_i,y_i,r_i)$, among $c_i=(r_i,g_i,b_i)$ It's the color of this water drop ,$p_i=(x_i,y_i)$ and $r_i$ The center and radius of the water drop respectively .

Given a rectangular or circular bounding box （ In a word, all color drops are covered ）, And multiple color drops inside $B\{B_1,B_2,...B_k\}$, We want to get a palette of these water droplets . Intuitively , Each color drop corresponds to a circular area , The pixels in the bounding box are closer to which water drop is located , The closer the color is . So , We traverse each position in the bounding box and calculate their color .

A pixel in the bounding box $p$ Receiving water drop $B_i$ The influence weight of can be expressed as ：
$$M_i(p)=F(B_i,p)=\{\begin{array}{ll}1-\frac{4d^6}{9b^6}+\frac{17d^4}{9b^4}-\frac{22d^2}{9b^2}& d\le b\\ 0& \text{ else }\end{array}\text{\hspace{1em}(1)}$$

among ,$d$ Express $p$ To Water drop $B_i$ The center of the circle $(x_i,y_i)$ Distance of ,$b$ Is an adjustment parameter, which can be taken as the radius, i.e : $b=r_i$.

During palette drawing , The same pixel is affected by the sum of the weights of multiple water droplets Draw only when it is greater than a given threshold , Otherwise it's white .
$$c(p)=\{\begin{array}{ll}\frac{{\sum }_i{M}_i(p)\cdot c_i}{{\sum }_i{M}_i(p)}& {\sum }_i{M}_i(p)>=T\\ white& \text{ else }\end{array}\text{\hspace{1em}(2)}$$
here $T=0.6$.

Actually , The boundary of the palette of water droplet generation is The formula (2) Corresponding $c(p)=T$ The isoline of the , Blogger Birdy_C Draw a diagram showing the composite effect of two water drops .

It should be noted that , Modify the formula （1） in $b$ The value of can change the influence range of each water drop . We make $z=d/b$, Then the above formula will be $d<b$ When established ,$M_i(p)$ Can be written as ：

$$M_i(p)=1-\frac{4}{9}{x}^6+\frac{17}{9}{x}^4-\frac{22}{9}{x}^2$$
The image of this function is as follows ： It can be seen that the dry function is 0,1 Monotonically decreasing between , That is, when we change, we grow $b$, $x=d/b$ smaller , thus $M_i(p)$ Bigger , Therefore, the influence range of water droplets becomes larger .

The color palette effect is obtained by the generation of multiple water drops given in the paper ：

Two 、 Simple implementation

#include <vector> 
#include <opencv2/opencv.hpp>
using namespace std;
using namespace cv;

void DrawPlayfulPalette() {
    
	vector<Vec6d> blobs; //r,g,b,x,y
	blobs.push_back(Vec6d(255, 0, 0, 120, 45));
	blobs.push_back(Vec6d(0, 0, 255, 120, 135));
	blobs.push_back(Vec6d(0, 255, 0, 50, 90));
	
	int rows = 200, cols = 200;
	cv::Mat img = cv::Mat(rows, cols, CV_8UC3, Scalar(255, 255, 255));

	for (int r = 0; r < rows; r++) {
    
		uchar* data = img.ptr<uchar>(r);
		for (int c = 0; c < cols; c++) {
    
			Vec2d pix_pos(r , c);

			Vec3d sum_color(0, 0, 0);
			Vec3i res_color(0, 0, 0);
			double sum_w = 0;

			for (int i = 0; i < blobs.size(); i++) {
    
				Vec3d blob_color(blobs[i][0], blobs[i][1], blobs[i][2]);
				Vec2d blob_pos(blobs[i][3], blobs[i][4]);

				double d2 = (pix_pos - blob_pos).dot(pix_pos - blob_pos);
				double b2 = 70 * 70;
				double db = d2 / b2;

				double w = d2  <= b2 ? 1 - 4 / 9 * pow(db, 3) + 17 / 9 * pow(db, 2) - 22 / 9 * db : 0;
				sum_w += w;
				sum_color += w * blob_color;
			}
			res_color = sum_w < 0.6 ? Vec3d(255, 255, 255): sum_color / sum_w;
			data[3 * c + 0] = res_color[2];
			data[3 * c + 1] = res_color[1];
			data[3 * c + 2] = res_color[0];
		}
	}
	imshow("PlayfulPalette", img);
	waitKey();
}

Draw a few simple palette effects ：

The rest of the article focuses on how to keep historical records , I'm not very interested in , So I won't repeat .