PNG pronounced ping is a format for storing bitmapped (raster) images on computers. It was created originally to replace the GIF file format when it was announced that the companies who created the GIF format wanted royalties. PNG uses indexed colors and lossless compression (like a .GIF file), but without those copyright limitations; it cannot be animated like a GIF image.
PNG images are in many ways better than .GIF as they also include an 8-bit transparency channel, which allows the colors in the image to fade from opaque to transparent; GIF images only support fully opaque or fully transparent pixels. PNG supports palettes of 24-bit RGB colors, RGB images or greyscale or RGB images. PNG was intended to be able to transfer images on the Internet, not professional graphics, and so does not support other colour spaces (such as CMYK).
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WebP is an image format developed by Google in 2010. The format allows users to save an image in either lossy or lossless format. Google has made bold claims about the compression efficiency of the format stating that it can be up to 34% smaller than the equivalent JPEG or PNG file. Google believes that through the adoption of a more efficient image format, the speed of the web as a whole can be increased due to the volume of images being viewed at any one time across the world.
WebP lossy compression works by a technique of prediction. Each block of pixels are predicted based on other blocks of pixels surrounding it. The difference between the prediction and reality is then encoded. Due to the efficiency of the prediction technique many of the blocks contain a zero difference which results in greater compression and thus a smaller file size. WebP lossless compression works by using parts of the image that have already been analysed to construct other parts of the image.