That is not the Christian practice of self-denial.
Self-denial for the Christian is rightly defined by Jonathan Edwards in his book, The Religious Affections, as a duty with two parts:
This is the principal part of the great Christian duty of self-denial. That duty consists in two things, viz., first, in a man's denying his worldly inclinations, and in forsaking and renouncing all worldly objects and enjoyments; and secondly, in denying his natural self-exaltation, and renouncing his own dignity and glory, and in being emptied of himself; so that he does freely and from his very heart, as it were, renounce himself and annihilate himself.
Self-denial means denying the world and it means denying pride, two things that are no easy tasks. It almost feels like it would be easier to don a monk robe, shave my head, and live in solitude. Unfortunately this does not address self-denial's two core issues and thus is not the correct and godly form of self-denial.
Denying the pleasures of the world and annihilating our own pride are two tasks much deeper and more complex than the aesthetic denial we associate with self-denial. Let me explain.
First, denying the pleasures of the world means we set out to stop our ears to temptation and train our eyes on Christ. As the apostle John wrote in his epistle,
For all that is in the world—the desires of the flesh and the desires of the eyes and pride of life—is not from the Father but is from the world. And the world is passing away along with its desires, but whoever does the will of God abides forever.
Anyone can skip meals or live in solitude but it takes a Christian to, by the power of God, hear the world's clamor and ignore it. Daily we're tempted. Often it's as easy as the click of "Send" or "Retweet." We're tempted to look at things, go places, listen to songs, watch programs, say words, and think thoughts that are cultural norms but ungodly practices. Self-denial means denying ourselves the fleeting pleasures of a fading world and doing the will of God.
Second, annihilating our pride means mortifying the greatest sin that attempts to destroy our relationship with God. I'm reminded of Jon Bloom who said that pride is the pathological core of all our sin, because it is the most vicious affront against God's character. Pride is is our attempt to say that we know better than God. It is a part of our sinful natures and that's why we must battle against it. Self-denial means denying the nature of our flesh and killing the pride that lives inside of us.
As Jesus said in Matthew 16:24,
Then Jesus told his disciples, "If anyone would come after me, let him deny himself and take up his cross and follow me."
Thus as Christians, we have a duty to practice self-denial. This is not merely aesthetic, though it may eventually manifest itself as that. It is a heart issue. Are you denying the pleasures of the world and the pride that lives inside of you? Are you taking up your cross daily and following Christ? Because that is what it means to be a Christian.